Simplifying Fractions

Show your work for each problem.

1.
Which fraction is in simplest form?
1. a) $\frac{10}{15}$
2. b) $\frac{3}{7}$
3. c) $\frac{4}{8}$
4. d) $\frac{6}{9}$
Answer: $\frac{3}{7}$
$\frac{3}{7}$ is in simplest form because 3 and 7 have no common factors. The others can be simplified: $\frac{4}{8} = \frac{1}{2}$ , $\frac{6}{9} = \frac{2}{3}$ , $\frac{10}{15} = \frac{2}{3}$ .
2.
Simplify $\frac{4}{8}$ . Enter only the numerator of your answer.
Answer: 1
The GCF of 4 and 8 is 4. Dividing both: $\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$ . The numerator is 1.
3.
What is $\frac{6}{12}$ in simplest form?
1. a) $\frac{3}{6}$
2. b) $\frac{1}{2}$
3. c) $\frac{1}{3}$
4. d) $\frac{2}{4}$
Answer: $\frac{1}{2}$
The GCF of 6 and 12 is 6. $\frac{6 \div 6}{12 \div 6} = \frac{1}{2}$ . Note: $\frac{2}{4}$ and $\frac{3}{6}$ are equivalent but not fully simplified.
4.
Simplify $\frac{10}{15}$ 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 $\frac{18}{24}$ completely. What is the denominator of the simplified fraction?
Answer: 4
The GCF of 18 and 24 is 6. $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$ . The denominator is 4.
6.
Which fraction does NOT simplify to $\frac{1}{3}$ ?
1. a) $\frac{4}{14}$
2. b) $\frac{3}{9}$
3. c) $\frac{5}{15}$
4. d) $\frac{7}{21}$
Answer: $\frac{4}{14}$
$\frac{4}{14} = \frac{2}{7}$ , not $\frac{1}{3}$ . The others: $\frac{3}{9} = \frac{5}{15} = \frac{7}{21} = \frac{1}{3}$ .
7.
Simplify $\frac{24}{36}$ using the GCF method.
Answer: 2/3
1. The factors of 24 are 1, 2, 3, 4, $\square$ , 8, 12, 24. Which factor is missing? 6
2. The factors of 36 are 1, 2, 3, 4, 6, $\square$ , 12, 18, 36. Which factor is missing? 9
3. What is the GCF (the largest number in both lists)? 12
4. Divide 24 by 12: 2
5. Divide 36 by 12: 3
8.
A recipe calls for $\frac{8}{12}$ cup of flour. Write this amount in simplest form. What is the numerator?
Answer: 2
GCF(8, 12) = 4. $\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$ cup of flour. The numerator is 2.
9.
Is $\frac{15}{28}$ in simplest form? Check it step by step.
Answer: yes
1. Write 15 as a product of primes: $15 = 3 \times \square$ . What goes in the box? 5
2. Write 28 as a product of primes: $28 = 2 \times 2 \times \square$ . What goes in the box? 7
3. 15 has the prime factors 3 and 5, and 28 has 2 and 7. What is the GCF of 15 and 28? 1
4. Is the fraction in simplest form? 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 $\frac{42}{56}$ completely. What is the denominator of the simplified fraction?
Answer: 4
GCF(42, 56) = 14. $\frac{42 \div 14}{56 \div 14} = \frac{3}{4}$ . The denominator is 4.
12.
Simplify $\frac{48}{72}$ by finding the GCF using prime factorization.
Answer: 2/3
1. Prime factorization of 48: $48 = 2^{\square} \times 3$ . What exponent goes in the box? 4
2. Prime factorization of 72: $72 = 2^3 \times 3^{\square}$ . What exponent goes in the box? 2
3. GCF (take common primes with lowest power): 24
4. Divide 48 by 24: 2
5. Divide 72 by 24: 3
13.
45 out of 60 students passed a test. What fraction of the students passed, in simplest form?
1. a) $\frac{15}{20}$
2. b) $\frac{3}{4}$
3. c) $\frac{9}{12}$
4. d) $\frac{45}{60}$
Answer: $\frac{3}{4}$
GCF(45, 60) = 15. $\frac{45 \div 15}{60 \div 15} = \frac{3}{4}$ . Note: all other options are equivalent but not fully simplified.
14.
Simplify $\frac{63}{84}$ completely.
Answer: 3/4
1. Is 63 divisible by 3? yes
2. Is 84 divisible by 3? yes
3. Divide both by 3: $\frac{63}{84} = \frac{21}{\square}$ . What goes in the box? 28
4. Can this be simplified further? What is the GCF of 21 and 28? 7
5. Divide both by 7: $\frac{21}{28} = \frac{\square}{4}$ . What goes in the box? 3
15.
A store gives a discount of 35 cents for every dollar spent (35 out of 100 cents). Write this discount as a fraction of a dollar in simplest form. What is its denominator?
Answer: 20
GCF(35, 100) = 5. $\frac{35 \div 5}{100 \div 5} = \frac{7}{20}$ . The discount is seven-twentieths of each dollar. The denominator is 20.