Multiplying and Dividing Decimals: practice solutions, Grade 5

Rate this post

Practice solutions Grade 5 : Multiplying and Dividing Decimals — Zyro the alien explorer of Planète Maths

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

1 Multiply by 10, 100, and 1,000 ★★★

Each digit moves one place to the left for every factor of 10.

$3.7 \times 10 = 37$
$0.46 \times 100 = 46$
$5.2 \times 1{,}000 = 5{,}200$ (we add two zeros as placeholders)
$0.008 \times 1{,}000 = 8$
$12.35 \times 10 = 123.5$

2 Divide by 10, 100, and 1,000 ★★★

Each digit moves one place to the right for every factor of 10.

$45 \div 10 = 4.5$
$6.3 \div 100 = 0.063$
$820 \div 1{,}000 = 0.82$
$7.5 \div 10 = 0.75$
$0.9 \div 10 = 0.09$

3 Find the missing number ★★★

From 2.8 to 280 the digits move two places left, so the number is $100$.
From 91 to 0.91 the digits move two places right, so we divide by $100$.
Undo the multiplication by 10: $6.5 \div 10 = 0.65$.
Undo the division by 1,000: $0.034 \times 1{,}000 = 34$.

4 Decimal times a whole number ★★★

$4 \times 6 = 24$ tenths, so $0.4 \times 6 = 2.4$.
$13 \times 5 = 65$, one decimal place: $6.5$.
$25 \times 4 = 100$, one decimal place: $10.0 = 10$.
$32 \times 3 = 96$, one decimal place: $9.6$.
$7 \times 8 = 56$ hundredths, so $0.07 \times 8 = 0.56$.

5 Notebooks at the store ★★★

We repeat the price 4 times: $2.30 \times 4$.

$230 \times 4 = 920$, and the price has two decimal places, so the total is $9.20$.

Maya pays $\$9.20$.

6 Divide by a whole number ★★★

$8.4 \div 4 = 2.1$. Check: $2.1 \times 4 = 8.4$.
$9.6 \div 3 = 3.2$. Check: $3.2 \times 3 = 9.6$.
$0.72 \div 6 = 0.12$. Check: $0.12 \times 6 = 0.72$.
$5.5 \div 5 = 1.1$. Check: $1.1 \times 5 = 5.5$.
$3.6 \div 9 = 0.4$. Check: $0.4 \times 9 = 3.6$.

7 Place the decimal point ★★★

The digits are always 312. Count the decimal places in both factors.

1 + 1 = 2 places: $3.12$.
2 + 0 = 2 places: $3.12$.
0 + 3 = 3 places: $0.312$.
1 + 2 = 3 places: $0.312$.

8 Read the area model ★★★

The rectangle has 7 columns and 6 rows.
It shows $0.7 \times 0.6$. It contains $7 \times 6 = 42$ little squares, which is 42 hundredths. So $0.7 \times 0.6 = 0.42$.
Shade 5 columns and 9 rows: $5 \times 9 = 45$ squares. So $0.5 \times 0.9 = 0.45$.

9 Multiply with more digits ★★★

$34 \times 6 = 204$, one decimal place: $20.4$.
$525 \times 4 = 2{,}100$, two decimal places: $21.00 = 21$.
$85 \times 12 = 1{,}020$, two decimal places: $10.20 = 10.2$.
$607 \times 5 = 3{,}035$, two decimal places: $30.35$.

10 Decimal times decimal ★★★

$15 \times 24 = 360$, 2 places: $3.60 = 3.6$.
$8 \times 35 = 280$, 1 + 2 = 3 places: $0.280 = 0.28$.
$42 \times 5 = 210$, 1 + 1 = 2 places: $2.10 = 2.1$.
$6 \times 9 = 54$, 2 + 1 = 3 places: $0.054$.

11 Estimate to place the point ★★★

Round: $6.8 \approx 7$ and $4.9 \approx 5$, so the product should be close to $7 \times 5 = 35$.

Only $33.32$ is close to 35. Also, 1 + 1 = 2 decimal places gives $33.32$. So $6.8 \times 4.9 = 33.32$.

12 Flour for the bakery ★★★

Multiply the amount per loaf by the number of loaves: $0.35 \times 14$.

$35 \times 14 = 490$, and 0.35 has two decimal places, so the product is $4.90 = 4.9$.

The baker needs 4.9 kilograms of flour.

13 Divide, then check ★★★

$15.6 \div 4 = 3.9$, since $3.9 \times 4 = 15.6$.
$7.2 \div 8 = 0.9$, since $0.9 \times 8 = 7.2$.
$0.45 \div 5 = 0.09$, since $0.09 \times 5 = 0.45$.
$14.7 \div 7 = 2.1$, since $2.1 \times 7 = 14.7$.
$9 \div 4$: $9 = 9.00$, and $900 \div 4 = 225$ hundredths, so the answer is $2.25$. Check: $2.25 \times 4 = 9$.

14 Whole number divided by a decimal ★★★

There are 2 halves in each whole, so $4 \div 0.5 = 8$.
Multiply both numbers by 10: $90 \div 3 = 30$.
Multiply both numbers by 100: $600 \div 25 = 24$.
Multiply both numbers by 10: $20 \div 1 = 20$.

15 Inches, centimeters, and miles ★★★

$5.5 \times 2.54$: $55 \times 254 = 13{,}970$, 1 + 2 = 3 places: $13.970 = 13.97$. The phone is 13.97 cm tall.
$72 \times 2.54$: $72 \times 254 = 18{,}288$, 2 places: $182.88$. The pole is 182.88 cm tall.
$3 \times 1.61 = 4.83$. The trail is 4.83 km long.

16 True or false? ★★★

True. For example $70 \times 0.1 = 7$ and $70 \div 10 = 7$. Both move each digit one place to the right.
False. $5.2 \times 0.4 = 2.08$, which is less than 5.2. Multiplying by a number smaller than 1 makes the result smaller.
False. $6 \div 0.5 = 12$, which is greater than 6. Dividing by a number smaller than 1 makes the result bigger.
True. $9 \times 9 = 81$, and 1 + 1 = 2 decimal places, so $0.9 \times 0.9 = 0.81$.

17 Find the mistake ★★★

Leo multiplied $3 \times 4 = 12$ but forgot to place the decimal point. Each factor has 1 decimal place, so the product needs 2 decimal places. Also, 1.2 is bigger than both factors, which is impossible when we multiply two numbers smaller than 1.
$0.3 \times 0.4 = 0.12$. On the grid, 3 columns by 4 rows make 12 squares out of 100, which is 0.12.
No. He divided by 2 instead of 0.5. We compute $25 \div 5 = 5$, so $2.5 \div 0.5 = 5$. Check: $5 \times 0.5 = 2.5$.

18 Fruit stand ★★★

$3.5 \times 1.20$: $35 \times 120 = 4{,}200$, 1 + 2 = 3 places: $4.200$. The apples cost $\$4.20$.
$2 \times 1.75 = 3.50$. The pears cost $\$3.50$.
Total: $4.20 + 3.50 = 7.70$. Change: $10 - 7.70 = 2.30$. Lena gets $\$2.30$ back.

19 Pouring juice ★★★

$7.2 \div 0.3 = 72 \div 3 = 24$. So 24 cups.
$7.2 \div 0.45 = 720 \div 45 = 16$. Check: $16 \times 0.45 = 7.2$. So 16 bottles.
The small cups need more: $24 - 16 = 8$ more containers.

20 Drone flight ★★★

$0.45 \times 12$: $45 \times 12 = 540$, 2 places: $5.40 = 5.4$. It flies 5.4 km.
$9 \div 0.45 = 900 \div 45 = 20$. Check: $20 \times 0.45 = 9$. It needs 20 minutes.

21 Number puzzles ★★★

The number is $4{,}250 \div 1{,}000 = 4.25$. Divided by 10 it gives $0.425$.
Use the opposite operation: $1.35 \times 4 = 5.4$. Check: $5.4 \div 4 = 1.35$.
$4.8 \div 6 = 0.8$. Check: $0.8 \times 6 = 4.8$.

22 Garden bed and soil ★★★

Area = length times width = $2.5 \times 1.2$. We compute $25 \times 12 = 300$, 1 + 1 = 2 places: $3.00$. The area is 3 square meters.
$3 \div 0.5 = 30 \div 5 = 6$. We need 6 bags.
$6 \times 4.25 = 25.50$. The total cost is $\$25.50$.