MATH 095 Chapter 1 Review Solutions
1. List all the factors of 48.
Factors of 48 are : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48
2. Find the prime factorization of 240.
3. Write the prime factorization for 12 and 75. Then find the LCM of 12 and 75.
4. Write the prime factorization for 15, 36, and 54. Then
find the LCM for 15, 36 and
54.
5. Write an equivalent expression with the given denominator.
6. Write an equivalent expression with the given denominator.
Problems 7 – 9: Simplify
Problems 10 – 13: Evaluate
10.
for a =6 and b =4
11.
for x =30 and y =9
12. −7x2 for
13. 3x2 for 
16. The opposite of − 3 is 3.
17. The opposite of 
is
18. The reciprocal of − 3 is 
.
19. The reciprocal of 
is
When 
When 
20. Find 
when
and 
21. Find 
when
and 
When 
When 
Problems 22 – 27: Write as an algebraic expression.
| 22. 10 more than y |
 |
| 23. 8 less than z |
 |
| 24. 7 more than 3 times x |
 |
| 25. 7% of some number | 0.07x |
| 26. the sum of y and z |
 |
| 27. the product of 4 and c |
 |
Problems 28 – 31: Insert < or > to write a true statement.
28. − 2 > − 5
29. −3.1 < −3.04
32. Locate the following numbers on a number line:
Problems 33 – 50: Compute and simplify.
33. 6+ ( −9 )+ ( −8 )+ 7 = 13 + (−17) = − 4
Problems 51 – 52: Multiply
Problems 53 – 55: Factor
Problems 56 – 61: Simplify
62. The temperature in Antarctica dropped from −59° F to
−73° F . How many degrees did the
temperature drop?
Temp dropped14° F.
63. The simple interest I on a principal of P dollars at
interest rate r for time t, in years, is given
by I=Pr t. Find the simple interest on a principal of $5,400 at 4% interest for
5 years
The interest is $1,080
64. On the first, second, and third downs, a football team
had these gains and losses: 5-yd gain,
12-yd loss, and 15-yd gain, respectively. Find the total gain (or loss).
5 + (−12) + 15 = 8 The total gain is 8 yards.
65. The temperature of a chemical compound was 5°C at 4:15
p.m. During a reaction, it dropped
3°C per minute until 4:27 p.m. What was the temperature at 4:27 p.m.?
T temp at 4 : 27 p.m.
The temp at 4 : 27 p.m. was 31 C.
66. Last year a certain make of car cost $17,500. This
year the same car cost $18,200. What was
the percent increase in the price?
The price of the car increased by 4%.