Q1.
Find the sums and differences: (a) 3/10 + 3 4/100 (b) 9 5/10 7/100 + 2 1/10 3/100 (c) 15 6/10 4/100 + 14 3/10 6/100 (d) 7 7/100 – 4 4/100 (e) 8 6/100 – 5 3/100 (f) 12 6/10 2/100 – 9/10 9/100
Answer
Line up units with units, tenths with tenths and hundredths with hundredths.
| In decimal form | Working | Answer | |
|---|---|---|---|
| (a) | 0.30 + 3.04 | 0 + 3 units, 3 + 0 tenths, 0 + 4 hundredths | 3 34⁄100 = 3.34 |
| (b) | 9.57 + 2.13 | 11 units, 6 tenths, 10 hundredths → 11 7⁄10 | 11 7⁄10 = 11.70 |
| (c) | 15.64 + 14.36 | 29 units, 9 tenths, 10 hundredths → 30 | 30 |
| (d) | 7.07 – 4.04 | 3 units, 0 tenths, 3 hundredths | 3 3⁄100 = 3.03 |
| (e) | 8.06 – 5.03 | 3 units, 0 tenths, 3 hundredths | 3 3⁄100 = 3.03 |
| (f) | 12.62 – 0.99 | borrow twice: 11 15⁄10 12⁄100 – 0 9⁄10 9⁄100 | 11 63⁄100 = 11.63 |
Full working for (b):
9 5⁄10 7⁄100 + 2 1⁄10 3⁄100 = 11 6⁄10 10⁄100
10 hundredths = 1 tenth
= 11 7⁄10 0⁄100 = 11 7⁄10
9 5⁄10 7⁄100 + 2 1⁄10 3⁄100 = 11 6⁄10 10⁄100
10 hundredths = 1 tenth
= 11 7⁄10 0⁄100 = 11 7⁄10
Full working for (c):
15 6⁄10 4⁄100 + 14 3⁄10 6⁄100 = 29 9⁄10 10⁄100
= 29 10⁄10 = 29 + 1 = 30
15 6⁄10 4⁄100 + 14 3⁄10 6⁄100 = 29 9⁄10 10⁄100
= 29 10⁄10 = 29 + 1 = 30
Why it happens: in (c) the hundredths make a whole tenth and the tenths then make a whole unit, so the fractional part disappears completely and a clean whole number 30 is left.
Tip: in (f) it helps to write 9⁄10 9⁄100 as 0.99 first. Then 12.62 – 0.99 = 12.62 – 1 + 0.01 = 11.63 in one mental step.