Fractions: Understanding, Comparing, and Solving Problems

Question 1

Which fraction is greater, 2/3 or 3/4? Explain your answer using equivalent fractions.

Accepted Answer

2/3 is greater because 6/9 is equivalent to 2/3 and 6/8 is equivalent to 3/4, and 6/9 is greater than 6/8.

Answer

2/3 is greater because it has a larger numerator.

Answer

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

Question 2

What is a unit fraction? Give two examples.

Accepted Answer

A fraction with a numerator of 1 and any non-zero whole number in the denominator.

Answer

A fraction with both numerator and denominator equal to 1.

Answer

A fraction with a numerator greater than 1 and a denominator of 1.

Answer

A fraction with a denominator of 1 and any non-zero whole number in the numerator.

Question 3

Express the fraction 3/8 as a decimal. Describe the steps you took to convert the fraction.

Accepted Answer

0.375

Answer

0.4

Answer

3.8

Answer

0.8

Question 4

When we multiply a fraction by a unit fraction, like 2/2, what happens to the value of the original fraction? Explain your answer using the example of multiplying 3/4 by 2/2.

Accepted Answer

The value of the fraction stays the same.

Answer

The value of the fraction becomes smaller than the original fraction.

Answer

The value of the fraction becomes larger than the original fraction.

Question 5

Convert the mixed number 2 1/2 to an improper fraction. Explain the steps involved in the conversion process and how it relates to the original mixed number.

Accepted Answer

5/2

Answer

3/2

Answer

2/5

Answer

7/2

Question 6

John's pizza is cut into 8 equal slices. He eats 3 slices. What fraction of the pizza did John eat?

Accepted Answer

3/8

Answer

1/8

Answer

5/8

Answer

8/3

Question 7

Arrange these fractions from smallest to largest: 1/2, 1/4, 3/8, 1/8

Accepted Answer

1/8, 1/4, 3/8, 1/2

Answer

1/8, 1/4, 1/2, 3/8

Answer

1/4, 1/8, 3/8, 1/2

Answer

3/8, 1/2, 1/4, 1/8

Question 8

A cake is divided into 6 equal pieces. If 2 pieces are eaten, what fraction of the cake is left?

Accepted Answer

4/6

Answer

1/6

Answer

2/6

Answer

6/6

Question 9

A farmer has 2/5 of an acre of land planted with corn. He plants an additional 1/10 of an acre with corn. What fraction of his land is now planted with corn?

Accepted Answer

3/5

Answer

1/5

Answer

3/10

Answer

6/15

Question 10

Which fraction is equivalent to 2/4?

Accepted Answer

1/2

Answer

1/4

Answer

4/2

Question 11

Order the following fractions from smallest to largest: 1/2, 1/4, 3/8

Accepted Answer

1/2, 1/4, 3/8

Answer

1/4, 1/2, 3/8

Answer

3/8, 1/4, 1/2

Question 12

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

Accepted Answer

3/8

Answer

1/8

Answer

1/5

Question 13

Which of the following fractions is the largest?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Question 14

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

Accepted Answer

2/3 is larger

Answer

1/2 is larger

Answer

They are equal

Answer

Cannot be compared

Question 15

Add the fractions 1/4 and 1/8. What is the result?

Accepted Answer

1/2

Answer

1/8

Answer

1/4

Answer

2/4

Question 16

Subtract the fraction 1/6 from 1/2. What is the answer?

Accepted Answer

1/12

Answer

1/6

Answer

1/2

Answer

1/3

Question 17

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

Accepted Answer

3/8

Answer

1/2

Answer

1/4

Answer

5/8

Question 18

What is the least common multiple of 4 and 6?

Accepted Answer

12

Answer

2

Answer

4

Answer

8

Question 19

Convert the fraction 1/4 to its decimal form and convert the decimal form back to the fraction.

Accepted Answer

1/4 = 0.25 and 0.25 = 1/4

Answer

1/4 = 0.125 and 0.125 = 1/4

Answer

1/4 = 0.5 and 0.5 = 1/4

Answer

1/4 = 25 and 25 = 1/4

Question 20

What is the sum of one-third and one-fourth?

Accepted Answer

Seven-twelfths

Answer

One-seventh

Answer

One-half

Answer

One-twelfth

Question 21

Which of these is a mixed number?

Accepted Answer

One and one-half

Answer

One-half

Answer

Two-thirds

Answer

Three-fourths

Question 22

Which of these represents the fraction 5/6?

Accepted Answer

Five out of six

Answer

Five out of twelve

Answer

Six out of twelve

Answer

Six out of five

Question 23

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

Accepted Answer

3/8

Answer

1/8

Answer

5/8

Answer

7/8

Question 24

Solve the following addition problem: 1/3 + 1/6

Accepted Answer

2/3

Answer

1/9

Answer

1/2

Answer

1

Question 25

Order the following fractions from least to greatest: 1/2, 3/4, 2/3, 4/5

Accepted Answer

1/2, 2/3, 3/4, 4/5

Answer

4/5, 3/4, 2/3, 1/2

Answer

1/2, 3/4, 4/5, 2/3

Answer

2/3, 3/4, 4/5, 1/2

Question 26

A pizza is cut into 8 slices. If you eat 3 slices, what fraction of the pizza have you eaten?

Accepted Answer

3/8

Answer

3/5

Answer

5/8

Answer

8/3

Question 27

Which fraction is the smallest? Provide a brief explanation.

Accepted Answer

1/8

Answer

1/4

Answer

1/2

Answer

3/8

Question 28

When subtracting fractions with like denominators, which step should you take first?

Accepted Answer

Subtract the numerators.

Answer

Subtract the denominators.

Answer

Multiply the numerators.

Answer

Divide the numerators.

Question 29

A pizza is cut into 8 equal slices. If Maria eats 3 slices, what fraction of the pizza has she eaten?

Accepted Answer

3/8

Answer

1/2

Answer

1/4

Answer

3/4

Question 30

Which fraction is greater than 1/2?

Accepted Answer

3/4

Answer

1/4

Answer

1/8

Answer

1/16

Question 31

Subtract 1/4 from 3/4

Accepted Answer

1/2

Answer

2/4

Answer

3/4

Answer

1/4

Question 32

If you ate 3 slices of a pizza that was cut into 8 equal slices, what fraction of the pizza did you eat?

Accepted Answer

3/8

Answer

7/8

Answer

5/8

Answer

1/8

Question 33

Which fraction is in its simplest form?

Accepted Answer

1/3

Answer

3/6

Answer

2/4

Answer

4/8

Question 34

Compare the fractions 1/2 and 3/4. Which fraction is larger?

Accepted Answer

3/4

Answer

Both are equal

Answer

1/2

Answer

Cannot be determined

Question 35

Find the value of x in the fraction equation: 3/x = 1/2

Accepted Answer

6

Answer

1.5

Answer

3

Question 36

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

Accepted Answer

3/8

Answer

5/8

Answer

1/8

Answer

6/8

Question 37

If a pizza is cut into 8 equal slices and you eat 3 slices, what fraction of the pizza have you eaten?

Accepted Answer

3/8

Answer

5/8

Answer

1/4

Question 38

Which point on the number line represents the fraction 2/5?

Accepted Answer

The point that is 2/5 of the distance from 0 to 1.

Answer

The point that is 3/5 of the distance from 0 to 2.

Answer

The point that is 3/5 of the distance from 0 to 1.

Answer

The point that is 2/5 of the distance from 0 to 2.

Question 39

What is the reciprocal of the fraction 3/4?

Accepted Answer

4/3

Answer

2/3

Answer

1/4

Answer

3/2

Question 40

Order the following fractions from smallest to largest: 1/3, 1/2, 1/4

Accepted Answer

1/4 < 1/3 < 1/2

Answer

1/4 < 1/2 < 1/3

Answer

1/3 < 1/4 < 1/2

Answer

1/2 < 1/3 < 1/4

Question 41

Find the area of a rectangle with a length of 1/2 unit and a width of 1/4 unit.

Accepted Answer

1/8 square unit

Answer

1/4 square unit

Answer

2/8 square unit

Question 42

Which of the following fractions is a proper fraction?

Accepted Answer

1/3

Answer

2/3

Answer

1/1

Answer

3/1

Question 43

Which of the following fractions is an improper fraction?

Accepted Answer

7/4

Answer

3/5

Answer

6/7

Answer

1/2

Question 44

Which fraction is equal to one half?

Accepted Answer

2/4

Answer

4/4

Answer

3/4

Answer

1/4

Question 45

Put these fractions in order from smallest to biggest: 1/4, 1/3, 1/2

Accepted Answer

1/4, 1/3, 1/2

Answer

1/3, 1/2, 1/4

Answer

1/2, 1/3, 1/4

Answer

1/4, 1/2, 1/3

Question 46

What is 1/2 plus 1/4?

Accepted Answer

3/4

Answer

1/6

Answer

5/4

Answer

1/8

Question 47

Which fraction is bigger than one whole?

Accepted Answer

5/4

Answer

1/2

Answer

3/5

Answer

2/3

Question 48

What fraction shows three out of eight equal pieces?

Accepted Answer

3/8

Answer

3/5

Answer

8/3

Answer

5/8

Question 49

Which fraction is the same as one half?

Accepted Answer

4/8

Answer

2/3

Answer

2/1

Answer

1/4

Question 50

Order these fractions from smallest to biggest: 1/4, 3/4, 2/4

Accepted Answer

1/4, 2/4, 3/4

Answer

2/4, 1/4, 3/4

Answer

3/4, 2/4, 1/4

Question 51

You ate 2/5 of a pizza and your friend ate 1/5. How much pizza did you eat together?

Accepted Answer

3/5

Answer

3/10

Answer

1/5

Answer

2/10

Question 52

Sarah had 5/6 of a cake and ate 2/6 of it. How much cake is left?

Accepted Answer

3/6

Answer

7/6

Answer

3/12

Answer

2/6

Question 53

If 1/3 of a number is 6, what is the number?

Accepted Answer

18

Answer

3

Answer

2

Answer

9