Fractions: Understanding, Comparing, and Operating

Question 1

Which fraction is greater, 3/4 or 5/8? Show your work.

Accepted Answer

3/4 is greater because 3/4 * 8/5 = 24/20, which is greater than 5/8 * 4/3 = 20/24.

Answer

3/4 is greater because it has a larger numerator.

Answer

5/8 is greater because it has a smaller denominator.

Answer

The fractions are equal.

Question 2

When comparing fractions visually, which statement is true?

Accepted Answer

Visual comparison can be a starting point, but other methods should be used to confirm equivalence.

Answer

Visual comparison is always accurate.

Answer

Visual comparison works only if the fractions have the same denominator.

Answer

Visual comparison should never be used.

Question 3

Change the improper fraction 7/3 into a mixed number.

Accepted Answer

2 1/3

Answer

3 1/7

Answer

1/3

Question 4

In the fraction 2/7, what does the top number (2) show?

Accepted Answer

The number of equal parts that are shaded

Answer

The total number of equal parts in the whole

Question 5

What is the answer to 2/5 divided by 3/4?

Accepted Answer

8/15

Answer

10/15

Answer

6/15

Question 6

A game has a 1/4 chance of being won. What percentage represents this chance?

Accepted Answer

25%

Answer

20%

Answer

30%

Question 7

In the fraction 5/7, what does the bottom number (7) represent?

Accepted Answer

The total number of equal parts in the whole

Answer

The value of the fraction

Answer

The part of the whole that is shaded

Answer

The number of parts in the top number

Question 8

Change the mixed number 2 1/4 to an improper fraction.

Accepted Answer

9/4

Answer

8/4

Answer

5/4

Question 9

Compare the fractions 3/4 and 5/8. Which fraction is larger?

Accepted Answer

5/8

Answer

3/4

Answer

Both are equal

Answer

Cannot be determined

Question 10

Divide the fraction 3/4 by the fraction 1/2. What is the quotient?

Accepted Answer

3/2

Answer

1/2

Answer

1/6

Answer

6/2

Question 11

Which of the following is a mixed number?

Accepted Answer

1 1/2

Answer

1/2

Answer

2/3

Answer

3/4

Question 12

Which fraction is closest in value to the decimal number 0.75?

Accepted Answer

3/4

Answer

2/3

Answer

1/2

Answer

1/4

Question 13

Mixed numbers and fractions can represent the same quantity. Explain how the mixed number 1 1/2 and the fraction 3/2 are equivalent. Describe the steps to convert between them.

Accepted Answer

1 1/2 is equal to 3/2.

Answer

1 1/2 is greater than 3/2.

Answer

3/2 is greater than 1 1/2.

Answer

1 1/2 and 3/2 cannot be converted into each other.

Question 14

Which fraction is larger: two-sevenths or three-eighths?

Accepted Answer

Three-eighths

Answer

Two-sevenths

Question 15

Arrange these fractions in order from least to greatest on a number line: 1/2, 2/3, 3/4

Accepted Answer

1/2, 2/3, 3/4

Answer

3/4, 2/3, 1/2

Answer

2/3, 1/2, 3/4

Answer

3/4, 1/2, 2/3

Question 16

Convert the improper fraction 7/3 to a mixed number.

Accepted Answer

1 1/3

Answer

2 1/4

Answer

3 1/2

Answer

4 1/3

Question 17

A store offers a discount of 25% on a product. Express this discount as a fraction and a decimal.

Accepted Answer

1/4, 0.25

Answer

1/5, 0.5

Answer

1/3, 0.33

Answer

1/2, 0.50

Question 18

To multiply two fractions, what should you do?

Accepted Answer

Multiply the numerators and denominators of the fractions.

Answer

Add the numerators and add the denominators of the fractions.

Answer

Multiply the first fraction by the denominator of the second fraction.

Question 19

How does finding equivalent fractions help us understand the concept of fraction equivalence?

Accepted Answer

Equivalent fractions have the same value, even though their numerators and denominators are different.

Answer

Finding equivalent fractions involves changing the numerator and denominator to make the fraction simpler.

Answer

Equivalent fractions are always greater than the original fraction.

Answer

Finding equivalent fractions is unrelated to the concept of fraction equivalence.

Question 20

Convert the mixed number 2 3/4 to an improper fraction:

Accepted Answer

11/4

Answer

3/4

Answer

5/4

Answer

8/4

Question 21

Which fraction is different from 2/5?

Accepted Answer

3/7

Answer

4/10

Answer

6/15

Question 22

Which fraction is larger: 5/6 or 2/3? Show your work using a number line or fraction circle.

Accepted Answer

5/6

Answer

2/3

Answer

They are equal

Question 23

To represent the fraction 2/3 on a number line, how should you divide and shade the line?

Accepted Answer

Divide the line into 3 equal parts and shade 2 of them.

Answer

Divide the line into 2 equal parts and shade 3 of them.

Answer

Divide the line into 6 equal parts and shade 2 of them.

Answer

Divide the line into 3 equal parts and shade 1 of them twice.

Question 24

Change the decimal 0.75 into a fraction in its simplest form.

Accepted Answer

3/4

Answer

1/2

Answer

2/3

Answer

1/4

Question 25

Which fraction is greater than 1? Give a clear example to support your answer.

Accepted Answer

3/2

Answer

1/3

Answer

4/4

Answer

2/5

Question 26

Convert the fraction 3/8 to a decimal. Show your work and explain each step.

Accepted Answer

0.375

Answer

0.4

Answer

0.5

Answer

0.625

Question 27

Which fraction is equivalent to 3/4?

Accepted Answer

6/8

Answer

1/4

Answer

5/6

Answer

2/6

Question 28

A pizza is cut into 8 equal slices. You eat 3 slices. What fraction of the pizza have you eaten?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Question 29

Which of these pictures shows the fraction 3/4?

Accepted Answer

A circle divided into 4 equal parts with 3 parts shaded

Answer

A rectangle divided into 3 equal parts with 2 parts shaded

Answer

A square divided into 8 equal parts with 6 parts shaded

Question 30

Which fraction is the same as 2/3?

Accepted Answer

4/6

Answer

1/2

Answer

3/5

Question 31

A recipe for bread requires 3/4 cup of flour. If you want to make twice the amount of bread, how many cups of flour do you need?

Accepted Answer

1 1/2 cups

Answer

1/2 cup

Answer

3/8 cup

Answer

3/2 cups

Question 32

A recipe requires 1 cup of sugar. If the ratio of flour to sugar is 2:1, how many cups of flour are needed?

Accepted Answer

2 cups

Answer

1 cup

Answer

3 cups

Question 33

Simplify the fraction -15/25. If the answer is a mixed number, express it as a mixed number.

Accepted Answer

-3/5

Answer

-5/3

Answer

3/5

Answer

-2/3

Question 34

Which fraction is greater than 1/2?

Accepted Answer

3/4

Accepted Answer

5/8

Accepted Answer

7/8

Answer

1/4

Question 35

What is the decimal equivalent of the fraction 3/8?

Accepted Answer

0.375

Answer

0.25

Answer

0.5

Question 36

Find the sum of one-half and one-fourth.

Accepted Answer

Three-fourths

Answer

One-sixth

Answer

Five-sixths

Answer

One-eighth

Question 37

Which fraction below is equivalent to 3/4?

Accepted Answer

6/8

Answer

1/2

Answer

2/3

Answer

5/6

Question 38

Compare 1/3 and 2/5. Which fraction is bigger?

Accepted Answer

2/5

Answer

1/3

Answer

They are the same

Answer

I can't tell without a calculator

Question 39

Find the sum of 1/4 and 1/6.

Accepted Answer

5/12

Answer

1/2

Answer

2/3

Answer

3/8

Question 40

Find the difference between 3/5 and 1/2.

Accepted Answer

1/6

Answer

1/10

Answer

1/3

Answer

2/5

Question 41

Which of these is a mixed number?

Accepted Answer

2 1/2

Answer

1/2

Answer

3/4

Answer

0.5

Question 42

Turn the mixed number 2 1/3 into an improper fraction.

Accepted Answer

7/3

Answer

5/3

Answer

3/7

Answer

1/3

Question 43

Change the improper fraction 5/2 to a mixed number.

Accepted Answer

2 1/2

Answer

1/2

Answer

3

Answer

2/5

Question 44

Which fraction has a numerator that is greater than or equal to its denominator?

Accepted Answer

5/3

Answer

1/2

Answer

3/4

Answer

2/3

Question 45

Compare the fractions 1/3 and 1/2. Which fraction is bigger?

Accepted Answer

1/2

Answer

1/3

Answer

The fractions are equal

Answer

Not possible to tell

Question 46

A pizza is cut into 8 equal slices. If I eat 3 slices, what part of the pizza have I eaten?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Answer

3/4

Question 47

Simplify the fraction 6/12. What is the simplest form of 6/12?

Accepted Answer

1/2

Answer

2/3

Answer

3/4

Answer

4/5

Question 48

Find the least common denominator of 1/4 and 1/6. What is the smallest number that both 4 and 6 can divide into evenly?

Accepted Answer

12

Answer

2

Answer

4

Answer

6

Question 49

Subtract the fraction 1/4 from the fraction 3/8. What is 3/8 minus 1/4?

Accepted Answer

5/8

Answer

1/8

Answer

1/4

Answer

3/8

Question 50

Compare the fractions 1/2 and 3/5. Which fraction is greater?

Accepted Answer

3/5

Answer

1/2

Answer

Cannot be determined

Answer

Both are equal

Question 51

Convert the improper fraction 9/4 to a mixed number.

Accepted Answer

2 1/4

Answer

1 1/4

Answer

3 1/4

Answer

4 1/4

Question 52

Which fraction is greater than 1/2?

Accepted Answer

3/4

Answer

1/3

Answer

2/5

Answer

1/4

Question 53

Which fraction is equivalent to 3/6?

Accepted Answer

1/2

Answer

3/4

Answer

2/3

Answer

1/3

Question 54

Compare 2/5 and 3/8. Which fraction is greater?

Accepted Answer

3/8

Answer

Cannot be determined

Answer

They are equivalent

Answer

2/5

Question 55

A pizza is cut into 8 equal slices. If Alex eats 3/4 of the pizza, how many slices does he eat?

Accepted Answer

6

Answer

8

Answer

4

Answer

2

Question 56

Which of the following fractions is equivalent to 3/4?

Accepted Answer

6/8

Answer

2/5

Answer

4/7

Answer

5/9

Question 57

Compare the fractions 1/3 and 2/5. Which fraction is greater?

Accepted Answer

2/5

Answer

Equal

Answer

Cannot be determined

Answer

1/3

Question 58

Divide 1/2 by 1/4. What is the quotient?

Accepted Answer

2

Answer

1/8

Answer

4

Answer

1/2

Question 59

Which of the following is a mixed number equivalent to 5/2?

Accepted Answer

2 1/2

Answer

3 1/4

Answer

1 2/5

Question 60

Which fraction represents the same value as 3 / 4?

Accepted Answer

9 / 12

Answer

11 / 16

Answer

7 / 10

Answer

5 / 6

Question 61

What is the sum of 1 / 3 and 1 / 4?

Accepted Answer

7 / 12

Answer

5 / 12

Answer

11 / 12

Answer

9 / 12

Question 62

What is the quotient when you divide 3 / 4 by 1 / 2?

Accepted Answer

3 / 2

Answer

4 / 3

Answer

2 / 3

Answer

1 / 2

Question 63

Which fraction is bigger than 1?

Accepted Answer

5 / 4

Answer

9 / 10

Answer

3 / 5

Answer

7 / 8

Question 64

Which fraction is less than 0?

Accepted Answer

-3 / 5

Answer

5 / 6

Answer

2 / 3

Answer

1 / 4