Equivalent Fractions
Which fraction is equivalent to 3/4?
A. 3/8
B. 6/8
C. 4/6
D. 5/8
Answer: B. 6/8
Multiplying the numerator and denominator by 2:
3 × 2 / 4 × 2 = 6/8
Question: Which is greater?
3/5 or 1/5
Answer: 3/5
When the denominators are the same, compare the numerators.
3 > 1, so:
3/5 > 1/5
Question: Express 6/12 in simplest form.
Answer: 1/2
Divide the numerator and denominator by 6:
6 ÷ 6 = 1
12 ÷ 6 = 2
So:
6/12 = 1/2
Question: What is:
2/7 + 3/7
Answer: 5/7
Because the denominators are the same, add the numerators:
2 + 3 = 5
Question: A student says:
“4/6 is greater than 5/6 because 6 is bigger than 5.”
Is the student correct?
Answer: No.
The denominators are the same, so compare the numerators.
5 > 4
Therefore:
5/6 > 4/6
Question: Which two fractions are equivalent to 4/5?
A. 8/10
B. 12/15
C. 5/6
D. 16/25
Answer: A and B
4/5 = 8/10
and
4/5 = 12/15
Question: Which is greater?
5/8 or 3/8
Answer: 5/8
Both fractions have denominator 8, and:
5 > 3
Therefore:
5/8 > 3/8
Question: Express 9/15 in simplest form.
Answer: 3/5
Divide both by 3:
9 ÷ 3 = 3
15 ÷ 3 = 5
So:
9/15 = 3/5
Question: What is:
8/9 − 2/9
Answer: 6/9 = 2/3
First subtract:
8/9 − 2/9 = 6/9
Then simplify:
6/9 = 2/3
Question: A student says:
“3/8 + 2/8 = 5/16.”
Is the student correct?
Answer: No.
When the denominators are the same, keep the denominator:
3/8 + 2/8 = 5/8
The answer is 5/8, not 5/16.
Question: Fill in the missing number:
5/7 = ___/21
Answer: 15
The denominator was multiplied by 3:
7 × 3 = 21
So multiply the numerator by 3:
5 × 3 = 15
Therefore:
5/7 = 15/21
Question: Put these fractions in order from least to greatest:
1/2, 3/8, 5/8
Answer: 3/8, 1/2, 5/8
One way to compare them is to use eighths:
1/2 = 4/8
So:
3/8 < 4/8 < 5/8
Question: Find the missing number:
4/9 = 20/___
Answer: 45
The numerator was multiplied by 5:
4 × 5 = 20
So multiply the denominator by 5:
9 × 5 = 45
Therefore:
4/9 = 20/45
Question: Express the answer in simplest form:
5/12 + 3/12
Answer: 2/3
First:
5/12 + 3/12 = 8/12
Then simplify:
8/12 = 2/3
Question: A student says:
“10/15 in simplest form is 2/3.”
Is the student correct?
Answer: Yes.
Divide the numerator and denominator by 5:
10 ÷ 5 = 2
15 ÷ 5 = 3
So:
10/15 = 2/3
Question: A student says:
“2/3 and 8/12 are not equivalent because the numbers are different.”
Is the student correct? Explain.
Answer: No.
They are equivalent because:
2/3 × 4/4 = 8/12
Both fractions represent the same amount.
Question: Which fraction is the greatest?
2/3, 3/5, 5/8
Answer: 2/3
Using a common denominator of 120:
2/3 = 80/120
3/5 = 72/120
5/8 = 75/120
So:
2/3 is the greatest.
Question: Find the missing number:
___/18 = 2/3
Answer: 12
Since:
3 × 6 = 18
multiply the numerator by 6:
2 × 6 = 12
So:
12/18 = 2/3
Question: A pitcher contains 7/8 liter of lemonade.
The family drinks 3/8 liter.
How much lemonade is left?
Answer: 1/2 liter
7/8 − 3/8 = 4/8
Simplify:
4/8 = 1/2
Question: Two students compare 3/4 and 5/8.
Who is correct? Explain.
Answer: Ava is correct.
Convert 3/4 into eighths:
3/4 = 6/8
Now compare:
6/8 > 5/8
Therefore:
3/4 > 5/8
Question: I am thinking of a fraction.
Answer: 18
To get from 4 to 24:
4 × 6 = 24
So:
3 × 6 = 18
The fraction is 18/24.
Question: Put these fractions in order from least to greatest:
3/4, 2/3, 5/8, 7/12
Answer: 7/12, 5/8, 2/3, 3/4
Using a common denominator of 24:
7/12 = 14/24
5/8 = 15/24
2/3 = 16/24
3/4 = 18/24
Therefore:
7/12 < 5/8 < 2/3 < 3/4
Question: A fraction is equivalent to 7/10.
Its denominator is 40.
What is the numerator?
Answer: 28
The denominator changes from 10 to 40:
10 × 4 = 40
So multiply the numerator by 4:
7 × 4 = 28
The equivalent fraction is:
28/40
Question: Maya spends 3/10 of an hour practicing piano and 4/10 of an hour practicing violin.
What fraction of an hour does she spend practicing music altogether?
Give your answer in simplest form.
Answer: 7/10 of an hour
3/10 + 4/10 = 7/10
Since 7 and 10 have no common factor greater than 1, 7/10 is already in simplest form.
A recipe calls for 5/6 cup of flour.
A baker has already added 2/6 cup.
Then the baker accidentally adds another 1/6 cup.
How much more flour is needed to reach the amount the recipe calls for?
Answer: 2/6 cup = 1/3 cup
The baker has added:
2/6 + 1/6 = 3/6
The recipe needs:
5/6
So:
5/6 − 3/6 = 2/6
Simplify:
2/6 = 1/3
The baker needs 1/3 cup more.