Written solutions to the chapter problems. Check each step, then correct yourself.
1 Sharing stickers ★★★
The total is 12 and there are 4 shares, so we divide: \(12 \div 4 = 3\).
Check: \(3 \times 4 = 12\).
Answer: each friend gets 3 stickers.
2 Bags of pencils ★★★
The total is 18 and each group has 6, so we divide: \(18 \div 6 = 3\).
Check: \(3 \times 6 = 18\).
Answer: she can fill 3 bags.
3 Reading an array ★★★
a) There are 3 rows of 5 dots: \(3 \times 5 = 15\) dots in all.
b) Splitting the 15 dots into 3 rows gives \(15 \div 3 = 5\). Splitting them into columns of 3 gives \(15 \div 5 = 3\).
4 Quick division facts ★★★
a) \(4 \times 5 = 20\), so \(20 \div 4 = 5\).
b) \(2 \times 8 = 16\), so \(16 \div 2 = 8\).
c) \(5 \times 6 = 30\), so \(30 \div 5 = 6\).
d) \(3 \times 9 = 27\), so \(27 \div 3 = 9\).
5 Naming the parts ★★★
The dividend is the total: 35.
The divisor is the number we divide by: 5.
The quotient is the answer: 7.
6 True or false? ★★★
a) True, because \(4 \times 6 = 24\).
b) False, because \(5 \times 3 = 15\), not 18. The correct answer is \(18 \div 3 = 6\) since \(6 \times 3 = 18\).
c) False. Dividing by 1 does not change the number, so \(10 \div 1 = 10\).
7 Jumps on a number line ★★★
Mia starts at 21 and makes jumps of 7 until she reaches 0. She makes 3 jumps.
So the equation is \(21 \div 7 = 3\).
8 Fact family of 6, 7 and 42 ★★★
The product is 42, so it goes first in the divisions.
\(6 \times 7 = 42\), \(7 \times 6 = 42\), \(42 \div 6 = 7\) and \(42 \div 7 = 6\).
9 Missing numbers ★★★
a) \(n = 56 \div 8 = 7\). Check: \(8 \times 7 = 56\).
b) \(n = 63 \div 9 = 7\). Check: \(7 \times 9 = 63\).
c) \(8 \times n = 72\), so \(n = 9\). Check: \(72 \div 9 = 8\).
d) The total is 6 groups of 4, so \(n = 6 \times 4 = 24\). Check: \(24 \div 4 = 6\).
10 Dividing by 1 and by itself ★★★
a) \(9 \div 1 = 9\), because any number divided by 1 stays the same.
b) \(0 \div 5 = 0\), because 0 cookies shared among 5 friends is 0 each.
c) \(8 \div 8 = 1\), because any number divided by itself is 1.
d) \(100 \div 1 = 100\).
11 Cherry bowls ★★★
Total: 32. Number of bowls: 4. We divide: \(32 \div 4 = 8\).
Check: \(8 \times 4 = 32\).
Answer: there are 8 cherries in each bowl.
12 Field trip vans ★★★
Total: 45 students. Each group has 9. We divide: \(45 \div 9 = 5\).
Check: \(5 \times 9 = 45\).
Answer: 5 vans are needed.
13 Find the mistake ★★★
No. \(5 \times 40 = 200\), not 8.
The multiplication that matches \(40 \div 8 = 5\) must have 40 as the product: \(5 \times 8 = 40\) (or \(8 \times 5 = 40\)). The total 40 always stays alone on one side of the equation.
14 Dividing by 4 ★★★
Use the 4 times table:
| Number | 8 | 12 | 20 | 32 | 36 |
|---|---|---|---|---|---|
| Divided by 4 | 2 | 3 | 5 | 8 | 9 |
For example \(4 \times 8 = 32\), so \(32 \div 4 = 8\).
15 Pages per day ★★★
a) \(54 \div 6 = 9\), because \(9 \times 6 = 54\). She reads 9 pages each day.
b) \(9 \times 9 = 81\). She could read 81 pages in 9 days.
16 Marbles and gifts ★★★
Step 1: \(63 \div 7 = 9\), so each friend receives 9 marbles.
Step 2: \(9 - 2 = 7\).
Answer: each friend has 7 marbles left.
17 The muffin sale ★★★
Number of boxes: \(40 \div 5 = 8\).
Boxes left after the sale: \(8 - 3 = 5\).
Muffins left: \(5 \times 5 = 25\).
Answer: 25 muffins are left. (Another way: she sold \(3 \times 5 = 15\) muffins and \(40 - 15 = 25\).)
18 Missing dividends and divisors ★★★
a) \(n \div 6 = 7\) means \(n = 7 \times 6 = 42\). For \(63 \div n = 9\), we need \(9 \times n = 63\), so \(n = 7\).
b) \(36 \div 4 = 9\) and \(56 \div 7 = 8\). Since \(9 > 8\), \(36 \div 4\) is greater.
19 Write your own problem ★★★
Many answers are possible. Here is one example of each.
Sharing: 28 marbles are shared equally among 4 children. How many marbles does each child get? \(28 \div 4 = 7\), so each child gets 7 marbles.
Grouping: 28 students make teams of 4. How many teams are there? \(28 \div 4 = 7\), so there are 7 teams.
Both stories use the same equation, because \(7 \times 4 = 28\).
20 Can we share it? ★★★
Look at the multiples of 4: 4, 8, 12, 16, 20, 24, 28.
The number 25 is not in the list: \(4 \times 6 = 24\) and \(4 \times 7 = 28\). So no whole number times 4 gives 25.
Answer: Jada is not right. 25 cannot be shared equally among 4 players with no cards left over.
Test yourself: quick challenge for Grade 3
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