โ˜ฐ Year plan ยท Mathematics

Dividing decimals by whole numbers and by decimals

Week 12 ยท Dividing decimals by whole numbers and by decimals ยท 3 lessons
2

Dividing a decimal by a decimal

Discover Mathematics P5: Term 1, Unit 5, Lessons 15โ€“17
GoalMake the divisor a whole number by multiplying both numbers by 10 or 100, then divide.
New words
equivalent division ยท a division with the same answer, found by multiplying both numbers by the same power of tendecimal divisor ยท a divisor that has digits after the decimal pointwhole-number divisor ยท a divisor with no decimal part
Explanation

It is easier to divide by a whole number than by a decimal. If you multiply both the dividend and the divisor by 10, the answer does not change: 6 รท 2 = 3 and 60 รท 20 = 3. So 4.8 รท 0.6 becomes 48 รท 6 = 8. Multiply by 10 when the divisor has one decimal place, by 100 when it has two. The point moves the same number of places in both numbers; write a 0 if you need to: 7.2 รท 0.09 = 720 รท 9 = 80. After the change, divide as in the last lesson. Check by multiplying: 8 ร— 0.6 = 4.8.

OriginalMultiply both byWhole-number divisionAnswer
4.8 รท 0.61048 รท 68
7.2 รท 0.09100720 รท 980
3 รท 0.25100300 รท 2512
Worked examples
DividendDivisor
Before4.80.6
ร— 10486
Work out 4.8 รท 0.6. Multiply both numbers by 10: 48 รท 6 = 8. Check: 8 ร— 0.6 = 4.8.
Work out 7.2 รท 0.09. The divisor has two decimal places, so multiply both by 100: 720 รท 9 = 80. Check: 80 ร— 0.09 = 7.2.
0.250.250.250.250.250.250.250.250.250.250.250.253
Mariam pours 3 L of juice into cups of 0.25 L. How many cups? 3 รท 0.25 = 300 รท 25 = 12 cups.
Class activity

Match the pairs. Write six decimal divisions on cards, for example 2.4 รท 0.4, 0.9 รท 0.3, 5 รท 0.5, 1.6 รท 0.08, 0.72 รท 0.09 and 4.5 รท 1.5, and write the matching whole-number divisions (24 รท 4, 9 รท 3, 50 รท 5, 160 รท 8, 72 รท 9, 45 รท 15) on other cards. Mix the cards, match them in pairs and work out each answer.

Practice
1
Work out 6.3 รท 0.7.
2
Work out 0.96 รท 0.08.
3
Work out 9 รท 1.5 and 2.45 รท 0.7.
4
A 7.5 m rope is cut into pieces of 0.75 m. How many pieces?
5
Seif says 1.2 รท 0.4 = 0.3. What did he do wrong? Give the right answer.