Equivalent Fractions

Show your work for each problem.

1.
Which fraction is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
. Both fractions represent the same value: half.
2.
Which fraction is NOT equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
equals 0.8, while equals 0.75. The other fractions all simplify to .
3.
Complete:
Answer: 4
Since , we multiply the numerator by 2 as well: . So .
4.
Simplify to lowest terms. Write only the numerator.
Answer: 1
The GCF of 4 and 8 is 4. . The numerator is 1.
5.
Are and equivalent fractions?
1. a)Yes
2. b)No
Answer: Yes
. Yes, they are equivalent!
6.
Which fraction is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The other fractions simplify to different values.
7.
Complete:
Answer: 10
, so . Therefore .
8.
Simplify to lowest terms. Write your answer as a fraction (e.g., 2/3).
Answer: 2/3
GCF of 12 and 18 is 6. .
9.
Emma ate of a cake and Leo ate of an identical cake. Who ate more?
1. a)Emma ate more
2. b)Cannot be determined
3. c)Leo ate more
4. d)They ate the same amount
Answer: They ate the same amount
and . Both ate exactly half!
10.
If , what is ?
Answer: 12
, so we multiply the numerator by 3: . Therefore .
11.
Find three fractions equivalent to .
Answer: 6/10, 9/15, 12/20
1. Multiply by . What do you get? 6/10
2. Multiply by . What do you get? 9/15
3. Multiply by . What do you get? 12/20
12.
Simplify step by step to lowest terms.
Answer: 2/3
1. List some factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
2. List some factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
3. What is the greatest common factor (GCF) of 24 and 36? 12
4. Divide both by the GCF. What is ? 2/3
13.
Use cross multiplication to check if and are equivalent.
Answer: Yes, they are equivalent
1. Multiply the first numerator by the second denominator: 120
2. Multiply the first denominator by the second numerator: 120
3. Are the cross products equal? (yes/no) yes
4. So are the fractions equivalent? (yes/no) yes
14.
Find the value of if .
Answer: 15
, so . Therefore and .
15.
A recipe uses cup of flour. If you want to make 1.5 times the recipe, how much flour do you need? Express as a simplified fraction.
Answer: 1
1. Convert 1.5 to a fraction: 3/2
2. Multiply the fractions: 6/6
3. Simplify : 1
16.
Which pair of fractions is NOT equivalent?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
but . These are different values! The other pairs all simplify to the same fraction.
17.
Find the missing values:
Answer: a = 15, b = 28
1. For : What is ? 5
2. So 15
3. For : What is ? 7
4. So 28
18.
Tom has of a chocolate bar. Maria has of an identical bar. Do they have the same amount? Prove it.
Answer: Yes, they have the same amount
1. Simplify Tom's fraction: (GCF of 8 and 12 is 4) 2/3
2. Simplify Maria's fraction: (GCF of 10 and 15 is 5) 2/3
3. Are the simplified fractions equal? (yes/no) yes
4. So do Tom and Maria have the same amount? (yes/no) yes