Pre-Algebra Exam 1 Solutions
1. Order from smallest to largest:
SOLUTION
−25 < −3 < 0 < 3
SOLUTION
2. Solve:
SOLUTION
n = 5 − 2
n = 3
SOLUTION
3. Combine:
SOLUTION
= 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.