Multiplication Facts and Properties: practice solutions, Grade 3 – download the PDF

1 Skip counting by 5 ★★★

Counting by 5 gives 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.

35 is the 7th number in the list, so the fact is \(7 \times 5 = 35\).

2 Facts of 2, 5 and 10 ★★★

a) \(2 \times 7 = 14\) (double 7). b) \(2 \times 9 = 18\). c) \(10 \times 6 = 60\). d) \(10 \times 10 = 100\). e) \(5 \times 8 = 40\). f) \(5 \times 7 = 35\).

3 Reading an array ★★★

There are 3 rows with 6 stickers in each row, so \(3 \times 6 = 18\).

Turning the picture, there are 6 columns of 3, so \(6 \times 3 = 18\).

There are 18 stickers.

4 Facts of 3 and 4 ★★★

a) \(3 \times 4 = 12\). b) \(3 \times 7 = 14 + 7 = 21\). c) \(4 \times 6 = 24\) (6, 12, 24). d) \(4 \times 8 = 32\) (8, 16, 32). e) \(3 \times 9 = 18 + 9 = 27\). f) \(4 \times 9 = 36\) (9, 18, 36).

5 Bags of oranges ★★★

There are 4 equal groups of 5, so \(4 \times 5 = 20\).

The grocer uses 20 oranges.

6 True or false? ★★★

a) True. b) False: \(2 \times 8 = 16\). c) True. d) False: \(3 \times 5 = 15\). e) False: \(4 \times 4 = 16\).

7 The nines trick ★★★

a) \(30 - 3 = 27\). b) \(50 - 5 = 45\). c) \(70 - 7 = 63\). d) \(90 - 9 = 81\).

Check: the digits of each product add up to 9 (2 + 7, 4 + 5, 6 + 3, 8 + 1).

8 Harder facts ★★★

a) \(6 \times 6 = 36\). b) \(6 \times 8 = 48\). c) \(7 \times 7 = 49\). d) \(7 \times 8 = 56\). e) \(8 \times 8 = 64\). f) \(6 \times 7 = 5 \times 7 + 7 = 35 + 7 = 42\).

9 Find the missing factor ★★★

a) \(4 \times 7 = 28\), so the missing number is 7. b) \(9 \times 6 = 54\), so 9. c) \(8 \times 5 = 40\), so 5. d) \(3 \times 7 = 21\), so 3. e) \(6 \times 10 = 60\), so 10.

10 Splitting an array ★★★

a) The right part has \(8 - 5 = 3\) columns. \(6 \times 8 = 6 \times 5 + 6 \times 3 = 30 + 18 = 48\).

b) \(8 \times 7 = 8 \times 5 + 8 \times 2 = 40 + 16 = 56\).

11 Changing the grouping ★★★

a) \((2 \times 3) \times 4 = 6 \times 4 = 24\) and \(2 \times (3 \times 4) = 2 \times 12 = 24\). Both are 24, which is the associative property.

b) \(5 \times 2 = 10\), then \(10 \times 7 = 70\). The product is 70.

12 Multiples of 10 ★★★

a) \(3 \times 2 = 6\), so 6 tens, or 60. b) \(5 \times 3 = 15\), so 150. c) \(7 \times 4 = 28\), so 280. d) \(6 \times 5 = 30\), so 300. e) \(9 \times 3 = 27\), so 270. f) \(8 \times 6 = 48\), so 480.

13 Ribbons of two sizes ★★★

a) \(6 \times 8 = 48\). Maya has 48 inches of ribbon, which is 4 feet because 12 inches make 1 foot.

b) \(5 \times 9 = 45\). Her brother has 45 centimeters of ribbon.

14 Wheels on cars ★★★

a) The bar for 3 cars reaches 12, so 3 cars have 12 wheels.

b) Each car adds 4 wheels, so \(7 \times 4 = 28\) wheels.

c) \(10 \times 4 = 40\), so 10 cars have 40 wheels.

15 Nine groups the clever way ★★★

\(9 \times 7\) is one group fewer than \(10 \times 7\). So \(9 \times 7 = 70 - 7 = 63\).

In the same way, \(10 \times 8 = 80\), and taking away one group of 8 gives \(9 \times 8 = 80 - 8 = 72\).

16 Cookies for orders ★★★

a) \(6 \times 4 = 24\) cookies in the first boxes, and \(8 \times 3 = 24\) cookies in the others.

b) \(24 + 24 = 48\) cookies in all.

c) \(48 < 50\), so there are not enough cookies. The baker is 2 cookies short.

17 A frog on the number line ★★★

a) After 6 hops it is at \(6 \times 7 = 42\).

b) \(7 \times 8 = 56\), so it reaches 56 after 8 hops.

c) No. The landing spots are the facts of 7: 49, then 56. The number 50 is not a product of 7, since it falls between \(7 \times 7 = 49\) and \(7 \times 8 = 56\).

18 Find the mistake ★★★

The product \(7 \times 8\) is 56, not 54. Check by doubling: \(7 \times 4 = 28\) and \(28 + 28 = 56\).

For \(6 \times 30\), Liam forgot the zero. \(6 \times 3 = 18\) means 18 tens, so \(6 \times 30 = 180\).

19 Multiples of 10 and grouping ★★★

First way: \((3 \times 2) \times 40 = 6 \times 40 = 240\) because \(6 \times 4 = 24\) and 24 tens is 240.

Second way: \(3 \times (2 \times 40) = 3 \times 80 = 240\) because \(3 \times 8 = 24\).

Both give 240, as the associative property promises.

20 Mystery product ★★★

The products of 6 near that range are 24 (\(6 \times 4\)) and 30. The products of 8 near that range are 24 (\(8 \times 3\)) and 32. Only 24 is in both lists and between 20 and 30.

I am 24: \(6 \times 4 = 24\) and \(8 \times 3 = 24\).

21 Unknown factors ★★★

a) \(9 \times 8 = 72\), so 9. b) \(7 \times 9 = 63\), so 9. c) \(6 \times 9 = 54\), so 6. d) \(8 \times 7 = 56\), so 7.

22 Equal rows of desks ★★★

We look for facts with product 24 where both factors are 8 or less.

\(3 \times 8 = 24\): 3 rows of 8 desks. \(4 \times 6 = 24\): 4 rows of 6. \(6 \times 4 = 24\): 6 rows of 4. \(8 \times 3 = 24\): 8 rows of 3.

The facts \(2 \times 12\), \(12 \times 2\), \(1 \times 24\) and \(24 \times 1\) do not fit the rule, because 12 and 24 are more than 8.