☰ Year plan · Mathematics

Dividing decimals by whole numbers and by decimals

Week 12 · Dividing decimals by whole numbers and by decimals · 3 lessons
1

Dividing a decimal by a whole number

Discover Mathematics P5: Term 1, Unit 5, Lessons 15–17
GoalDivide a decimal by a whole number step by step, put the point in the quotient and check by multiplying.
New words
dividend · the number that is being divideddivisor · the number we divide byremainder · what is left after sharing; we regroup it into the next place
Explanation

Divide a decimal the way you divide whole numbers, one place at a time, from the left. Write the decimal point in the quotient straight above the point in the dividend. When something is left over, regroup it: 1 one is 10 tenths, 1 tenth is 10 hundredths. If the dividend runs out and there is still a remainder, write a 0 at the end of it and carry on: 5.4 = 5.400. Always check by multiplying: quotient × divisor must give the dividend. A whole number can also give a decimal answer: 6 ÷ 8 = 0.75, because 6 = 6.00.

9.36 ÷ 4 = 2.34
StepShareResult
Ones9 ÷ 42, 1 left
Tenths13 ÷ 43, 1 left
Hundredths16 ÷ 44
Worked examples
9.36 ÷ 4 = 2.34
OnesTenthsHundredths
234
Work out 9.36 ÷ 4. Ones: 9 ÷ 4 = 2, 1 left, which is 10 tenths. Tenths: 10 + 3 = 13 tenths, 13 ÷ 4 = 3, 1 left, which is 10 hundredths. Hundredths: 10 + 6 = 16, 16 ÷ 4 = 4. So 9.36 ÷ 4 = 2.34. Check: 4 × 2.34 = 9.36.
5.4 ÷ 8 = 0.675
OnesTenthsHundredthsThousandths
0675
Work out 5.4 ÷ 8. Ones: 5 ÷ 8 = 0, 5 left. Tenths: 54 tenths ÷ 8 = 6, 6 left. Write 5.4 as 5.40: 60 hundredths ÷ 8 = 7, 4 left. Write 5.400: 40 thousandths ÷ 8 = 5. So 5.4 ÷ 8 = 0.675. Check: 8 × 0.675 = 5.4.
1.61.61.61.61.61.61.61.61.614.4
A 14.4 m rope is cut into 9 equal pieces. 14.4 ÷ 9 = 1.6, so each piece is 1.6 m. Check: 9 × 1.6 = 14.4.
Class activity

Share and check. Take a total from a shopping receipt, for example 36.6 LE, and divide it among 6 people on paper. Write each step by place. Then multiply the share by 6 to check that you get the total back. Try again with 7.5 LE shared by 4 and see why you need to add zeros.

Practice
1
Work out 8.4 ÷ 6 and 15.6 ÷ 12.
2
Work out 2.7 ÷ 5.
3
Work out 6 ÷ 8 by writing 6 as 6.000.
4
Four friends share a bill of 25.2 LE equally. How much does each pay?
5
Marwan says 4.5 ÷ 5 = 9. Use an estimate to show he is wrong, then find the right answer.