**1. Order from smallest to largest:
SOLUTION
−25 < −3 < 0 < 3**

**2. Solve:**

**SOLUTION**

n = 5 − 2

n = 3

**SOLUTION
**

**3. Combine:
**

= 2/3

SOLUTION

**SOLUTION
**

4. Seven people are sharing a pizza. Two greedy people eat
1/4 of the pizza each, while

a third person eats 1/6 . If we divide the remaining pizza evenly among the
remaining

people, how much do they each get?

**SOLUTION**

How much pizza has been eaten?

The LCD is 6.

Therefore, there is of the pizza remaining.

The number of people remaining is 7 - 3 = 4 people to
share the remaining pizza. So

each remaining person gets

of the pizza.

5. (a) Find the Greatest Common Factors of the following
pairs of numbers:

(a) (8,32) (b) (21,49) (c) (39,57)

**SOLUTION**

(a) by prime factorization:

8: 2 × 2 × 2 32: 2 × 2 × 2 × 2 × 2 The GCF is the largest subset in common

between the two, in this case 2 × 2 × 2 or 8. (b)

21: 3 × 7

49: 7 × 7

**GCF: 7**

(c)

39: 3 × 13

57: 3 × 19

**GCF: 3**

.

(b) Find the Least Common Multiple of each pair of
numbers:

(a) (9,15) (b) (12,14) (c) (18,7)

(a) by prime factorization:

9: 3 × 3

15: 3 × 5

The LCM is the set of primes that includes both prime
factorizations as subsets.

In this case 3 × 3 × 5 = 45

(b) 12: 2 × 2 × 3

14: 2 × 7

LCM: 2 × 2 × 3 × 7 = 84

(c) 18: 9 × 2

7: 7

LCM:9 × 2 × 7 = 126

6. (a) What sums do the following number lines represent?

**SOLUTION**

(a) 0 − 2 = −2

(b) −2 − 4 = −6

(c) −2 − 2 − 2 = −6 or −2 × 3 = 6

(b) Solve:

(a) n = 5 + 2 × 4

**SOLUTION**

n = 5 + 8 = 13

(b) x = 4 × −2 + 6

**SOLUTION**

x = −8 + 6 = −2

(c) y = −9 ÷ 3 + 2

**SOLUTION** y = −3 + 2 = −1

7. Solve:

**SOLUTION **First multiply both sides by the LCM. LCM
= 30. Multiply all terms

by 30 to get:

10x + 15 = 12

Now solve:

Subtract 15 from both sides:

10x = −3

Divide by 10:

x = −3/10

8. The price of grapefruits is 25% less this week than it
was last week. If grapefruits cost

$3 per pound this week, what was their cost last week?

**SOLUTION
**Let my variable be x, the price of grapefruit last week. Then I can write:

The grapefruits cost $4 per pound last week.