Multiplication Patterns

1. (a) The teacher needs $56$ juice boxes in packs of $7$:

$56 \div 7 = 8$

She needs to buy $8$ packs.

(b) Division is the same as finding an unknown factor. The question $56 \div 7 = \text{?}$ is the same as asking: $7 \times \text{?} = 56$. Since $7 \times 8 = 56$, the answer is $8$.

2. (a) $6 \times 8 = 6 \times (5 + 3)$

(b) Using the distributive property, we multiply $6$ by each part separately:

$6 \times (5 + 3) = (6 \times 5) + (6 \times 3)$

$= 30 + 18$

$= 48$

So $6 \times 8 = 48$.

3. (a) $9 \times 7 = 63$

(b) $72 \div 8 = 9$

(c) $6 \times 6 = 36$

(d) $45 \div 9 = 5$

(e) $8 \times 7 = 56$

4. (a) The pattern adds $4$ each time:

$24 + 4 = 28, \quad 28 + 4 = 32, \quad 32 + 4 = 36$

The next three numbers are $28$, $32$, and $36$.

(b) All the numbers are even. When you multiply any number by $4$ (an even number), the product is always even. You can also see that adding $4$ to an even number always gives another even number.

(c) No, $50$ is not in this pattern. Every number in the pattern is a multiple of $4$. We check: $50 \div 4 = 12$ remainder $2$. Since $50$ is not evenly divisible by $4$, it is not a multiple of $4$ and does not appear in the pattern.

5. (a) $8 \times 6 = 8 \times 5 + 8 \times 1 = 40 + 8 = 48$. Strategy: $6$ is one more than $5$, so add one more group of $8$.

(b) $8 \times 4 = 8 \times 5 - 8 \times 1 = 40 - 8 = 32$. Strategy: $4$ is one less than $5$, so subtract one group of $8$.

(c) $16 \times 5 = (2 \times 8) \times 5 = 2 \times (8 \times 5) = 2 \times 40 = 80$. Strategy: $16$ is double $8$, so the product is double $40$.