Multiplication and Factors

1. Tom has 3 cards. His sister has 5 times as many:

$3 \times 5 = 15$

His sister has $15$ baseball cards.

The comparison equation is: sister's cards $= 5 \times$ Tom's cards, or $15 = 5 \times 3$.

2. Step 1 — Cost of markers:

$4 \times \$6 = \$24$

Step 2 — Cost of paper:

$3 \times \$8 = \$24$

Step 3 — Total cost:

$\$24 + \$24 = \$48$

Step 4 — Compare to budget:

$\$50 - \$48 = \$2$

Yes, the school has enough money. They will spend \48$and have$$2$ left over.

3. We find all pairs of whole numbers that multiply to 36:

• $1 \times 36$
• $2 \times 18$
• $3 \times 12$
• $4 \times 9$
• $6 \times 6$

The factor pairs of 36 are: $(1, 36)$, $(2, 18)$, $(3, 12)$, $(4, 9)$, and $(6, 6)$.

36 is a composite number because it has more than two factors. A prime number has exactly two factors (1 and itself), but 36 has many factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

4. Let $k$ represent the number of laps Kevin ran. Kevin ran 3 times as many as Maya:

$k = 3 \times 4$

$k = 12$

Kevin ran $12$ laps.

5. 29 is prime. We check whether any number from 2 up to 5 divides evenly into 29 (we only need to check up to $\sqrt{29} \approx 5.4$):

• $29 \div 2 = 14$ remainder $1$ (not divisible)
• $29 \div 3 = 9$ remainder $2$ (not divisible)
• $29 \div 5 = 5$ remainder $4$ (not divisible)

No number other than 1 and 29 divides it evenly, so 29 is prime.

28 is composite. We can find factors other than 1 and 28:

• $28 \div 2 = 14$ (divides evenly)

Since $28 = 2 \times 14$, the number 28 has factors beyond just 1 and itself. Therefore 28 is composite. Its factor pairs are: $(1, 28)$, $(2, 14)$, and $(4, 7)$.