Fraction Test — Questions and Answers

Question 1: Convert ⅖ to a percentage.

40% (Correct answer)
25%
50%
30%

Correct answer: 40%

To convert a fraction to a percentage, first convert it to a decimal by dividing the numerator by the denominator (2 ÷ 5 = 0.4). Then, multiply the decimal by 100 and add the percent symbol. So, 0.4 × 100 = 40%, making 40% the correct answer.

Question 2: Which fraction is NOT equivalent to 3/6?

5/10
1/2
4/8
2/3 (Correct answer)

Correct answer: 2/3

1/2, 5/10, and 4/8 all equal 1/2 just like 3/6 simplified, but 2/3 does not equal 1/2.

Question 3: Which of the following fractions is between 1/2 and 3/4?

1/3
7/8
1/4
5/8 (Correct answer)

Correct answer: 5/8

5/8 = 0.625, which falls between 1/2 (0.5) and 3/4 (0.75).

Question 4: Add 2 2/3 + 1 5/6.

3 1/2
3 7/6
4 7/6
4 1/2 (Correct answer)

Correct answer: 4 1/2

2 4/6 + 1 5/6 = 3 9/6 = 3 + 1 3/6 = 4 1/2.

Question 5: A bag of candy has 36 pieces. After giving 1/4 to one friend and 1/3 to another, how many pieces are left?

18
9
21 (Correct answer)
15

Correct answer: 21

1/4 × 36 = 9 and 1/3 × 36 = 12; total given = 21, so 36 − 21 = 15 pieces remain.

Question 6: Multiply 1 2/3 × 1 1/2.

1 5/6
2 1/3
3
2 1/2 (Correct answer)

Correct answer: 2 1/2

1 2/3 × 1 1/2 = 5/3 × 3/2 = 15/6 = 5/2 = 2 1/2.

Question 7: Which pair of fractions is equivalent?

1/4 and 2/6
1/3 and 2/5
1/2 and 3/6 (Correct answer)
2/4 and 3/5

Correct answer: 1/2 and 3/6

1/2 = 3/6 because dividing both 3 and 6 by 3 gives 1/2.

Question 8: What is ⅔×¾?

⁵⁄₇
¼
⁶⁄₁₂
½ (Correct answer)

Correct answer: ½

To multiply fractions, you multiply the numerators together and the denominators together. For ⅔ × ¾, multiply 2 by 3 to get 6 (numerator) and 3 by 4 to get 12 (denominator), resulting in ⁶⁄₁₂. This fraction simplifies to ½ by dividing both numerator and denominator by 6.

Question 9: Sarah read 2/5 of a book on Monday and 1/5 on Tuesday. What total fraction did she read?

2/10
3/5 (Correct answer)
3/10
1/5

Correct answer: 3/5

2/5 + 1/5 = 3/5 of the book was read over the two days.

Question 10: Which fraction is equivalent to 3/4?

3/8
6/10
4/5
6/8 (Correct answer)

Correct answer: 6/8

3/4 = 6/8 because multiplying both numerator and denominator by 2 gives an equivalent fraction.

Question 11: A pizza is cut into 8 equal slices. If 3 slices are eaten, what fraction of the pizza remains?

3/8
8/3
3/5
5/8 (Correct answer)

Correct answer: 5/8

8 − 3 = 5 slices remain, so the remaining fraction is 5/8.

Question 12: Lisa has $60. She spends 1/4 on a game and 1/3 on a book. How much money does she have left?

$25 (Correct answer)
$30
$20
$35

Correct answer: $25

She spent 1/4 + 1/3 = 7/12 of $60 = $35, leaving $60 − $35 = $25.

Question 13: Estimate 2 1/10 + 3 7/8 to the nearest whole number.

4
5
7
6 (Correct answer)

Correct answer: 6

2 1/10 ≈ 2 and 3 7/8 ≈ 4, so the estimated sum is about 6.

Question 14: Which fraction is approximately equal to 0.33?

1/5
1/4
2/5
1/3 (Correct answer)

Correct answer: 1/3

1/3 ≈ 0.333, which is the closest to 0.33.

Question 15: A tank is 3/4 full. After using some water it is 1/2 full. What fraction of the tank was used?

1/4 (Correct answer)
1/3
1/2
2/3

Correct answer: 1/4

3/4 − 1/2 = 3/4 − 2/4 = 1/4 of the tank was used.

Question 16: A class trip had 30 students. If 2/5 brought lunch from home, how many bought lunch at school?

15
18 (Correct answer)
12
10

Correct answer: 18

2/5 × 30 = 12 brought lunch, so 30 − 12 = 18 bought lunch at school.

Question 17: What is the 5th term in the sequence 1/5, 2/5, 3/5, 4/5?

6/5
1/5
4/5
5/5 (or 1) (Correct answer)

Correct answer: 5/5 (or 1)

The numerator increases by 1, so the 5th term is 5/5, which equals 1.

Question 18: Which fraction is greater: 3/4 or 5/8?

5/8
3/4 (Correct answer)
Cannot be determined
They are equal

Correct answer: 3/4

Converting to a common denominator: 3/4 = 6/8, which is greater than 5/8.

Question 19: A bag has 12 marbles. If 3/4 of them are blue, how many blue marbles are there?

9 (Correct answer)
4
3
8

Correct answer: 9

3/4 × 12 = 9 blue marbles.

Question 20: Order from least to greatest: 2/5, 1/2, 3/8

3/8, 2/5, 1/2 (Correct answer)
2/5, 3/8, 1/2
2/5, 1/2, 3/8
1/2, 2/5, 3/8

Correct answer: 3/8, 2/5, 1/2

3/8 = 0.375, 2/5 = 0.4, 1/2 = 0.5, so the ascending order is 3/8, 2/5, 1/2.

Question 21: Which fraction completes the pattern: 1/2, 2/4, 3/6, ___?

5/8
3/8
4/6
4/8 (Correct answer)

Correct answer: 4/8

Each term has numerator and denominator doubled: 1/2, 2/4, 3/6, 4/8 (all equal to 1/2).

Question 22: A runner completes 4 laps of 3/8 mile each. About how far does she run in total?

About 1 mile
About 1 1/2 miles (Correct answer)
About 2 miles
About 3 miles

Correct answer: About 1 1/2 miles

3/8 ≈ 1/2, so 4 × 1/2 = 2 miles; the exact answer is 1.5, so 1 1/2 miles is best.

Question 23: Which list shows fractions in descending order?

5/6, 2/3, 3/4
3/4, 5/6, 2/3
5/6, 3/4, 2/3 (Correct answer)
2/3, 3/4, 5/6

Correct answer: 5/6, 3/4, 2/3

5/6 ≈ 0.833, 3/4 = 0.75, 2/3 ≈ 0.667, confirming descending order.

Question 24: In the sequence 6/7, 5/7, 4/7, 3/7, what is the pattern?

Add 1/7 each time
Subtract 1/7 each time (Correct answer)
Divide by 7 each time
The numerator and denominator both decrease

Correct answer: Subtract 1/7 each time

Each term decreases by 1/7, as the numerator decreases by 1 while the denominator stays at 7.

Question 25: Which sequence shows fractions increasing by equal steps?

1/2, 1/3, 1/4, 1/5
1/5, 2/5, 3/5, 4/5 (Correct answer)
1/4, 1/2, 3/4, 5/4
2/3, 3/4, 4/5, 5/6

Correct answer: 1/5, 2/5, 3/5, 4/5

Each term in 1/5, 2/5, 3/5, 4/5 increases by exactly 1/5.

Question 26: A recipe calls for 2/3 cup of sugar; another calls for 3/4 cup. Which requires more sugar?

They require the same amount
3/4 cup (Correct answer)
Cannot be determined
2/3 cup

Correct answer: 3/4 cup

3/4 = 9/12 and 2/3 = 8/12, so 3/4 cup is more than 2/3 cup.

Question 27: A board is 5 3/4 feet long. If 2 1/4 feet is cut off, how much remains?

3 1/2 feet (Correct answer)
4 feet
3 feet
3 2/4 feet

Correct answer: 3 1/2 feet

5 3/4 − 2 1/4 = 3 2/4 = 3 1/2 feet.

Question 28: What is the missing fraction: 1/2, 1/4, 1/8, ___?

1/16 (Correct answer)
1/6
2/16
1/10

Correct answer: 1/16

The denominator doubles each time: 2, 4, 8, so next is 1/16.

Question 29: Find the missing numerator: ?/24 = 5/8

15 (Correct answer)
12
10
20

Correct answer: 15

Since 8 × 3 = 24, multiply the numerator 5 by 3 to get 15, making 15/24 = 5/8.

Question 30: What is the missing numerator? ?/6 = 2/3

2
3
5
4 (Correct answer)

Correct answer: 4

Since 3 × 2 = 6, multiply the numerator 2 by 2 to get 4, making 4/6 = 2/3.

Question 31: Which fraction is NOT between 1/2 and 1?

1/3 (Correct answer)
5/6
2/3
3/4

Correct answer: 1/3

1/3 ≈ 0.333, which is less than 1/2 = 0.5, so it is not between 1/2 and 1.

Question 32: What fraction comes next: 1/2, 3/4, 5/6, 7/8, ___?

10/11
8/9
9/10 (Correct answer)
9/11

Correct answer: 9/10

The numerators are odd numbers (1, 3, 5, 7, 9) and the denominators are even numbers (2, 4, 6, 8, 10), so the next term is 9/10.

Question 33: Which term does NOT belong in the sequence: 1/4, 3/4, 5/4, 7/4, 9/4, 11/4?

3/4
7/4
9/4
All terms belong (Correct answer)

Correct answer: All terms belong

All terms follow the rule of increasing numerators by 2 (odd numerators over 4), so all belong.

Question 34: Which fraction is smaller: 4/5 or 7/9?

Cannot be determined
7/9 (Correct answer)
They are equal
4/5

Correct answer: 7/9

4/5 = 36/45 and 7/9 = 35/45, so 7/9 < 4/5.

Question 35: Find the pattern rule: 1/3, 2/3, 3/3, 4/3, ...

Subtract 1/3 each time
Double the fraction each time
Add 1 each time
Add 1/3 each time (Correct answer)

Correct answer: Add 1/3 each time

Each term is 1/3 more than the previous term.

Question 36: How many equivalent fractions does any non-zero fraction have?

Infinitely many (Correct answer)
Exactly 10
Only 4
Only 2

Correct answer: Infinitely many

Any fraction has infinitely many equivalents because you can multiply numerator and denominator by any non-zero integer.

Question 37: A wall is 4/5 painted. After more work, 9/10 is painted. What additional fraction was painted?

1/5
1/10 (Correct answer)
1/2
5/10

Correct answer: 1/10

9/10 − 4/5 = 9/10 − 8/10 = 1/10 more was painted.

Question 38: In the proportion 3/4 = ?/20, what is the missing numerator?

15 (Correct answer)
16
18
12

Correct answer: 15

Since 4 × 5 = 20, multiply the numerator 3 by 5 to get 15, making 3/4 = 15/20.

Question 39: Estimate: 11/12 − 1/9 ≈ ?

About 1/2
About 3/4 (Correct answer)
About 1/4
About 1

Correct answer: About 3/4

11/12 ≈ 1 and 1/9 ≈ 0, so the difference is approximately 1; closest reasonable estimate is about 3/4 to 1.

Question 40: Which fraction is exactly halfway between 1/4 and 3/4?

2/3
1/2 (Correct answer)
3/8
1/3

Correct answer: 1/2

The midpoint of 1/4 and 3/4 is (1/4 + 3/4) / 2 = 1/2.

Fraction Test

A comprehensive mathematics assessment evaluating understanding of fractions, including operations, comparison, ordering, pattern recognition, and real-world word problem applications. Commonly used in elementary and middle school curricula to assess fraction proficiency.

Questions

45 min

Time Limit

70%

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