Rules of Decimals: Addition, Subtraction, Multiplication, Division






Rules of Decimals


1. Addition of Decimals (āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āϝ⧋āĻ—)


Steps



  • Find the decimal point. (āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻŦāĻŋāϚāĻžā§°āĻ•āĨ¤)

  • Line up the decimal points. (āϏāĻ•āϞ⧋ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻāϕ⧇ āĻļāĻžā§°ā§€āϤ ā§°āĻžāĻ–āĻ•āĨ¤)

  • Fill empty places with zeros if needed. (āĻ–āĻžāϞ⧀ āĻ āĻžāχ āĻĨāĻžāĻ•āĻŋāϞ⧇ 0 āĻŦāĻšā§ā§ąāĻžāĻ“āĻ•āĨ¤)

  • Add the numbers. (āϏāĻ‚āĻ–ā§āϝāĻžāĻŦā§‹ā§° āϝ⧋āĻ— āϕ⧰āĻ•āĨ¤)

  • Bring down the decimal point in the answer. (āωāĻ¤ā§āϤ⧰āϤ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻāϕ⧇ āĻ¸ā§āĻĨāĻžāύāϤ āĻŦāĻšā§ā§ąāĻžāĻ“āĻ•āĨ¤)


Example / āωāĻĻāĻžāĻšā§°āĻŖ






  10.50

+11.74

-----------

    22.24





Ans / āωāĻ¤ā§āϤ⧰ = 22.24


2. Subtraction of Decimals (āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻŦāĻŋā§Ÿā§‹āĻ—)

Steps



  • Find the decimal point. (āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻŦāĻŋāϚāĻžā§°āĻ•āĨ¤)

  • Line up the decimal points. (āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻŦā§‹ā§° āĻāϕ⧇ āĻļāĻžā§°ā§€āϤ ā§°āĻžāĻ–āĻ•āĨ¤)

  • Fill empty places with zeros if needed. (āĻĒā§ā§°ā§Ÿā§‹āϜāύ āĻš'āϞ⧇ 0 āϝ⧋āĻ— āϕ⧰āĻ•āĨ¤)

  • Subtract the numbers. (āĻŦāĻŋā§Ÿā§‹āĻ— āϕ⧰āĻ•āĨ¤)

  • Bring down the decimal point in the answer. (āωāĻ¤ā§āϤ⧰āϤ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻāϕ⧇ āĻ¸ā§āĻĨāĻžāύāϤ āĻŦāĻšā§ā§ąāĻžāĻ“āĻ•āĨ¤)


Example / āωāĻĻāĻžāĻšā§°āĻŖ






  12.70

-  9.23

---------

    3.47





 Ans / āωāĻ¤ā§āϤ⧰ = 3.47


3. Multiplication of Decimals (āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āϗ⧁āĻŖ)

Steps



  • Multiply as usual. (āϏāĻžāϧāĻžā§°āĻŖ āϗ⧁āĻŖā§° āĻĻ⧰⧇ āϗ⧁āĻŖ āϕ⧰āĻ•āĨ¤)

  • Ignore the decimal points at first. (āφ⧰āĻŽā§āĻ­āĻŖāĻŋāϤ⧇ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āωāĻĒ⧇āĻ•ā§āώāĻž āϕ⧰āĻ•āĨ¤)

  • Count the total decimal places in both numbers. (āĻĻā§ā§Ÿā§‹āϟāĻž āϏāĻ‚āĻ–ā§āϝāĻžāϤ āĻŽā§āĻ  āĻ•āĻŋāĻŽāĻžāύ āĻĻāĻļāĻŽāĻŋāĻ• āĻ¸ā§āĻĨāĻžāύ āφāϛ⧇ āĻ—āĻŖāύāĻž āϕ⧰āĻ•āĨ¤)

  • Put the decimal point in the answer accordingly. (āωāĻ¤ā§āϤ⧰āϤ āϏ⧇āχ āĻ…āύ⧁āϏ⧰āĻŋ āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻŦāĻšā§ā§ąāĻžāĻ“āĻ•āĨ¤)


Example / āωāĻĻāĻžāĻšā§°āĻŖ 






  1.2

x 2.5

--------

  300





Total decimal places = 2 + 1 = 3


Ans / āωāĻ¤ā§āϤ⧰ = 3.0


4. Division of Decimals (āĻĻāĻļāĻŽāĻŋāĻ• āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻ­āĻžāĻ—)

Steps



  • The divisor cannot have a decimal. (āĻ­āĻžāĻ—āĻ•ā§°ā§āϤāĻžāϤ āĻĻāĻļāĻŽāĻŋāĻ• āĻĨāĻžāĻ•āĻŋāĻŦ āĻ¨ā§‹ā§ąāĻžā§°ā§‡āĨ¤)

  • Move the decimal in the divisor until it becomes a whole number. (āĻ­āĻžāĻ—āĻ•ā§°ā§āϤāĻžā§° āĻĻāĻļāĻŽāĻŋāĻ• āϏ⧰āĻžāχ āĻĒā§‚ā§°ā§āĻŖ āϏāĻ‚āĻ–ā§āϝāĻž āϕ⧰āĻ•āĨ¤)

  • Move the decimal in the dividend by the same amount. (āϞāĻ­ā§āϝāĻžāĻ‚āĻļāϤ āĻāϕ⧇ āϏāĻ‚āĻ–ā§āϝāĻ• āĻ¸ā§āĻĨāĻžāύ āĻĻāĻļāĻŽāĻŋāĻ• āϏ⧰āĻžāĻ“āĻ•āĨ¤)

  • Divide as usual. (āϤāĻžā§° āĻĒāĻŋāĻ›āϤ āϏāĻžāϧāĻžā§°āĻŖ āĻ­āĻžāĻ— āϕ⧰āĻ•āĨ¤)


Example / āωāĻĻāĻžāĻšā§°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 / āωāĻ¤ā§āϤ⧰ = 4.7


Tips (āύāĻŋ⧟āĻŽ)

  • Addition & SubtractionLine up the decimal points. (āĻĻāĻļāĻŽāĻŋāĻ• āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻŦā§‹ā§° āĻāϕ⧇ āĻļāĻžā§°ā§€āϤ ā§°āĻžāĻ–āĻ•āĨ¤)

  • MultiplicationCount decimal places in both numbers. (āĻĻā§ā§Ÿā§‹āϟāĻž āϏāĻ‚āĻ–ā§āϝāĻžā§° āĻŽā§āĻ  āĻĻāĻļāĻŽāĻŋāĻ• āĻ¸ā§āĻĨāĻžāύ āĻ—āĻŖāύāĻž āϕ⧰āĻ•āĨ¤)

  • DivisionMake the divisor a whole number first. (āĻĒā§ā§°āĻĨāĻŽā§‡ āĻ­āĻžāĻ—āĻ•ā§°ā§āϤāĻžāĻ• āĻĒā§‚ā§°ā§āĻŖ āϏāĻ‚āĻ–ā§āϝāĻž āĻŦāύāĻžāĻ“āĻ•


MCQ

1. What is 5.6 + 2.4 ?

A. 7.0 B. 8.0 C. 9.0 D. 6.0

Ans: B. 8.0

Explanation: 5.6 + 2.4 = 8.0 āĻŦā§āϝāĻžāĻ–ā§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§āϝāĻžāĻ–ā§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§āϝāĻžāĻ–ā§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§āϝāĻžāĻ–ā§āϝāĻž: 8.4 ÷ 2 = 4.2