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
Step
Share
Result
Ones
9 ÷ 4
2, 1 left
Tenths
13 ÷ 4
3, 1 left
Hundredths
16 ÷ 4
4
Worked examples
9.36 ÷ 4 = 2.34
Ones
Tenths
Hundredths
2
3
4
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.
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.
1.4 and 1.3. (6 × 1.4 = 8.4 and 12 × 1.3 = 15.6.)
2
Work out 2.7 ÷ 5.
0.54. (5 × 0.54 = 2.7.)
3
Work out 6 ÷ 8 by writing 6 as 6.000.
0.75. (8 × 0.75 = 6.)
4
Four friends share a bill of 25.2 LE equally. How much does each pay?
25.2 ÷ 4 = 6.3, so 6.3 LE each. (4 × 6.3 = 25.2.)
5
Marwan says 4.5 ÷ 5 = 9. Use an estimate to show he is wrong, then find the right answer.
4.5 is less than 5, so the quotient must be less than 1. The right answer is 0.9, because 5 × 0.9 = 4.5.