Adding and Subtracting Decimals: practice solutions, Grade 5 – download the PDF

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7 October 20267 October 2026

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Practice solutions Grade 5 : Adding and Subtracting Decimals — Zyro the alien explorer of Planète Maths

Written solutions to the chapter problems. Check each step, then correct yourself.

1 Estimate by rounding ★★★

a) $7 + 3 = 10$. b) $9 + 3 = 12$. c) $16 - 8 = 8$. d) $21 - 4 = 17$.

The exact answers are $10.0$, $12.1$, $7.3$ and $16.8$, all close to the estimates.

2 Add decimals ★★★

a) $3.4 + 5.2 = 8.6$. b) $12.7 + 0.8 = 13.5$ (tenths: $7 + 8 = 15$, carry 1). c) $4.25 + 3.31 = 7.56$. d) $0.46 + 0.38 = 0.84$ (hundredths: $6 + 8 = 14$, carry 1; tenths: $4 + 3 + 1 = 8$).

3 Subtract decimals ★★★

a) $8.9 - 3.4 = 5.5$. b) $7.5 - 2.8 = 4.7$ (borrow: $15 - 8 = 7$, $6 - 2 = 4$). c) $9.86 - 4.32 = 5.54$. d) $6.47 - 0.25 = 6.22$.

4 Set it up vertically ★★★

Write $5.2$ as $5.20$ and line up the points:

$14.63$ on top, $5.20$ below. Hundredths: $3 + 0 = 3$. Tenths: $6 + 2 = 8$. Ones: $4 + 5 = 9$. Tens: $1$.

$5.2 + 14.63 = 19.83$.

5 True or false? ★★★

a) True: $35$ tenths $+ 24$ tenths $= 59$ tenths, which is $5.9$.

b) False: $7$ tenths $+ 5$ tenths $= 12$ tenths $= 1.2$, not $0.12$.

c) True: $6.3 - 0.3 = 6.0 = 6$.

6 Pencil case ★★★

a) $4.75 + 2.30 = 7.05$. He spends $7.05.

b) $10.00 - 7.05 = 2.95$. He gets $2.95 back.

7 Placeholder zeros ★★★

a) Write $6.4$ as $6.40$: $6.40 + 2.95 = 9.35$.

b) Write $8$ as $8.0$: $8.0 - 3.6 = 4.4$.

8 Estimate, then calculate ★★★

Estimate: $24 + 15 = 39$.

Exact: $23.78 + 15.46 = 39.24$.

The exact sum is close to the estimate, so the answer is reasonable.

9 Regrouping practice ★★★

a) $30.50 - 12.74 = 17.76$.

b) $5.03 - 2.48 = 2.55$.

c) $100.00 - 46.37 = 53.63$.

Check with addition: $17.76 + 12.74 = 30.50$, $2.55 + 2.48 = 5.03$, $53.63 + 46.37 = 100.00$.

10 Three addends ★★★

Write every number with two decimal places: $4.50 + 12.75 + 0.08$.

$4.50 + 12.75 = 17.25$, then $17.25 + 0.08 = 17.33$.

11 Find the mistake ★★★

Sam lined up the right-hand digits (the 6 and the 5) instead of the decimal points. He added $36 + 245 = 281$.

Correct setup: $3.60 + 2.45 = 6.05$. A quick estimate $4 + 2 = 6$ would have shown that $2.81$ was far too small.

12 Missing numbers ★★★

a) Subtract: $11.05 - 7.40 = 3.65$. Check: $7.4 + 3.65 = 11.05$.

b) Add: $6.90 + 4.38 = 11.28$. Check: $11.28 - 4.38 = 6.90$.

13 Rainfall ★★★

a) $1.35 + 0.80 = 2.15$, then $2.15 + 2.07 = 4.22$. The total is 4.22 inches.

b) $2.07 - 0.80 = 1.27$. Wednesday had 1.27 inches more.

14 Cutting a board ★★★

Pieces cut: $0.85 + 1.20 = 2.05$ meters.

Left: $2.50 - 2.05 = 0.45$. The piece left is 0.45 meter (45 centimeters).

15 Greater than 10? ★★★

a) $4.90 + 5.20 = 10.10$, greater than 10.

b) $3.75 + 6.20 = 9.95$, less than 10.

c) $5.08 + 4.93 = 10.01$, greater than 10.

16 Lunch money ★★★

a) $6.45 + 2.79 = 9.24$, then $9.24 + 1.35 = 10.59$. The total is $10.59.

b) $20.00 - 10.59 = 9.41$. His change is $9.41.

c) $9.50 - 9.41 = 0.09$. No, he is $0.09 short.

17 Perimeter of a triangle ★★★

The perimeter is the sum of the three sides: $3.45 + 4.80 + 6.15$.

$3.45 + 4.80 = 8.25$, then $8.25 + 6.15 = 14.40$.

The perimeter is 14.4 cm.

18 Swim meet ★★★

a) The fastest is Ava (28.67 s) and the slowest is Ben (31.2 s). $31.20 - 28.67 = 2.53$ seconds.

b) $28.67 + 31.20 = 59.87$, then $59.87 + 29.90 = 89.77$ seconds.

19 Digit puzzle ★★★

The ones digits are worth the most, so for the greatest sum put 7 and 5 in the ones places and 3 and 1 in the tenths places: $7.3 + 5.1 = 12.4$ (or $7.1 + 5.3 = 12.4$).

For the least sum put 1 and 3 in the ones places and 5 and 7 in the tenths places: $1.5 + 3.7 = 5.2$.

Greatest sum: 12.4. Least sum: 5.2.