Subtracting quantities with tenths
Not enough tenths? Split a unit.
The longest finger
Shylaja’s hand is 12 410 units long and her palm is 6 710 units long. The longest finger is the part left when the palm is taken away.
The tenths: we must take 7 tenths from 4 tenths. What can we do?
What this lesson covers
The idea
Subtraction starts from the tenths; if there are too few tenths, one unit is split into 10 one-tenths, then the tenths and after that the units are subtracted.
The longest finger
Shylaja’s hand is 12 4/10 units long and her palm is 6 7/10 units long. The longest finger is the part left when the palm is taken away.
The tenths: we must take 7 tenths from 4 tenths. What can we do?
- Take 4 from 7 instead
- Split one unit into 10 tenths first
- It cannot be done
Split a unit
Take the lower number away place by place, starting from the tenths. If a column is short, tap 1 → 10 to split one from its left.
Start from the tenths
Subtract the way we do with whole numbers: start from the smallest place.
Taking 6 7/10 from 12 4/10:
Subtraction starts from the tenths. If there are too few tenths, split one unit into 10 one-tenths. Then subtract the tenths, and after that the units.
- Step | Working
- Not enough tenths | 4 tenths is less than 7 tenths
- Split 1 unit into 10 tenths | 12 4/10 → 11 14/10
- Subtract the tenths | 14 − 7 = 7 tenths
- Subtract the units | 11 − 6 = 5 units
- Answer | 5 7/10
Notes
Subtraction starts from the tenths. Too few tenths? Split 1 unit into 10 tenths, subtract the tenths, then the units.
Check yourself
What is 8 2/10 − 3 5/10? Type a mixed number, like 2 1/10.
Answer: 4 7/10
8 2/10 = 7 12/10. Then 12 − 5 = 7 tenths and 7 − 3 = 4 units: 4 7/10.
In 6 3/10 − 2 8/10 there are too few tenths. What do we do first?
After a unit is split, 9 2/10 becomes 8 ?/10. What is the missing number of tenths?
Answer: 12 tenths
1 unit = 10 tenths, and 10 + 2 = 12. So 9 2/10 = 8 12/10.
- Take 3 from 8 instead, since 8 is bigger. Then we would be taking the numbers away the wrong way round. Split a unit instead.
- Split 1 unit into 10 tenths: 6 3/10 becomes 5 13/10 — correct. Yes. Now 13 tenths − 8 tenths = 5 tenths, and 5 − 2 = 3 units: 3 5/10.
- Add 1 unit to 2 8/10 only. That changes the number we subtract, so the answer changes. We split a unit of the number we start with.