Multiplying Multi-Digit Whole Numbers: practice solutions, Grade 4

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Practice solutions Grade 4 : Multiplying Multi-Digit Whole Numbers — Zyro the alien explorer of Planète Maths

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

1 Multiples of 10 and 100 ★★★

$3 \times 4 = 12$ and one zero: $30 \times 4 = 120$.
$8 \times 7 = 56$ and two zeros: $8 \times 700 = 5{,}600$.
$9 \times 4 = 36$ and three zeros: $9 \times 4{,}000 = 36{,}000$.
$6 \times 5 = 30$ and two zeros: $60 \times 50 = 3{,}000$.

2 Missing factors ★★★

$7 \times 7 = 49$, so the missing number is 70.
$6 \times 6 = 36$, so the missing number is 6.
$5 \times 9 = 45$, so the missing number is 9,000.
$8 \times 8 = 64$, so the missing number is 8.

3 Complete the area model ★★★

Split $15 = 10 + 5$ and $12 = 10 + 2$.

$100 + 20 + 50 + 10 = 180$. So $15 \times 12 = 180$.

4 Expanded form ★★★

$2{,}314 = 2{,}000 + 300 + 10 + 4$.

$2{,}000 \times 3 = 6{,}000$, $300 \times 3 = 900$, $10 \times 3 = 30$, $4 \times 3 = 12$.

$6{,}000 + 900 + 30 + 12 = 6{,}942$. The product is 6,942.

5 True or false? ★★★

False. $4 \times 3 = 12$, but there is one more zero: $4 \times 30 = 120$.
True. $6 \times 5 = 30$ and two zeros give 3,000.
False. $2 \times 2 = 4$ and two zeros give $20 \times 20 = 400$. The sum $20 + 20$ is 40, but the product is much greater.
True. $3 \times 7 = 21$ and three zeros give 21,000.

6 Muffins at the bakery ★★★

$60 \times 8 = 6 \times 8$ tens $= 48$ tens $= 480$.

There are 480 muffins on 8 trays.

7 Name the property ★★★

Commutative property: the order changes.
Associative property: the grouping changes.
Distributive property: 13 is split into $10 + 3$.
Identity property: multiplying by 1 does not change the number.
Zero property: any number times 0 is 0.

8 4-digit times 1-digit ★★★

$1{,}000 \times 5 = 5{,}000$, $200 \times 5 = 1{,}000$, $30 \times 5 = 150$, $8 \times 5 = 40$. The sum is $5{,}000 + 1{,}000 + 150 + 40 = 6{,}190$.
$7{,}000 \times 6 = 42{,}000$, $0 \times 6 = 0$, $50 \times 6 = 300$, $2 \times 6 = 12$. The sum is $42{,}000 + 300 + 12 = 42{,}312$.

9 Two 2-digit numbers ★★★

$34 \times 20 = 680$ and $34 \times 6 = 204$.

$680 + 204 = 884$. So $34 \times 26 = 884$.

10 Area model for 42 times 31 ★★★

Split $42 = 40 + 2$ and $31 = 30 + 1$.

$1{,}200 + 40 + 60 + 2 = 1{,}302$. So $42 \times 31 = 1{,}302$.

11 Estimate first ★★★

Estimate: $60 \times 30 = 1{,}800$. Exact: $63 \times 28 = 63 \times 20 + 63 \times 8 = 1{,}260 + 504 = 1{,}764$. The exact answer is close to the estimate.
Estimate: $6{,}000 \times 4 = 24{,}000$. Exact: $5{,}000 \times 4 + 900 \times 4 + 10 \times 4 + 7 \times 4 = 20{,}000 + 3{,}600 + 40 + 28 = 23{,}668$. It is a little less than the estimate because 5,917 was rounded up.

12 Find the mistake ★★★

Check with an estimate: $3{,}000 \times 4 = 12{,}000$ and $3{,}205$ is more than 3,000, so the product should be more than 12,000 by at least 800 or so.

Partial products: $3{,}000 \times 4 = 12{,}000$, $200 \times 4 = 800$, $0 \times 4 = 0$, $5 \times 4 = 20$. Total: $12{,}000 + 800 + 20 = 12{,}820$.

Mia forgot the 800 from the hundreds place. The correct product is 12,820.

13 Seats in the stadium ★★★

$48 \times 65 = 48 \times 60 + 48 \times 5 = 2{,}880 + 240 = 3{,}120$.

The section has 3,120 seats.

14 Mental math with properties ★★★

$7 \times 98 = 7 \times 100 - 7 \times 2 = 700 - 14 = 686$.
$6 \times 102 = 6 \times 100 + 6 \times 2 = 600 + 12 = 612$.
$25 \times 12 = 25 \times 4 \times 3 = 100 \times 3 = 300$.

15 Farm stand sales ★★★

Apples: $36 \times 14 = 360 + 144 = 504$, so 504 dollars.

Pears: $27 \times 18 = 270 \times 2 - 27 \times 2 = 540 - 54 = 486$, so 486 dollars.

Total: $504 + 486 = 990$. The stand earns $990.

16 Cargo ship ★★★

$2{,}000 \times 7 = 14{,}000$, $400 \times 7 = 2{,}800$, $60 \times 7 = 420$, $8 \times 7 = 56$. Sum: $14{,}000 + 2{,}800 + 420 + 56 = 17{,}276$ containers.
$20{,}000 - 17{,}276 = 2{,}724$. The company still needs to move 2,724 containers.

17 The missing digit ★★★

Try the possible numbers. $40 \times 23 = 920$, which is too small. $45 \times 23 = 1{,}035$, still too small. $46 \times 23 = 46 \times 20 + 46 \times 3 = 920 + 138 = 1{,}058$.

The hidden digit is 6, and the number is 46.

18 Which is greater? ★★★

$35 \times 48 = 35 \times 50 - 35 \times 2 = 1{,}750 - 70 = 1{,}680$.

$36 \times 47 = 36 \times 50 - 36 \times 3 = 1{,}800 - 108 = 1{,}692$.

$36 \times 47$ is greater by $1{,}692 - 1{,}680 = 12$.

19 Fundraiser goal ★★★

$80 \times 60 = 4{,}800$, so about 4,800 dollars.
$78 \times 62 = 78 \times 60 + 78 \times 2 = 4{,}680 + 156 = 4{,}836$ dollars.
No, because $4{,}836 < 5{,}000$. The band is missing $5{,}000 - 4{,}836 = 164$ dollars.

20 Garden area ★★★

$85 \times 27 = 85 \times 20 + 85 \times 7 = 1{,}700 + 595 = 2{,}295$. The area is 2,295 square feet.
The length is $3 \times 85 = 255$ feet. The area is $255 \times 27 = 5{,}100 + 1{,}785 = 6{,}885$ square feet. This is also $3 \times 2{,}295$, so the answer makes sense.

21 Greatest product ★★★

Put the two greatest digits, 5 and 4, in the tens places. Then try the ones digits: $52 \times 43 = 2{,}236$ and $53 \times 42 = 2{,}226$.

Check: $52 \times 43 = 2{,}080 + 156 = 2{,}236$. Any other arrangement with smaller tens digits gives a smaller product. The greatest product is 2,236.