Simplifying Fractions

Show your work for each problem.

1.
Which fraction is in simplest form?
1. a)
2. b)
3. c)
4. d)
Answer:
is in simplest form because 3 and 7 have no common factors. The others can be simplified: , , .
2.
Simplify . Enter only the numerator of your answer.
Answer: 1
The GCF of 4 and 8 is 4. Dividing both: . The numerator is 1.
3.
What is simplified?
1. a)
2. b)
3. c)
4. d)
Answer:
The GCF of 6 and 12 is 6. . Note: and are equivalent but not fully simplified.
4.
Simplify step by step.
Answer: 2/3
1. What is the GCF of 10 and 15? 5
2. Divide 10 by the GCF: 2
3. Divide 15 by the GCF: 3
5.
Simplify . Enter your answer as a fraction (e.g., 3/4).
Answer: 3/4
The GCF of 18 and 24 is 6. .
6.
Which fraction does NOT simplify to ?
1. a)
2. b)
3. c)
4. d)
Answer:
, not . The others: .
7.
Simplify using the GCF method.
Answer: 2/3
1. List the factors of 24: 1,2,3,4,6,8,12,24
2. List the factors of 36: 1,2,3,4,6,9,12,18,36
3. What is the GCF (largest common factor)? 12
4. Divide 24 by 12: 2
5. Divide 36 by 12: 3
8.
A recipe calls for cup of flour. What is this in simplest form? Enter as a fraction.
Answer: 2/3
GCF(8, 12) = 4. cup of flour.
9.
Is in simplest form? Explain your reasoning.
Answer: yes
1. List the factors of 15: 1,3,5,15
2. List the factors of 28: 1,2,4,7,14,28
3. What common factors do they share? 1
4. Is the fraction in simplest form? (yes/no) yes
10.
What is the GCF of 30 and 45?
1. a)3
2. b)5
3. c)15
4. d)9
Answer: 15
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Factors of 45: 1, 3, 5, 9, 15, 45. Common factors: 1, 3, 5, 15. The GCF is 15.
11.
Simplify . Enter your answer as a fraction.
Answer: 3/4
GCF(42, 56) = 14. .
12.
Simplify by finding the GCF using prime factorization.
Answer: 2/3
1. Prime factorization of 48: 2^4 x 3
2. Prime factorization of 72: 2^3 x 3^2
3. GCF (take common primes with lowest power): 24
4. Divide 48 by 24: 2
5. Divide 72 by 24: 3
13.
If 45 out of 60 students passed a test, what fraction passed in simplest form?
1. a)
2. b)
3. c)
4. d)
Answer:
GCF(45, 60) = 15. . Note: all other options are equivalent but not fully simplified.
14.
Simplify completely.
Answer: 3/4
1. Is 63 divisible by 3? yes
2. Is 84 divisible by 3? yes
3. Divide both by 3. What do you get? 21/28
4. Can this be simplified further? What is the GCF of 21 and 28? 7
5. Divide both by 7. Final answer: 3/4
15.
A store offers a discount of 35 cents for every dollar spent (35 out of 100). Express this as a simplified fraction.
Answer: 7/20
GCF(35, 100) = 5. . The discount is seven-twentieths of each dollar.