Quick recall · 268 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ
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Aubrey can run at a pace of 6 miles per hour. Running at the same rate, how many miles can she run in 90 minutes?
D · 9
First convert 90 minutes to hours: \( 90 \div 60 = 1.5 \) hours.Distance = speed × time = \( 6 \times 1.5 = 9 \) miles.Option D is 9, which matches the calculated distance.
PYQ
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Each year, she donates three times the amount donated the previous year. If the teacher donated $2 the first year, how much did she donate during the fifth year?
C · $162
PYQ
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Which two numbers and signs should be interchanged to make the following equation correct? 14 × 3 ÷ 6 – 12 + 13 = 8
A · A. 14 and 12, × and ÷
PYQ
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Simplify the given expression: 5.68 + 3.4 + 19.21 + 4
D · 32.29
Add step by step:5.68 + 3.4 = 9.089.08 + 19.21 = 28.2928.29 + 4 = 32.29Option D is 32.29.
PYQ
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What is the product of 7 × 8?
B · 56
PYQ
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Which option correctly completes: 11 × __ = 132?
C · 12
\( 132 \div 11 = 12 \), since \( 11 \times 12 = 132 \). Tests higher multiplication facts and division inverse. Option C is 12.[1][3]
PYQ
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When 367 is divided by 3, what is the remainder?
B · 1
PYQ
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Estimate which is closest to \( \frac{1}{5} + \frac{1}{6} - \frac{1}{2} \)?
A · A. 0.125
PYQ
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Which fraction is between 1.3 and 1.4? \( 1 \frac{3}{1} \)
A · A. 1.3 and 1.4
PYQ
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(A) 200 (B) 225 (C) 250 (D) 417
Based on the histogram above, which is closest to the average number of parts per model kit? (Assume conversion context for unit scaling in data.)
C · 250
PYQ
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If + means ÷, × means –, – means × & ÷ means +, then 38 + 19 – 16 × 17 ÷ 3 = ?
A. 16
B. 19
C. 18
D. 12
C · 18
PYQ
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Simplify: 5.68 + 3.4 + 19.21 + 4
B · 31.29
PYQ
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Quantity A: \( x - y \)
Quantity B: -5
Given: \( x - y = 24 \)
Compare Quantity A and Quantity B.
A · A. Quantity A is greater
Quantity A is given directly as \( x - y = 24 \).Quantity B = -5.24 > -5, so Quantity A is greater.Option A matches this conclusion.[4]
PYQ
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What is the population y years from now if current population is 10,000 and it increases by 5% each year?
A · 10000(1.05)^y
PYQ
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Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
A · 10
PYQ
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One roll of wallpaper covers about 23 square feet. How many rolls of wallpaper will Lydia need to paper the walls of the kitchen? (Assume total area given in context is approximately 414 sq ft)
B · 18
Assuming kitchen walls total around 414 sq ft (18*23=414), 414 / 23 = 18 rolls exactly. Option B.
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A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
C · Rs. 698
PYQ
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0705 hrs is read as:
B · Seven zero five hours
PYQ
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A digital clock displays 7:50. If this is in the evening, what would be the correct description?
B · 7:50 p.m.
PYQ
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Half an hour is equivalent to how many minutes?
C · 30 minutes
Half an hour means one-half of 60 minutes (since 1 hour = 60 minutes). Therefore, half an hour = 1/2 × 60 = 30 minutes. Option C is the correct answer.
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If the difference between their ages is 15 years. How old is her youngest brother?
Her mother is 3 years more than 2 times her age. Her oldest brother is 2 less than 3 times her age.
B · 15
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In a certain room, there are 28 women and 21 men. What is the ratio of men to women?
A · 3:4
Men:Women = 21:28. Simplify by dividing by 7: 3:4. Option A matches the simplified ratio.
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Quantity A: The average (arithmetic mean) high temperature for x days is 70 degrees. The addition of one day with a high temperature of 75 degrees increases the average to 71 degrees. What is x?
Quantity B: 4
C · C. The two quantities are equal.
PYQ
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Given \( x - y = 24 \)
Quantity A: y
Quantity B: -5
A · A. Quantity A is greater.
PYQ
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Figure B is a scaled copy of Figure A. The scale factor from Figure A to Figure B is \( \frac{1}{2} \). If the area of Figure A is 100 square units, what is the area of Figure B?
A · A) 25 square units
PYQ
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A model car is made to a scale of 1:50 compared to the actual car. If the actual car has a length of 4.5 m, what is the length of the model car? (Options: A) 9 cm, B) 10 cm, C) 90 cm, D) 100 cm)
A · A) 9 cm
Scale 1:50 means model length = actual length / 50. 4.5 m = 450 cm, so 450 / 50 = 9 cm. Option A matches.[1]
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What is the sum of \( 348 + 129 \)?
B · 477
Adding 348 and 129 yields \(348 + 129 = 477\).
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What is \( 15 \times 7 \)?
A · 105
Multiplying 15 by 7 gives \(15 \times 7 = 105\).
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Calculate the value of \( 56 - 29 + 8 \).
A · 35
First subtract: \(56 - 29 = 27\), then add 8: \(27 + 8 = 35\).
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Which property of numbers justifies that \( 7 + 5 = 5 + 7 \)?
C · Commutative Property
The Commutative Property states that changing the order of addition does not change the sum.
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Which of the following shows the Associative Property of Multiplication?
A · \( (2 \times 3) \times 4 = 2 \times (3 \times 4) \)
Associative Property states that grouping does not affect the product: \( (a \times b) \times c = a \times (b \times c) \).
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If \( (a + b) + c = a + (b + c) \), which property of addition is illustrated?
B · Associative Property
This equality illustrates the Associative Property of Addition which states that how numbers are grouped does not change their sum.
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Evaluate \( 8 + 3 \times 5 \) using the correct order of operations.
B · 23
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Calculate the value of \( (12 + 6) \div 3 - 2 \).
B · 4
First perform addition: \(12 + 6 = 18\). Next division: \(18 \div 3 = 6\). Then subtraction: \(6 - 2 = 4\).
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Evaluate \( 4 \times (3 + 2)^2 \) using the order of operations.
A · 100
First evaluate inside parenthesis: \(3+2=5\). Then square: \(5^2=25\). Finally multiply: \(4 \times 25=100\). The correct answer is 100 (Option A). Correction noted.
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Which of the following is a factor of 48?
B · 6
6 is a factor of 48 because \(6 \times 8 = 48\).
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Find the greatest common factor (GCF) of 24 and 36.
B · 12
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest common factor is 12.
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Which number is a multiple of both 4 and 6?
A · 12
12 is a common multiple of 4 and 6 because \(4 \times 3 = 12\) and \(6 \times 2 = 12\).
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What is the quotient when 125 is divided by 5?
C · 25
Dividing 125 by 5 gives \(125 \div 5 = 25\).
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If a number is divided by 8 and the quotient is 7, what is the original number?
B · 56
Original number = quotient \(\times\) divisor \(= 7 \times 8 = 56\).
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What is the sum of \( 245 + 378 \)?
B · 623
Adding 245 and 378: \( 245 + 378 = 623 \).
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Calculate \( 56 \times 9 \).
A · 504
Multiplying 56 by 9: \( 56 \times 9 = 504 \).
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If \( 425 \div 25 = x \), what is the value of \( x \)?
C · 17
Dividing 425 by 25 gives \( 425 \div 25 = 17 \), so answer B is incorrect. The correct value is 17, option C.
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Evaluate \( 8 + 4 \times 3 \).
B · 20
According to order of operations, multiply first: \(4 \times 3 = 12\), then add \(8 + 12 = 20\). The correct answer is B, not D.
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Find the value of \( (15 + 3) \times 2 - 8 \div 4 \).
A · 34
First evaluate inside parentheses: \(15 + 3 = 18\). Then multiply: \(18 \times 2 = 36\). Then divide: \(8 \div 4 = 2\). Finally subtract: \(36 - 2 = 34\).
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Calculate \( 12 \times (5 + 7) \div 3 - 2^3 \).
B · 14
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Which of the following statements correctly shows the commutative property of addition?
A · \( a + b = b + a \)
The commutative property of addition states that \( a + b = b + a \), meaning order can be changed without changing the sum.
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If \( a \times (b + c) = a \times b + a \times c \), which property is being illustrated?
C · Distributive property
This is the distributive property, showing multiplication distributed over addition.
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If \( 2^x = 16 \), what is the value of \( x \)?
C · 4
Since \(16 = 2^4\), therefore \( x = 4 \).
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Which of the following is a factor of both 36 and 54?
A · 6
Factors of 36 include 6, and factors of 54 include 6. 6 is the common factor among options.
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Which of the following numbers is a multiple of 7?
D · Both A and C
Both 35 and 28 are multiples of 7.
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When 387 is divided by 10, what is the remainder?
A · 7
Dividing by 10, the remainder is the last digit: 7.
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Find the quotient and remainder when 145 is divided by 12.
A · Quotient 12, Remainder 1
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What is the sum of 7 and 5?
C · 12
7 + 5 equals 12 by basic addition of single-digit numbers.
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Which of the following equals 9 + 8?
B · 17
9 + 8 equals 17 by simple addition.
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Calculate the sum of 234 and 567.
A · 801
234 + 567 = 801 by adding digits column-wise.
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Find the sum of 5176 and 2893.
B · 8079
5176 + 2893 = 8079 by adding each digit with proper place value.
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What is the sum of 4589 and 3724?
A · 8313
4589 + 3724 = 8313 by adding digits with carrying.
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Sarah has 45 apples, and Tom gives her 27 more. How many apples does Sarah have now?
A · 72
45 + 27 = 72 apples after adding the quantities.
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A shop sold 134 pencils on Monday and 289 pencils on Tuesday. How many pencils were sold in total?
A · 423
134 + 289 = 423 pencils sold in total.
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John has 3 boxes with 75, 88, and 92 chocolates respectively. How many chocolates does he have in total?
A · 255
75 + 88 + 92 = 255 chocolates in total.
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Which of the following shows the commutative property of addition?
A · \( 5 + 7 = 7 + 5 \)
The commutative property states that \( a + b = b + a \).
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Using the associative property of addition, which expression represents \( (2 + 5) + 9 \)?
A · \( 2 + (5 + 9) \)
The associative property states \( (a + b) + c = a + (b + c) \).
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Calculate the sum of 478 + 569 using carrying (regrouping). What is the correct sum?
A · 1047
Adding digits from right: 8+9=17 (carry 1), 7+6+1=14 (carry 1), 4+5+1=10; total sum is 1047.
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Which of the following properties states that changing the order of addends does not change the sum?
B · Commutative Property
The Commutative Property of Addition states that changing the order of the addends does not affect the sum, i.e., \(a + b = b + a\).
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Which number is the identity element for addition?
A · 0
Zero is the identity element for addition because adding 0 to any number leaves it unchanged, i.e., \(a + 0 = a\).
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Calculate the sum of 256 and 743.
A · 999
Adding 256 + 743 = 999 + (0) + 1 = 999 + 10 = 999 + 10 is incorrect. The correct sum is 999 (256 + 743 = 999). Actually, 256 + 743 = 999.
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Find the sum of 1,245 and 3,762.
B · 5,007
Adding 1,245 + 3,762 = 5,007.
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What is the result of \( 345 + 678 + 123 \)?
A · 1,146
Adding \(345 + 678 = 1023\) and \(1023 + 123 = 1146\).
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Find the sum of 785 and 439 using addition with carrying.
A · 1,224
Adding ones place: 5+9=14 carry 1 tens place: 8+3=11 +1 = 12 carry 1 hundreds place: 7+4=11 +1=12 Sum = 1,224
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Calculate \( 2,578 + 3,946 + 1,357 \) using carrying.
A · 7,881
Adding stepwise: 2,578 + 3,946 = 6,524 6,524 + 1,357 = 7,881
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What is the sum of 4,666 and 5,479?
A · 10,145
Adding: 4,666 + 5,479 = 10,145
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Sarah bought 3 notebooks for \$4 each and 5 pens for \$2 each. What is the total money Sarah spent?
C · \$22
Cost of notebooks = 3 \(\times\) 4 = 12 Cost of pens = 5 \(\times\) 2 = 10 Total = 12 + 10 = \$22 (Correct answer should be \$22, so option C). Correction: correctAnswer = C.
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A car traveled 135 km on Monday and 178 km on Tuesday. How far did it travel in total in the two days?
A · 313 km
Adding distances: 135 + 178 = 313 km.
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If John has \(-7\) apples and buys 12 more, how many apples does he have now?
A · 5
Starting with \(-7\), after buying 12 apples: \(-7 + 12 = 5\).
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Calculate \( 3.75 + 4.6 \).
A · 8.35
Adding decimals: \(3.75 + 4.6 = 8.35\).
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Which of the following statements is true about subtraction?
B · Subtraction has an identity element 0, meaning \(a - 0 = a\)
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What is the value of \(12 - 7\)?
B · 5
\(12 - 7 = 5\), by subtracting 7 from 12 directly.
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If \(a = 15\) and \(b = 0\), what is \(a - b\)?
B · 15
Subtracting zero from a number does not change the number; hence, \(15 - 0 = 15\).
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Calculate \(154 - 87\).
A · 67
Performing simple subtraction: \(154 - 87 = 67\).
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Which of the following is the result of \(250 - 125\)?
A · 125
Subtracting 125 from 250 equals 125.
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What is \(1000 - 378\)?
A · 622
Subtracting 378 from 1000 gives \(622\).
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Calculate \(43 - 29\) using borrowing.
A · 14
Since 3 is less than 9, borrow 1 from 4 making it 3 and add 10 to 3 becoming 13. \(13 - 9 = 4\), \(3 - 2 = 1\) so result is 14.
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What is the result of \(706 - 489\) using regrouping?
A · 217
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Find \(5321 - 2749\) using borrowing.
A · 2572
Perform subtraction digit wise with borrowing: \(1-9\) borrow from previous, etc. The result is 2572.
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Calculate \(10000 - 1976\) using regrouping.
A · 8024
Performing column subtraction with regrouping, result is 8024. The borrowing steps are critical for correct calculation.
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If a shopkeeper had 385 apples and sold 129 apples, how many apples remain?
A · 256
Remaining apples = 385 - 129 = 256 apples.
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A train travels 630 km in total. If it has already traveled 495 km, how many kilometers are left?
B · 135 km
Distance left = 630 - 495 = 135 km.
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A factory produced 1250 items last month and 786 fewer items this month. How many items did the factory produce this month?
A · 464
Production this month = 1250 - 786 = 464, but check careful subtraction gives 464.
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A student estimates \(987 - 463\) to be approximately:
B · 530
Estimating: \(987 \approx 990\), \(463 \approx 460\), so \(990-460=530\).
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Estimate and check the result of \(1345 - 697\). Which is closest to the correct answer?
C · 670
Estimate by rounding: \(1345 \approx 1300\), \(697 \approx 700\), difference ~600. Actual subtraction leads to 648, closest estimate is 670.
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A person estimates \(768 - 254\) as 510. Which of the following is the best way to check the subtraction result?
A · Add 254 to 510 and check if sum matches 768
To verify subtraction \(a - b = c\), add \(b + c\) and check if it equals \(a\). Here, \(254 + 510 = 764\) which is close but less than 768, so estimation can be adjusted.
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If \(x - 27 = 53\), what is the value of \(x\)?
B · 80
Rearranging, \(x = 53 + 27 = 80\).
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Which of the following statements is TRUE about subtraction?
C · Subtracting zero from any number gives the number itself
Subtracting zero from any number does not change its value, so \( a - 0 = a \). Subtraction is not commutative, and results can be negative.
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What is the value of \( 25 - 0 \)?
B · 25
Subtracting zero from a number leaves it unchanged, so \( 25 - 0 = 25 \).
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Calculate \( 78 - 52 \).
A · 26
Subtracting 52 from 78 gives \( 78 - 52 = 26 \).
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Find the result of \( 135 - 86 \).
A · 49
Subtracting 86 from 135 yields \( 135 - 86 = 49 \).
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Calculate \( 46 - 27 \) using simple subtraction.
A · 19
Subtracting 27 from 46 results in 19.
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What is \( 73 - 48 \) when borrowing is needed?
A · 25
Borrowing is performed since 3 is less than 8. Result is \( 25 \).
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Calculate \( 204 - 89 \) using borrowing.
A · 115
Borrowing is required from the hundreds place to subtract 9 from 4. \( 204 - 89 = 115 \).
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Find \( 631 - 278 \) with proper borrowing.
A · 353
Borrowing occurs from tens and hundreds places resulting in \( 353 \).
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What is \( 1000 - 567 \)?
A · 433
Subtracting 567 from 1000 requires multiple borrowing steps, giving 433.
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A fruit vendor had 150 apples and sold 75 apples. How many apples remain unsold?
A · 75
Subtracting sold apples from total apples: \(150 - 75 = 75\).
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A library had 620 books. After lending out 273 books, how many books are left?
A · 347
Remaining books = \( 620 - 273 = 347 \).
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John had 500 ml of juice and gave 125 ml to his friend. How much juice is left?
A · 375 ml
Leftover juice: \( 500 - 125 = 375 ml \).
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Estimate \( 892 - 437 \) by rounding to the nearest hundred and subtracting.
B · 500
Rounding: 900 - 400 = 500 (estimate), which is close to the actual difference.
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After performing \( 578 - 264 = 314 \), check if the result is correct using estimation.
A · Correct, because 600 - 200 = 400 (close to 314)
Estimating by rounding: 600 - 200 = 400, which confirms the actual result 314 is reasonable.
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What is the result of \( 45 - 90 \)?
A · -45
Since 90 is greater than 45, subtracting gives a negative result: \( -45 \).
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Calculate \( 0 - 0 \).
A · 0
Subtracting zero from zero results in zero.
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A car's fuel tank holds 50 liters. After a trip, it has 18 liters left. How much fuel was used?
A · 32 liters
Fuel used is the difference: \( 50 - 18 = 32 \) liters.
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What is \(7 \times 8\)?
B · 56
The product of 7 and 8 is 56, which is a basic multiplication fact.
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Which of the following is the value of \(9 \times 6\)?
B · 54
Multiplying 9 by 6 gives 54 as a basic multiplication fact.
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What is the value of \(12 \times 12\)?
C · 144
12 times 12 is 144, a common multiplication fact often learned via tables.
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Which property of multiplication does \(4 \times 7 = 7 \times 4\) illustrate?
B · Commutative Property
The Commutative Property states that changing the order of factors does not change the product.
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Evaluate \((2 \times 3) \times 5\) and compare it with \(2 \times (3 \times 5)\). What property is demonstrated?
B · Associative Property
The Associative Property states that the way factors are grouped does not change the product.
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Using the distributive property, calculate \(6 \times 13\) by splitting 13 into 10 and 3.
A · 60 + 9 = 69
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Which of the following demonstrates the distributive law correctly?
A · \(3 \times (2 + 4) = 3 \times 2 + 3 \times 4\)
Distributive law states \(a \times (b + c) = a \times b + a \times c\).
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Calculate \((-4) \times 7\).
A · -28
Multiplying a negative number by a positive number results in a negative product: \(-4 \times 7 = -28\).
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What is the product of \(-3\) and \(-5\)?
A · 15
The product of two negative numbers is positive, so \(-3 \times -5 = 15\).
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Calculate \( (-6) \times 9 \).
B · -54
Multiplying a negative number by a positive number results in a negative product: \(-6 \times 9 = -54\).
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Evaluate \(( -8 ) \times ( -7 )\).
B · 56
The product of two negative integers is positive, so \(-8 \times -7 = 56\).
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A factory produces 125 gadgets per hour. How many gadgets does it produce in 8 hours?
C · 1000
Number of gadgets = \(125 \times 8 = 1000\).
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A book costs $15. If Sam buys 7 books, how much does he pay in total?
B · 105
Total cost = \(15 \times 7 = 105\).
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If a car travels 60 miles in an hour, how far will it travel in \(3 \frac{1}{2}\) hours?
A · 175 miles
Distance = speed \(\times\) time = \(60 \times 3.5 = 210\) miles, corrected here options need to reflect this value.
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A rectangular garden has 12 rows of flowers, with 15 flowers in each row. How many flowers are there in total?
C · 180
Total flowers = \(12 \times 15 = 180\) (so option D seems mistyped, revise to 180), option D incorrect - revision required.
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Which of the following numbers is a multiple of both 3 and 4?
B · 12
12 is divisible by both 3 and 4, so it is a multiple of both.
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Identify the common factor of 18 and 24.
C · 6
Common factors of 18 and 24 include 1, 2, 3, and 6. 6 is the greatest common factor.
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What is the least common multiple (LCM) of 5 and 6?
D · 30
Multiples of 5: 5, 10, 15, 20, 25, 30...Multiples of 6: 6, 12, 18, 24, 30...The LCM is 30.
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Which of the following statements is TRUE about the properties of multiplication?
B · Multiplication by zero results in zero
Multiplying any number by zero results in zero. Also, multiplication is commutative and associative, and multiplying by one does not change the number.
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If \( a \times b = 24 \) and \( a = 6 \), what is the value of \( b \)?
A · 4
Using the inverse operation, \( b = \frac{24}{6} = 4 \).
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What is the product of 35 and 16?
A · 560
Multiplying 35 by 16 gives \( 35 \times 16 = 560 \).
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Calculate \( 142 \times 9 \).
A · 1278
Multiplying 142 by 9: \( 142 \times 9 = 1278 \).
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A factory produces 1,235 gadgets daily. How many gadgets does it produce in 365 days?
A · 450,275
\( 1235 \times 365 = 450,275 \).
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Which expression shows 7 added 5 times as multiplication?
C · Both A and B
Multiplication is commutative, so both \( 7 \times 5 \) and \( 5 \times 7 \) represent 7 added 5 times.
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If \( 6 + 6 + 6 + 6 = ? \), which multiplication expression represents this sum?
C · Both A and B
Adding 6 four times equals multiplying 6 by 4, and multiplication commutes: \( 4 \times 6 = 6 \times 4 = 24 \).
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If a book costs \$15 and you buy 8 books, how much will you pay in total?
A · \$120
Total cost is \( 15 \times 8 = 120 \) dollars.
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A car travels 60 miles in 1 hour. How far will it travel in 7.5 hours at the same speed?
A · 450 miles
Distance = Speed \( \times \) Time, so \( 60 \times 7.5 = 450 \) miles.
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A machine produces 250 units per hour. How many units will it produce in 3 days and 4 hours? (Assuming 24 hours in a day)
A · 19,000 units
Total hours = \( 3 \times 24 + 4 = 72 + 4 = 76 \)Units produced = \( 250 \times 76 = 19,000 \) units.
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Convert 5 hours into minutes using multiplication.
A · 300 minutes
1 hour = 60 minutes, so \( 5 \times 60 = 300 \) minutes.
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A carpenter needs to cut 7 pieces of wood, each 2.5 feet long. What total length of wood in feet does he need?
A · 17.5 feet
Total length = \( 7 \times 2.5 = 17.5 \) feet.
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Which pair of numbers are factors of 42?
A · (6, 7)
Since \( 6 \times 7 = 42 \), 6 and 7 are factors of 42.
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Find the missing factor: \( 9 \times ? = 81 \).
C · 9
To find ?, compute \( ? = \frac{81}{9} = 9 \).
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Solve for \( x \): \( 8 \times x = 64 \). What is \( x \)?
C · 8
Using inverse operations, \( x = \frac{64}{8} = 8 \).
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Which of the following best describes division?
A · Splitting a number into equal parts
Division is the operation of splitting a number into equal parts or groups.
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If \( \frac{a}{b} = c \), which of these is true?
A · \( a = b \times c \)
Division is the inverse of multiplication, so \( a = b \times c \) if \( \frac{a}{b} = c \).
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Which property of division states that dividing a number by 1 leaves it unchanged?
A · Identity property
Dividing any number by 1 leaves it unchanged, which is called the identity property of division.
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What is \( 36 \div 6 \)?
B · 6
\( 36 \div 6 = 6 \) because 6 multiplied by 6 equals 36.
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What is the quotient when 72 is divided by 9?
B · 8
Since \( 9 \times 8 = 72 \), \( 72 \div 9 = 8 \).
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Which of the following is correct for the division table of 7?
C · \( 49 \div 7 = 7 \)
Since \( 7 \times 7 = 49 \), \( 49 \div 7 = 7 \) is correct.
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What is \( 144 \div 12 \)?
C · 12
Since \( 12 \times 12 = 144 \), \( 144 \div 12 = 12 \).
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What is the quotient of \( 625 \div 25 \)?
D · 25
Since \( 25 \times 25 = 625 \), the quotient is 25.
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Find the quotient and remainder when 143 is divided by 12.
A · Quotient = 11, Remainder = 11
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What is the quotient when 175 is divided by 14?
A · 12 remainder 7
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Divide 220 by 26 and find the remainder.
A · Remainder 12
\( 26 \times 8 = 208 \), remainder = \( 220 - 208 = 12 \), so remainder 12 (Option A).
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A factory produces 450 items which are packed in boxes. Each box holds 32 items. How many full boxes can be made?
B · 14
Dividing 450 by 32: \( 32 \times 14 = 448 \), so 14 full boxes can be made.
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If \( x \) divided by 15 gives a quotient of 12 and a remainder of 7, what is \( x \)?
A · 187
Using division formula: \( x = 15 \times 12 + 7 = 180 + 7 = 187 \).
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A man distributes 490 apples equally among some children. If each child gets 12 apples, how many apples are left undistributed?
A · 10
Number of children = \( \lfloor \frac{490}{12} \rfloor = 40 \), distributed apples = \( 40 \times 12 = 480 \), leftover = 10.
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Ben is dividing 225 pencils equally into some boxes. If he has 6 boxes, how many pencils will be left undistributed after filling the boxes?
D · 10
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Which of the following numbers is divisible by 6?
B · 234
A number divisible by 6 must be divisible by 2 and 3. 234 is even and sum of digits (2+3+4=9) divisible by 3, so divisible by 6.
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Which of the following numbers is NOT divisible by 9?
C · 124
Sum of digits for 124 is 1+2+4=7, not divisible by 9, so 124 is not divisible by 9.
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If a number is divisible by both 4 and 5, it must be divisible by:
C · 20
LCM of 4 and 5 is 20, so number divisible by both 4 and 5 must be divisible by 20.
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Which statement is true about multiplication and division?
A · Division is the inverse of multiplication
Multiplication and division are inverse operations; dividing reverses multiplication.
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If \( 7 \times n = 56 \), find \( n \).
C · 8
Dividing both sides by 7: \( n = \frac{56}{7} = 8 \).
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If \( a \times b = 84 \) and \( a = 12 \), what is \( b \)? Also, find \( a \div b \).
A · \( b=7 \), \( a \div b = \frac{12}{7} \)
Since \( 12 \times b = 84 \), \( b = 7 \), then \( a \div b = \frac{12}{7} \).
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Which of the following best describes the operation of division?
B · Splitting a number into equal parts
Division is the process of splitting a number into equal parts or groups.
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If you divide 12 by 3, what does the operation represent?
B · Splitting 12 into 3 equal parts
Dividing 12 by 3 means splitting 12 into 3 equal parts.
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In the division expression \( 56 \div 7 = 8 \), what is the dividend?
C · 56
The dividend is the number being divided, which is 56.
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Which term refers to the result of a division?
A · Quotient
The quotient is the result obtained after division.
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In the division \( 43 \div 5 = 8 \) remainder \( 3 \), what is the divisor?
B · 5
The divisor is the number by which another number is divided, here 5.
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Calculate \( 156 \div 12 \).
A · 13
\( 12 \times 13 = 156 \) so the quotient is 13.
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Find the quotient and remainder when 125 is divided by 11.
A · Quotient 11, Remainder 4
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What is the quotient when 504 is divided by 21?
A · 24
21 times 24 is 504, so quotient is 24 without remainder.
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When dividing 289 by 17, what is the quotient and remainder?
A · 17 and 0
\(17 \times 17 = 289\), actually equal, so remainder 0, correct answer should be 17 quotient remainder 0; option A matches it.
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Which property does division NOT generally satisfy?
B · Associativity
Division is not associative, i.e. \( (a \div b) \div c eq a \div (b \div c) \).
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If \( a \div b = c \), which of the following statements is TRUE?
B · \( a = b \times c \)
By definition of division, \( a = b \times c \).
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Find the value of \( (48 \div 6) \div 2 \) and \( 48 \div (6 \div 2) \). Which statement is true?
C · \( (48 \div 6) \div 2 < 48 \div (6 \div 2) \)
\( (48 \div 6) \div 2 = 8 \div 2 = 4 \) and \( 48 \div (6 \div 2) = 48 \div 3 = 16 \), so first is less than second.
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A factory produces 450 items in 15 days. How many items does it produce per day?
A · 30
Items per day = \( 450 \div 15 = 30 \).
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If 100 meters of rope is cut into pieces each 7 meters long, how many full pieces will there be and what is the leftover length?
A · 14 pieces, 2 meters leftover
\( 100 \div 7 = 14 \) full pieces with remainder \( 100 - 14 \times 7 = 2 \) meters.
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A total of 840 pages need to be divided equally into 24 chapters. How many pages does each chapter have?
A · 35 pages
Pages per chapter = \( 840 \div 24 = 35 \).
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A number when divided by 9 leaves a remainder of 4. If the quotient is 23, what is the number?
A · 211
Number = Dividend = (Divisor \times Quotient) + Remainder = \( 9 \times 23 + 4 = 207 + 4 = 211 \). Correction: 9*23=207 plus 4=211, which corresponds to option A. So correct answer is A.
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If \( 48 \) is divided by \( x \) and the quotient is \( 6 \), which of the following can be the divisor?
A · 8
Quotient \( = \frac{Dividend}{Divisor} \) implies \( x = \frac{48}{6} = 8 \).
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Which of the following is NOT true about division and factors?
D · Division is commutative
Division is NOT commutative; changing divisor and dividend changes the result.
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Calculate \( \frac{\frac{3}{4}}{\frac{1}{2}} \).
B · \( \frac{3}{2} \)
Dividing fractions: \( \frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{3\times 2}{4} = \frac{6}{4} = \frac{3}{2} \).
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What is the result of dividing 7.2 by 0.3?
A · 24
Convert division by decimal: \( 7.2 \div 0.3 = 72 \div 3 = 24 \).
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Which of the following represents a proper fraction?
C · \( \frac{3}{4} \)
A proper fraction has a numerator smaller than the denominator. Here, \( \frac{3}{4} \) is the only proper fraction.
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Simplify the fraction \( \frac{36}{48} \).
A · \( \frac{3}{4} \)
Both numerator and denominator can be divided by 12: \( \frac{36\div12}{48\div12} = \frac{3}{4} \).
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Which type of fraction is \( \frac{11}{5} \)?
B · Improper fraction
An improper fraction has numerator greater than denominator. \( \frac{11}{5} \) fits this definition.
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Calculate \( \frac{2}{5} + \frac{3}{10} \).
B · \( \frac{7}{10} \)
Convert to common denominator 10: \( \frac{2}{5} = \frac{4}{10} \). Then, \( \frac{4}{10}+\frac{3}{10}=\frac{7}{10} \).
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Evaluate \( \frac{3}{4} \times \frac{8}{9} \).
B · \( \frac{2}{3} \)
Multiply numerators and denominators: \( \frac{3 \times 8}{4 \times 9} = \frac{24}{36} = \frac{2}{3} \).
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Find \( \frac{5}{6} - \frac{1}{4} \).
A · \( \frac{7}{12} \)
Common denominator is 12: \( \frac{5}{6} = \frac{10}{12}, \frac{1}{4} = \frac{3}{12} \). Then \( \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \).
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Calculate \( \frac{3}{7} \div \frac{6}{7} \).
A · \( \frac{1}{2} \)
Dividing by a fraction equals multiplying by its reciprocal: \( \frac{3}{7} \times \frac{7}{6} = \frac{3}{6} = \frac{1}{2} \).
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Convert the fraction \( \frac{3}{8} \) to decimal.
A · 0.375
\( \frac{3}{8} = 3 \div 8 = 0.375 \).
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Express \( 0.625 \) as a fraction in simplest form.
A · \( \frac{5}{8} \)
\( 0.625 = \frac{625}{1000} = \frac{5}{8} \) after simplification.
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Which decimal is equivalent to the fraction \( \frac{7}{20} \)?
A · 0.35
\( \frac{7}{20} = 7 \div 20 = 0.35 \).
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In the decimal number 46.507, what digit is in the hundredths place?
B · 0
Counting digits after the decimal point: tenths is 5, hundredths is 0, thousandths is 7. Therefore, hundredths digit is 0.
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What is the place value of the digit 6 in 2.364?
B · Hundredths
Digits after decimal: 3 is tenths, 6 is hundredths, 4 is thousandths. So 6 is in hundredths place.
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Calculate \( 3.75 \times 1.2 \).
D · 4.50
Multiplying decimals: \( 3.75 \times 1.2 = 4.50 \).
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Find the result of \( 7.5 - 3.28 \).
A · 4.22
Subtracting decimals: \( 7.5 - 3.28 = 4.22 \).
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Which is greater: \( \frac{5}{8} \) or 0.6?
A · \( \frac{5}{8} \)
\( \frac{5}{8} = 0.625 \) which is greater than 0.6.
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Arrange the following in ascending order: 0.45, \( \frac{3}{5} \), 0.48, \( \frac{7}{15} \).
A · \( \frac{7}{15} \), 0.45, 0.48, \frac{3}{5}
Convert all to decimal: \( \frac{7}{15} \approx 0.4667, \frac{3}{5} = 0.6 \). So ascending order: \( 0.45 < 0.4667 < 0.48 < 0.6 \).
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Which of the following represents the fraction \( \frac{3}{4} \) in simplest terms?
C · \( \frac{3}{4} \)
The fraction \( \frac{3}{4} \) is already in its simplest form; options A, B, and D are equivalent but not simplest terms.
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Which of these fractions is greater than \( \frac{2}{5} \)?
C · \( \frac{1}{2} \)
Among the options, \( \frac{1}{2} = 0.5 \) is greater than \( \frac{2}{5} = 0.4 \). The others are smaller than \( \frac{2}{5} \).
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Express the sum \( \frac{3}{7} + \frac{2}{7} \) as a single fraction in simplest form.
B · \( \frac{5}{7} \)
Since denominators are the same, add numerators: \( 3 + 2 = 5 \), so sum is \( \frac{5}{7} \).
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Calculate \( \frac{5}{8} \times \frac{3}{4} \).
A · \( \frac{15}{32} \)
Multiply numerators and denominators: \( \frac{5 \times 3}{8 \times 4} = \frac{15}{32} \).
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Find the result of \( \frac{7}{9} - \frac{2}{3} \).
A · \( \frac{1}{9} \)
Convert \( \frac{2}{3} \) to \( \frac{6}{9} \), then subtract: \( \frac{7}{9} - \frac{6}{9} = \frac{1}{9} \).
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Divide \( \frac{3}{5} \) by \( \frac{2}{7} \).
A · \( \frac{21}{10} \)
Dividing by a fraction is multiplying by its reciprocal: \( \frac{3}{5} \times \frac{7}{2} = \frac{21}{10} \).
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Convert the fraction \( \frac{7}{10} \) to its decimal equivalent.
B · 0.7
\( \frac{7}{10} = 0.7 \) because dividing numerator by denominator: 7 ÷ 10 = 0.7.
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Which decimal corresponds to the fraction \( \frac{5}{8} \)?
A · 0.625
\( \frac{5}{8} = 5 \div 8 = 0.625 \).
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Express the decimal 0.375 as a fraction in simplest form.
A · \( \frac{3}{8} \)
0.375 = \( \frac{375}{1000} = \frac{3}{8} \) after simplifying by dividing numerator and denominator by 125.
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What is the sum of 3.6 and 2.75?
A · 6.35
Adding decimals: 3.6 + 2.75 = 6.35. However, since 3.6 = 3.60, 3.60 + 2.75 = 6.35, which matches option A not B. Correct answer is A actually.
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Multiply 4.2 by 0.3.
A · 1.26
Multiply normally: 42 × 3 = 126, then place decimal: 1 decimal place + 1 decimal place = 2 decimals, so answer is 1.26.
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A recipe requires \( \frac{2}{3} \) of a cup of sugar. If Amy wants to make half the recipe, how much sugar in cups does she need?
A · \( \frac{1}{3} \)
Half of \( \frac{2}{3} \) is \( \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \).
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John spent \$12.50 on snacks which was \( \frac{5}{8} \) of the money he had. How much money did he initially have?
A · \$20.00
If \( \frac{5}{8} \) equals 12.50, the total is \( 12.50 \div \frac{5}{8} = 12.50 \times \frac{8}{5} = 20.00 \). Wait, that is \( \$20.00 \) not \$25.00. Actual correct answer is A.
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If a car uses \( \frac{3}{5} \) of a tank of gas driving 120 km, how far can it go on a full tank assuming constant usage?
A · 200 km
Using proportion: \( \frac{3}{5} \) tank → 120 km, so full tank → \( 120 \times \frac{5}{3} = 200 \) km.
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Which of the following correctly defines the principle of unit conversion?
C · Changing the numerical value by changing the measurement unit to keep the quantity constant
Unit conversion involves changing the numerical value according to the conversion factor such that the actual quantity remains the same.
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If you convert 5 kilometers to meters, what will be the numerical value?
C · 5000 meters
1 kilometer is equal to 1000 meters, so 5 km = 5 × 1000 = 5000 meters.
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Convert 3500 milliliters (mL) to liters (L).
B · 3.5 L
1 liter = 1000 milliliters. Therefore, 3500 mL = 3500 ÷ 1000 = 3.5 L.
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Which of these equals exactly 1 inch?
D · Both A and B
1 inch equals exactly 2.54 centimeters or 25.4 millimeters, so options A and B are both correct.
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A length of 5 feet is to be converted to meters. Using 1 foot = 0.3048 meters, what is the length in meters?
A · 1.52 m
5 feet × 0.3048 m/foot = 1.524 meters, approximately 1.52 m.
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Convert 3 hours 45 minutes to minutes.
A · 225 minutes
3 hours = 3 × 60 = 180 minutes + 45 minutes = 225 minutes total.
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If an event lasts 2.5 hours, how many seconds does it last?
A · 9000 seconds
2.5 hours = 2.5 × 60 = 150 minutes; 150 minutes × 60 = 9000 seconds. Correction: Option A is correct.
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A rectangular tank is 2 meters long, 1 meter wide, and 0.5 meters deep. What is the volume in liters? (1 cubic meter = 1000 liters)
D · 1000 liters
Volume = length × width × height = 2 × 1 × 0.5 = 1 cubic meter = 1000 liters. Correction needed.
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A square plot has each side measuring 100 feet. What is the area in square yards? (1 yard = 3 feet)
A · 1111.11 sq yards
100 feet = 100 ÷ 3 ≈ 33.33 yards; area = 33.33^2 ≈ 1111.11 square yards. Correction: Actually, 33.33 yards squared = 1111.11 sq yards. So option A is correct.
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A person walks 3 miles in 60 minutes. How many feet does the person walk per minute? (1 mile = 5280 feet)
D · 264 feet/min
Total feet = 3 × 5280 = 15840 feet; per minute = 15840 ÷ 60 = 264 feet/min. Correction: Option D is correct.
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A recipe requires 500 grams of flour, but your scale only measures kilograms. What is the amount in kilograms?
B · 0.5 kg
1000 grams = 1 kilogram, so 500 grams = 0.5 kilograms.
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A car's speedometer shows a speed in miles per hour (mph). If the speedometer reads 75 mph, what is the speed in meters per second and kilometers per hour? (1 mile = 1609 meters)
A · 33.53 m/s; 120.7 km/h
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A cube has edge length of 30 inches. Find its volume in cubic centimeters. (1 inch = 2.54 cm). Which of the following options is closest?
A · 44200 cm³
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A rectangular prism has dimensions 5.75 ft × 3.25 ft × 2.5 ft. Convert its volume into liters. (1 ft = 0.3048 m; 1 cubic meter = 1000 liters)
A · 1329 liters
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If 1 horse power (hp) = 550 ft-lb/s, convert it into Watts. Given 1 ft = 0.3048 m and 1 lb = 0.4536 kg. (Use g = 9.8 m/s²). Which value is closest?
A · 745 W
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Assertion (A): 1 cubic foot equals approximately 7.48 gallons (US).
Reason (R): 1 US gallon equals 231 cubic inches and 1 cubic foot equals 1728 cubic inches.
A · Both A and R are true and R is the correct explanation of A
Step 1: 1 cubic foot = 1728 in³
Step 2: 1 US gallon = 231 in³
Step 3: Number of gallons in one cubic foot = 1728 / 231 ≈ 7.48 gallons
Both A and R are true and R explains A correctly.
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What is the sum of 245 and 176?
B · 421
Adding 245 and 176 gives 245 + 176 = 421.
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Find the product of 14 and 6.
B · 84
Multiplying 14 by 6 yields 14 \times 6 = 84.
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Calculate \( (45 + 15) \times 2 - 30 \div 5 \). What is the result?
A · 114
First, solve inside parentheses: 45 + 15 = 60.Multiply by 2: 60 \times 2 = 120.Divide 30 by 5: 30 \div 5 = 6.Subtract: 120 - 6 = 114.
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What is the value of \( 8 + 12 \times 3 \)?
D · 44
Order of operations: multiplication first.12 \times 3 = 36.Then addition: 8 + 36 = 44.
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Evaluate \( (5 + 7) \times (10 - 6) \div 4 \).
A · 24
Calculate parentheses:5 + 7 = 12 and 10 - 6 = 4.Then multiply: 12 \times 4 = 48.Divide by 4: 48 \div 4 = 12.
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Find the value of \( 3 + 6 \times (5^2 - 20 \div 2) + 4 \).
A · 43
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Which of the following is a factor of 84?
B · 12
Factors of 84 include 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.12 is a factor of 84.
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What is the least common multiple (LCM) of 6 and 8?
A · 24
Multiples of 6: 6, 12, 18, 24, 30...Multiples of 8: 8, 16, 24, 32...LCM is the smallest common multiple = 24.
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If 144 is divided by an unknown number, the quotient is 12. What is the divisor?
A · 12
Division formula: \( \text{Dividend} = \text{Divisor} \times \text{Quotient} \).So, divisor = 144 \div 12 = 12.
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What is the remainder when 250 is divided by 12?
B · 10
Divide 250 by 12:12 \times 20 = 240; remainder 250 - 240 = 10.Check options and calculation again:Remainder = 10 which corresponds to option B.
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A farmer has 480 apples. He wants to pack them equally into boxes such that each box contains 15 apples. How many boxes can he fill?
A · 32
Number of boxes = \( \frac{480}{15} = 32 \).
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If 3 pencils cost \$1.50, how much would 7 pencils cost?
A · \$3.50
Cost per pencil = \$1.50 \div 3 = \$0.50.Cost of 7 pencils = 7 \times \$0.50 = \$3.50.
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A bus travels 60 km in 1.5 hours. How far will it travel in 4 hours at the same speed?
A · 160 km
Speed = distance/time = 60 \div 1.5 = 40 km/hr.Distance in 4 hr = 40 \times 4 = 160 km.Re-check calculation: 40*4=160 matches option A, correct answer should be 160 km.
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Which of the following numbers is the largest?
C · 15
Among the options, 15 is the largest number.
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Identify the smallest number from the list: 0.5, 0.75, 0.45, 0.65.
B · 0.45
0.45 is the smallest decimal among the given numbers.
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If \( x > 3 \) and \( x < 5 \), which of the following could be the value of \( x \)?
C · 4
4 lies between 3 and 5, so it satisfies \( x > 3 \) and \( x < 5 \).
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Which of the following is greater: \( \frac{3}{4} \) or 0.7?
A · \( \frac{3}{4} \)
\( \frac{3}{4} = 0.75 \), and since 0.75 > 0.7, \( \frac{3}{4} \) is greater.
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Arrange the following numbers in ascending order: \( \frac{2}{5}, 0.38, \frac{3}{7} \).
D · \( 0.38 < \frac{2}{5} < \frac{3}{7} \)
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Which decimal is closest in value to \( \frac{7}{8} \)?
B · 0.875
\( \frac{7}{8} = 0.875 \), which exactly matches option B.
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Which of the following is the greatest ratio?
C · 5:8
Convert to decimal: 3/5 = 0.6, 4/7 ~ 0.571, 5/8 = 0.625, 7/15 ~ 0.467. 5/8 (0.625) is the greatest ratio.
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If \( \frac{x}{4} = \frac{3}{6} \), which of the following is true?
A · \( x = 2 \)
Cross multiply: 6x = 12 \( \Rightarrow x = 2 \). But checking carefully, \( \frac{x}{4} = \frac{3}{6} = 0.5 \) so \( x = 2 \). So correct answer is A.
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A and B work together. A completes \( \frac{2}{5} \) of a job and B completes the rest. What is the ratio of work done by A to B?
A · 2:3
B did \( 1 - \frac{2}{5} = \frac{3}{5} \). Ratio A:B = \( \frac{2}{5} : \frac{3}{5} = 2:3 \).
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A car travels 150 km in 3 hours. Another car travels 200 km in 5 hours. Which car has the better speed?
A · First car
Speed of first car = 150\/3=50 km/h, second car = 200\/5=40 km/h, so first car is faster.
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Two friends, P and Q, complete a job. Q alone takes twice as long as P. If they work together, who does more work?
A · P does more work
P is faster; if Q is twice as slow, P does more work when combined.
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A number rounded to the nearest thousand is 8000. Which of the following could be the number?
C · 8499
Numbers from 7500 to 8499 round to 8000, so 8499 is valid.
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What is the meaning of 45% in terms of parts per hundred?
A · 45 parts out of 100
Percentage means 'per hundred', so 45% means 45 parts out of 100.
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If a student scored 75% marks in an exam, what fraction corresponds to his score?
A · \( \frac{3}{4} \)
75% as a fraction = \( \frac{75}{100} = \frac{3}{4} \) after simplification.
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Which of the following correctly represents 0.625 as a percentage?
B · 62.5%
To convert decimal to percent, multiply by 100. Thus, 0.625 × 100 = 62.5%.
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Express \( \frac{3}{8} \) as a percentage.
A · 37.5%
\( \frac{3}{8} = 0.375 \). Multiplying by 100 gives 37.5%.
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Convert 112.5% to a decimal.
A · 1.125
Divide percentage by 100 to convert to decimal: \( 112.5\% = \frac{112.5}{100} = 1.125 \).
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What is 20% of 250?
A · 50
20% of 250 = \( \frac{20}{100} \times 250 = 50 \).
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A population of a town increased from 40,000 to 46,000. What was the percentage increase?
B · 15%
Percentage increase = \( \frac{46000 - 40000}{40000} \times 100 = \frac{6000}{40000} \times 100 = 15\% \). The correct calculation gives 15%, option B is correct.
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The price of a jacket is decreased from \( \$200 \) to \( \$170 \). What is the percentage decrease?
A · 15%
Percentage decrease = \( \frac{200 - 170}{200} \times 100 = \frac{30}{200} \times 100 = 15\% \), so option A is correct.
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A shopkeeper sold a table for \( \$1,150 \) making a 15% profit. What was the cost price of the table?
A · \( \$1,000 \)
Let cost price be \( x \). Selling price = \( x + 15\% \text{ of } x = 1.15x = 1150 \implies x = \frac{1150}{1.15} = 1000 \).
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If a product is bought for \( \$800 \) and sold for \( \$680 \), what is the percentage loss?
A · 15%
Loss = \( 800 - 680 = 120 \). Percentage loss = \( \frac{120}{800} \times 100 = 15\% \) actually 15%, option A is correct.
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At 10% discount, a jacket is sold for \( \$1,125 \). What is its marked price?
A · \( \$1,250 \)
Selling price = Marked price - 10% of Marked price = 0.9 × Marked price. \( 0.9 \times M = 1125 \Rightarrow M = \frac{1125}{0.9} = 1250 \).
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A company's revenue increased by 20% in the first year and then decreased by 10% in the second year. If the original revenue was \( \$50{,}000 \), what is the revenue at the end of the second year?
A · \( \$54{,}000 \)
After 1st year: \( 50{,}000 \times 1.20 = 60{,}000 \).After 2nd year: \( 60{,}000 \times 0.90 = 54{,}000 \).
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A student scored 72 out of 90 in an exam. What was his score in percentage?
A · 80%
Percentage = \( \frac{72}{90} \times 100 = 80\% \).
