Basic Operations

Introduction to Basic Arithmetic Operations

Mathematics is a language we use every day, whether we realize it or not. The four basic arithmetic operations-addition, subtraction, multiplication, and division-are the building blocks of all math. They help us count money, measure ingredients, calculate distances, and solve problems in exams like the Assam Direct Recruitment Examination (ADRE) for Grade IV posts.

Understanding these operations well is essential because they form the foundation for more advanced topics such as fractions, percentages, and algebra. In this chapter, we will explore each operation carefully, learn how to perform them step-by-step, and see how they connect to real-life situations.

Addition

What is Addition? Addition is the process of combining two or more numbers to find their total. When you add, you are putting groups together to find out how many there are altogether.

For example, if you have 3 apples and your friend gives you 5 more, how many apples do you have now? You add 3 and 5 to get 8.

Diagram explanation: Starting at 0 on the number line, move 3 steps forward (blue line), then 5 more steps forward (green line). You land at 8, which is the sum of 3 and 5.

Properties of Addition

Commutative Property: Changing the order of numbers does not change the sum. For example, \(3 + 5 = 5 + 3\).
Associative Property: When adding three or more numbers, the way you group them does not change the sum. For example, \((2 + 3) + 4 = 2 + (3 + 4)\).

Subtraction

What is Subtraction? Subtraction is the process of finding the difference between two numbers or removing a certain quantity from another. It answers questions like "How many are left?" or "How much more or less?"

For example, if you have 9 sweets and you give away 4, how many sweets remain? You subtract 4 from 9 to find the answer.

Diagram explanation: Starting at 9 on the number line, move 4 steps backward (red line) to reach 5, which is the difference.

Important Note

Unlike addition, subtraction is not commutative. This means that \(9 - 4 eq 4 - 9\). The order matters because subtracting a larger number from a smaller one can lead to negative numbers, which we will learn about later.

Multiplication

What is Multiplication? Multiplication is a shortcut for repeated addition. Instead of adding the same number many times, you multiply.

For example, if you have 4 packets of biscuits and each packet contains 6 biscuits, instead of adding \(6 + 6 + 6 + 6\), you multiply \(4 \times 6\) to get the total number of biscuits.

Multiplication Table (1 to 10)

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

Properties of Multiplication

Commutative Property: \(a \times b = b \times a\)
Associative Property: \((a \times b) \times c = a \times (b \times c)\)
Distributive Property: \(a \times (b + c) = a \times b + a \times c\)

Division

What is Division? Division is the process of splitting a number into equal parts or groups. It tells us how many times one number fits into another.

For example, if you have 20 chocolates and want to share them equally among 4 friends, division helps you find out how many chocolates each friend gets.

graph TD    A[Start: Dividend (20)] --> B[Divide by Divisor (4)]    B --> C[Find Quotient (5)]    C --> D[Check for Remainder (0)]    D --> E[Result: Each friend gets 5 chocolates]

Division with Remainder

Sometimes, division does not result in a whole number. For example, dividing 100 by 6:

6 goes into 100 sixteen times (because \(6 \times 16 = 96\))
There is a remainder of 4 (because \(100 - 96 = 4\))

This means the quotient is 16 and the remainder is 4.

Order of Operations (BODMAS)

When a math problem has more than one operation, the order in which you perform them matters. To get the correct answer, follow the BODMAS rule:

Brackets first
Orders (powers and roots)
Division and Multiplication (from left to right)
Addition and Subtraction (from left to right)

graph TD    A[Start] --> B{Are there Brackets?}    B -- Yes --> C[Calculate inside Brackets]    B -- No --> D{Are there Orders?}    D -- Yes --> E[Calculate Powers/Roots]    D -- No --> F{Division or Multiplication?}    F -- Yes --> G[Calculate from Left to Right]    F -- No --> H{Addition or Subtraction?}    H -- Yes --> I[Calculate from Left to Right]    I --> J[End]    G --> J    E --> F    C --> D

Worked Examples

Example 1: Addition of Two Numbers Easy

Add 256 and 489.

Step 1: Write the numbers one below the other, aligning digits by place value:

      256    + 489

Step 2: Add the units place: \(6 + 9 = 15\). Write 5 and carry over 1 to the tens place.

Step 3: Add the tens place: \(5 + 8 = 13\), plus the carryover 1 makes 14. Write 4 and carry over 1 to the hundreds place.

Step 4: Add the hundreds place: \(2 + 4 = 6\), plus the carryover 1 makes 7.

Answer: The sum is 745.

Example 2: Subtraction with Borrowing Medium

Subtract 732 from 1000.

Step 1: Write the numbers aligned by place value:

      1000    -  732

Step 2: Start from the units place: 0 - 2 is not possible, so borrow 1 from the tens place.

Step 3: The tens place is 0, so borrow 1 from the hundreds place. The hundreds place is also 0, so borrow 1 from the thousands place.

Step 4: After borrowing, the thousands place becomes 0, hundreds place becomes 9, tens place becomes 9, and units place becomes 10.

Step 5: Now subtract units: \(10 - 2 = 8\).

Step 6: Subtract tens: \(9 - 3 = 6\).

Step 7: Subtract hundreds: \(9 - 7 = 2\).

Answer: The difference is 268.

Example 3: Multiplication of Two-Digit Numbers Medium

Multiply 23 by 45.

Step 1: Write the numbers vertically:

      23    x 45

Step 2: Multiply 23 by 5 (units digit of 45):

      23 x 5 = 115

Step 3: Multiply 23 by 4 (tens digit of 45), remember to add a zero at the units place:

      23 x 4 = 92 -> 920 (because it is 40, not 4)

Step 4: Add the two results:

      115    + 920    -----     1035

Answer: \(23 \times 45 = 1035\).

Example 4: Division with Remainder Medium

Divide 100 by 6 and find the quotient and remainder.

Step 1: Find how many times 6 fits into 100 without exceeding it.

\(6 \times 16 = 96\), which is less than 100.

Step 2: Calculate the remainder:

\(100 - 96 = 4\).

Answer: Quotient is 16 and remainder is 4.

Example 5: Mixed Operations Using BODMAS Hard

Solve \(25 + 12 \times 3 - 18 \div 6\).

Step 1: According to BODMAS, first do multiplication and division from left to right.

Calculate \(12 \times 3 = 36\).

Calculate \(18 \div 6 = 3\).

Step 2: Now the expression becomes:

\(25 + 36 - 3\).

Step 3: Perform addition and subtraction from left to right:

\(25 + 36 = 61\).

\(61 - 3 = 58\).

Answer: The result is 58.

Formula Bank

Addition

\[ a + b = c \]

where: \(a, b\) are addends; \(c\) is the sum

Subtraction

\[ a - b = c \]

where: \(a\) is minuend; \(b\) is subtrahend; \(c\) is difference

Multiplication

\[ a \times b = c \]

where: \(a, b\) are factors; \(c\) is product

Division

\[ a \div b = q \text{ remainder } r \]

where: \(a\) is dividend; \(b\) is divisor; \(q\) is quotient; \(r\) is remainder

Order of Operations

BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction

N/A

Tips & Tricks

Tip: Use multiplication tables to quickly recall products without repeated addition.

When to use: While solving multiplication and division problems to save time.

Tip: Check subtraction answers by adding the difference to the smaller number; it should equal the larger number.

When to use: To verify subtraction answers quickly.

Tip: Remember BODMAS to avoid mistakes in mixed operation problems.

When to use: Whenever multiple operations appear in a single problem.

Tip: Break large addition or subtraction into smaller parts using place value (units, tens, hundreds).

When to use: When dealing with large numbers to reduce errors.

Tip: For division with remainder, multiply quotient by divisor and add remainder to check the answer.

When to use: To verify division answers involving remainders.

Common Mistakes to Avoid

❌ Adding digits without aligning place values.

✓ Always align numbers by units, tens, hundreds before adding.

Why: Misalignment causes incorrect sums.

❌ Subtracting a larger digit from a smaller one without borrowing.

✓ Use the borrowing method to subtract correctly.

Why: Ignoring borrowing leads to negative or wrong digits.

❌ Confusing multiplication and addition in word problems.

✓ Identify keywords like "each", "times" for multiplication, and "total" for addition.

Why: Misinterpretation leads to wrong operation choice.

❌ Ignoring remainder in division problems.

✓ Always note remainder if division is not exact.

Why: Remainder affects final answer and interpretation.

❌ Not following order of operations in mixed problems.

✓ Apply BODMAS strictly to solve correctly.

Why: Skipping order leads to wrong results.

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100

The Joy of Learning

Login

The Joy of Learning

Sign-up

The Joy of Learning

Forgot Password

Introduction to Basic Arithmetic Operations

Addition

Properties of Addition

Subtraction

Important Note

Multiplication

Multiplication Table (1 to 10)

Properties of Multiplication

Division

Division with Remainder

Order of Operations (BODMAS)

Worked Examples

Formula Bank

Tips & Tricks

Common Mistakes to Avoid

Try Practice next.

Rank

eBook

Online Test Series + eBook

Book is added to your cart!

x	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42	49	56	63	70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54	63	72	81	90
10	10	20	30	40	50	60	70	80	90	100