Rules of Decimals: Addition, Subtraction, Multiplication, Division
Rules of Decimals
1. Addition of Decimals (āĻĻāĻļāĻŽāĻŋāĻ āϏāĻāĻā§āϝāĻžā§° āϝā§āĻ)
Steps
- Find the decimal point. (āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻŦāĻŋāĻāĻžā§°āĻāĨ¤)
- Line up the decimal points. (āϏāĻāϞ⧠āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻāĻā§ āĻļāĻžā§°ā§āϤ ā§°āĻžāĻāĻāĨ¤)
- Fill empty places with zeros if needed. (āĻāĻžāϞ⧠āĻ āĻžāĻ āĻĨāĻžāĻāĻŋāϞ⧠0 āĻŦāĻšā§ā§ąāĻžāĻāĻāĨ¤)
- Add the numbers. (āϏāĻāĻā§āϝāĻžāĻŦā§ā§° āϝā§āĻ āĻā§°āĻāĨ¤)
- Bring down the decimal point in the answer. (āĻāϤā§āϤ⧰āϤ āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻāĻā§ āϏā§āĻĨāĻžāύāϤ āĻŦāĻšā§ā§ąāĻžāĻāĻāĨ¤)
Example / āĻāĻĻāĻžāĻšā§°āĻŖ
Ans / āĻāϤā§āϤ⧰ = 22.24
2. Subtraction of Decimals (āĻĻāĻļāĻŽāĻŋāĻ āϏāĻāĻā§āϝāĻžā§° āĻŦāĻŋā§ā§āĻ)
Steps
- Find the decimal point. (āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻŦāĻŋāĻāĻžā§°āĻāĨ¤)
- Line up the decimal points. (āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§āĻŦā§ā§° āĻāĻā§ āĻļāĻžā§°ā§āϤ ā§°āĻžāĻāĻāĨ¤)
- Fill empty places with zeros if needed. (āĻĒā§ā§°ā§ā§āĻāύ āĻš'āϞ⧠0 āϝā§āĻ āĻā§°āĻāĨ¤)
- Subtract the numbers. (āĻŦāĻŋā§ā§āĻ āĻā§°āĻāĨ¤)
- Bring down the decimal point in the answer. (āĻāϤā§āϤ⧰āϤ āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻāĻā§ āϏā§āĻĨāĻžāύāϤ āĻŦāĻšā§ā§ąāĻžāĻāĻāĨ¤)
Example / āĻāĻĻāĻžāĻšā§°āĻŖ
Ans / āĻāϤā§āϤ⧰ = 3.47
3. Multiplication of Decimals (āĻĻāĻļāĻŽāĻŋāĻ āϏāĻāĻā§āϝāĻžā§° āĻā§āĻŖ)
Steps
- Multiply as usual. (āϏāĻžāϧāĻžā§°āĻŖ āĻā§āĻŖā§° āĻĻā§°ā§ āĻā§āĻŖ āĻā§°āĻāĨ¤)
- Ignore the decimal points at first. (āĻā§°āĻŽā§āĻāĻŖāĻŋāϤ⧠āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻāĻĒā§āĻā§āώāĻž āĻā§°āĻāĨ¤)
- Count the total decimal places in both numbers. (āĻĻā§ā§ā§āĻāĻž āϏāĻāĻā§āϝāĻžāϤ āĻŽā§āĻ āĻāĻŋāĻŽāĻžāύ āĻĻāĻļāĻŽāĻŋāĻ āϏā§āĻĨāĻžāύ āĻāĻā§ āĻāĻŖāύāĻž āĻā§°āĻāĨ¤)
- Put the decimal point in the answer accordingly. (āĻāϤā§āϤ⧰āϤ āϏā§āĻ āĻ āύā§āϏ⧰āĻŋ āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§ āĻŦāĻšā§ā§ąāĻžāĻāĻāĨ¤)
Example / āĻāĻĻāĻžāĻšā§°āĻŖ
Total decimal places = 2 + 1 = 3
Ans / āĻāϤā§āϤ⧰ = 3.0
4. Division of Decimals (āĻĻāĻļāĻŽāĻŋāĻ āϏāĻāĻā§āϝāĻžā§° āĻāĻžāĻ)
Steps
- The divisor cannot have a decimal. (āĻāĻžāĻāĻā§°ā§āϤāĻžāϤ āĻĻāĻļāĻŽāĻŋāĻ āĻĨāĻžāĻāĻŋāĻŦ āύā§ā§ąāĻžā§°ā§āĨ¤)
- Move the decimal in the divisor until it becomes a whole number. (āĻāĻžāĻāĻā§°ā§āϤāĻžā§° āĻĻāĻļāĻŽāĻŋāĻ āϏ⧰āĻžāĻ āĻĒā§ā§°ā§āĻŖ āϏāĻāĻā§āϝāĻž āĻā§°āĻāĨ¤)
- Move the decimal in the dividend by the same amount. (āϞāĻā§āϝāĻžāĻāĻļāϤ āĻāĻā§ āϏāĻāĻā§āϝāĻ āϏā§āĻĨāĻžāύ āĻĻāĻļāĻŽāĻŋāĻ āϏ⧰āĻžāĻāĻāĨ¤)
- Divide as usual. (āϤāĻžā§° āĻĒāĻŋāĻāϤ āϏāĻžāϧāĻžā§°āĻŖ āĻāĻžāĻ āĻā§°āĻāĨ¤)
Example / āĻāĻĻāĻžāĻšā§°āĻŖ
14.1 ÷ 3 = 4.7
Steps
- 3 goes into 14 4 times → 4 × 3 = 12
- Subtract: 14 − 12 = 2
- Bring down 1 → 21
- Put the decimal point in the answer
- 3 goes into 21 7 times → 7 × 3 = 21
- Remainder = 0
Ans / āĻāϤā§āϤ⧰ = 4.7
Tips (āύāĻŋā§āĻŽ)
- Addition & Subtraction: Line up the decimal points. (āĻĻāĻļāĻŽāĻŋāĻ āĻŦāĻŋāύā§āĻĻā§āĻŦā§ā§° āĻāĻā§ āĻļāĻžā§°ā§āϤ ā§°āĻžāĻāĻāĨ¤)
- Multiplication: Count decimal places in both numbers. (āĻĻā§ā§ā§āĻāĻž āϏāĻāĻā§āϝāĻžā§° āĻŽā§āĻ āĻĻāĻļāĻŽāĻŋāĻ āϏā§āĻĨāĻžāύ āĻāĻŖāύāĻž āĻā§°āĻāĨ¤)
- Division: Make the divisor a whole number first. (āĻĒā§ā§°āĻĨāĻŽā§ āĻāĻžāĻāĻā§°ā§āϤāĻžāĻ āĻĒā§ā§°ā§āĻŖ āϏāĻāĻā§āϝāĻž āĻŦāύāĻžāĻāĻ
MCQ
Explanation: 5.6 + 2.4 = 8.0 āĻŦā§āϝāĻžāĻā§āϝāĻž: 5.6 + 2.4 = 8.0
2. What is 9.5 − 4.2 ?
A. 5.3 B. 4.3 C. 6.3 D. 3.3
Ans: A. 5.3
Explanation: 9.5 − 4.2 = 5.3 āĻŦā§āϝāĻžāĻā§āϝāĻž: 9.5 − 4.2 = 5.3
3. What is 1.5 × 2 ?
A. 2 B. 3 C. 4 D. 5
An: B. 3
Explanation: 1.5 × 2 = 3.0 āĻŦā§āϝāĻžāĻā§āϝāĻž: 1.5 × 2 = 3.0
4. What is 8.4 ÷ 2 ?
A. 3.2 B. 4.2 C. 5.2 D. 6.2
Ans: B. 4.2
Explanation: 8.4 ÷ 2 = 4.2 āĻŦā§āϝāĻžāĻā§āϝāĻž: 8.4 ÷ 2 = 4.2