Fractions Quiz

11 – 25 Questions 9 min

This fractions quiz on multiplying and dividing fractions zeroes in on patterns built from numerators and denominators 1, 2, 3, 4, and 8. You will practice simplification, reciprocals, and mixed operations, which directly supports middle school and early high school students, tutors, and teachers who teach procedural fluency.

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Part 1 — Questions

Answer each question on paper. Do not turn the page until you are ready to check your work.

Compute the product: \(\dfrac{1}{2} \times \dfrac{3}{4}\).

\(\dfrac{4}{6}\)
\(\dfrac{1}{6}\)
\(\dfrac{3}{8}\)
\(\dfrac{2}{3}\)

To multiply \(\dfrac{1}{2}\) by \(\dfrac{3}{4}\), you multiply the numerators and denominators to get \(\dfrac{3}{8}\).

True
False

Evaluate and simplify: \(\dfrac{3}{8} \times \dfrac{4}{9}\).

\(\dfrac{7}{8}\)
\(\dfrac{12}{72}\)
\(\dfrac{6}{9}\)
\(\dfrac{1}{6}\)

The reciprocal of \(\dfrac{3}{4}\) is \(\dfrac{4}{3}\).

True
False

You find that \(\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8}\). Select all fractions that are equivalent to \(\dfrac{3}{8}\).

A.\(\dfrac{5}{16}\)
B.\(\dfrac{9}{24}\)
C.\(\dfrac{12}{32}\)
D.\(\dfrac{1}{4}\)
E.\(\dfrac{6}{16}\)

When multiplying fractions, you should add the numerators and multiply the denominators.

True
False

A recipe uses \(\dfrac{3}{4}\) cup of sugar per batch. You have \(1\dfrac{1}{2}\) cups of sugar. How many full batches can you make?

1
2
1\dfrac{1}{2}
2\dfrac{1}{2}

Jordan bikes \(\dfrac{3}{4}\) of a mile each lap. He completes \(2\dfrac{1}{2}\) laps. How many miles does he bike in total?

\(2\dfrac{1}{4}\)
\(1\dfrac{7}{8}\)
\(1\dfrac{1}{2}\)
\(1\dfrac{3}{4}\)

You want to simplify \(\dfrac{2}{3} \times \dfrac{3}{8}\) efficiently. Select all strategies that correctly simplify this product.

A.Cancel the 3s to write \(\dfrac{2}{3} \times \dfrac{3}{8}\) as \(\dfrac{2}{1} \times \dfrac{1}{8}\).
B.Divide 2 by 3 and 3 by 8 separately instead of using fractions.
C.Rewrite the product as \(\dfrac{6}{24}\), then reduce by dividing numerator and denominator by 6.
D.Add \(\dfrac{2}{3}\) and \(\dfrac{3}{8}\) to get \(\dfrac{25}{24}\).
E.Change \(\dfrac{3}{8}\) to \(\dfrac{8}{3}\) and multiply.

10.

A submarine descends at a rate of \(\dfrac{3}{4}\) meter per second. After 8 seconds, its vertical change is represented by \((-\dfrac{3}{4}) \times 8\). What is this value?

\(-2\)
\(\dfrac{3}{2}\)
\(-6\)
6

11.

A container holds \(\dfrac{3}{8}\) liter of juice. Each serving is \(\dfrac{1}{4}\) liter. How many full servings can you pour?

2\dfrac{1}{2}
2
1
1\dfrac{1}{2}

12.

You are checking products of signed fractions. Select all computations that give a negative result.

A.\((-\dfrac{3}{4}) \div (-\dfrac{1}{2})\)
B.\((-\dfrac{1}{2}) \times \dfrac{3}{4}\)
C.\((-\dfrac{1}{2}) \times (-\dfrac{3}{4})\)
D.\(\dfrac{3}{8} \times \dfrac{1}{4}\)
E.\(\dfrac{1}{2} \times (-\dfrac{3}{4})\)

13.

A board is \(3\dfrac{1}{2}\) meters long. Each small piece needs to be \(\dfrac{7}{8}\) meter long. How many small pieces can be cut from the board?

4\dfrac{1}{2}
3
3\dfrac{1}{2}
4

14.

You want to evaluate \(\dfrac{3}{4} \div \dfrac{1}{2}\). Select all expressions that correctly represent this calculation or its result.

A.\((3 \div 4) \div (1 \div 2)\)
B.\(\dfrac{3}{4} \times \dfrac{2}{1}\)
C.\(\dfrac{3}{4} \div \dfrac{1}{2} = \dfrac{4}{6}\)
D.\(\dfrac{3}{4} \times \dfrac{1}{2}\)
E.\(\dfrac{3}{4} \div \dfrac{1}{2} = \dfrac{3}{2}\)

15.

Evaluate \(\bigl(\dfrac{3}{8} \times \dfrac{4}{3}\bigr) \div \dfrac{1}{2}\).

1
\(\dfrac{1}{2}\)
2
\(\dfrac{1}{4}\)

16.

Evaluate \(\dfrac{3}{4} \div \dfrac{3}{8} \div \dfrac{1}{2}\), working from left to right.

17.

Mia hikes \(1\dfrac{3}{4}\) miles each day for 4 days, then hikes only half that daily distance on the fifth day. How many miles does she hike in total over the five days?

7\dfrac{1}{2}
7\dfrac{7}{8}
7\dfrac{3}{4}
8

18.

Arrange the steps in the correct order to compute \(\dfrac{3}{4} \div \dfrac{2}{3}\).

Put these in the correct order (write 1–6 beside each):

____Flip \(\dfrac{2}{3}\) to its reciprocal \(\dfrac{3}{2}\).
____Change the operation from division to multiplication.
____Write the original expression \(\dfrac{3}{4} \div \dfrac{2}{3}\).
____Multiply \(\dfrac{3}{4}\) by \(\dfrac{3}{2}\).
____Simplify the product to get \(\dfrac{9}{8}\).
____Keep the first fraction \(\dfrac{3}{4}\).

Part 2 — Answer key

Compare your answers after you have finished Part 1.

Compute the product: \(\dfrac{1}{2} \times \dfrac{3}{4}\).
\(\dfrac{3}{8}\)
To multiply \(\dfrac{1}{2}\) by \(\dfrac{3}{4}\), you multiply the numerators and denominators to get \(\dfrac{3}{8}\).
True
Evaluate and simplify: \(\dfrac{3}{8} \times \dfrac{4}{9}\).
\(\dfrac{1}{6}\)
The reciprocal of \(\dfrac{3}{4}\) is \(\dfrac{4}{3}\).
True
You find that \(\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8}\). Select all fractions that are equivalent to \(\dfrac{3}{8}\).
\(\dfrac{9}{24}\); \(\dfrac{12}{32}\); \(\dfrac{6}{16}\)
When multiplying fractions, you should add the numerators and multiply the denominators.
False
A recipe uses \(\dfrac{3}{4}\) cup of sugar per batch. You have \(1\dfrac{1}{2}\) cups of sugar. How many full batches can you make?
2
Jordan bikes \(\dfrac{3}{4}\) of a mile each lap. He completes \(2\dfrac{1}{2}\) laps. How many miles does he bike in total?
\(1\dfrac{7}{8}\)
You want to simplify \(\dfrac{2}{3} \times \dfrac{3}{8}\) efficiently. Select all strategies that correctly simplify this product.
Cancel the 3s to write \(\dfrac{2}{3} \times \dfrac{3}{8}\) as \(\dfrac{2}{1} \times \dfrac{1}{8}\).; Rewrite the product as \(\dfrac{6}{24}\), then reduce by dividing numerator and denominator by 6.
A submarine descends at a rate of \(\dfrac{3}{4}\) meter per second. After 8 seconds, its vertical change is represented by \((-\dfrac{3}{4}) \times 8\). What is this value?
\(-6\)
A container holds \(\dfrac{3}{8}\) liter of juice. Each serving is \(\dfrac{1}{4}\) liter. How many full servings can you pour?
1\dfrac{1}{2}
You are checking products of signed fractions. Select all computations that give a negative result.
\((-\dfrac{1}{2}) \times \dfrac{3}{4}\); \(\dfrac{1}{2} \times (-\dfrac{3}{4})\)
A board is \(3\dfrac{1}{2}\) meters long. Each small piece needs to be \(\dfrac{7}{8}\) meter long. How many small pieces can be cut from the board?
4
You want to evaluate \(\dfrac{3}{4} \div \dfrac{1}{2}\). Select all expressions that correctly represent this calculation or its result.
\((3 \div 4) \div (1 \div 2)\); \(\dfrac{3}{4} \times \dfrac{2}{1}\); \(\dfrac{3}{4} \div \dfrac{1}{2} = \dfrac{3}{2}\)
Evaluate \(\bigl(\dfrac{3}{8} \times \dfrac{4}{3}\bigr) \div \dfrac{1}{2}\).
1
Evaluate \(\dfrac{3}{4} \div \dfrac{3}{8} \div \dfrac{1}{2}\), working from left to right.
4
Mia hikes \(1\dfrac{3}{4}\) miles each day for 4 days, then hikes only half that daily distance on the fifth day. How many miles does she hike in total over the five days?
7\dfrac{7}{8}
Arrange the steps in the correct order to compute \(\dfrac{3}{4} \div \dfrac{2}{3}\).
Correct order: Write the original expression \(\dfrac{3}{4} \div \dfrac{2}{3}\). → Keep the first fraction \(\dfrac{3}{4}\). → Change the operation from division to multiplication. → Flip \(\dfrac{2}{3}\) to its reciprocal \(\dfrac{3}{2}\). → Multiply \(\dfrac{3}{4}\) by \(\dfrac{3}{2}\). → Simplify the product to get \(\dfrac{9}{8}\).

1Compute the product: \(\dfrac{1}{2} \times \dfrac{3}{4}\).

2To multiply \(\dfrac{1}{2}\) by \(\dfrac{3}{4}\), you multiply the numerators and denominators to get \(\dfrac{3}{8}\).

True / False

3Evaluate and simplify: \(\dfrac{3}{8} \times \dfrac{4}{9}\).

4The reciprocal of \(\dfrac{3}{4}\) is \(\dfrac{4}{3}\).

True / False

5You find that \(\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8}\). Select all fractions that are equivalent to \(\dfrac{3}{8}\).

Select all that apply

6When multiplying fractions, you should add the numerators and multiply the denominators.

True / False

7A recipe uses \(\dfrac{3}{4}\) cup of sugar per batch. You have \(1\dfrac{1}{2}\) cups of sugar. How many full batches can you make?

8Jordan bikes \(\dfrac{3}{4}\) of a mile each lap. He completes \(2\dfrac{1}{2}\) laps. How many miles does he bike in total?

9You want to simplify \(\dfrac{2}{3} \times \dfrac{3}{8}\) efficiently. Select all strategies that correctly simplify this product.

Select all that apply

10A submarine descends at a rate of \(\dfrac{3}{4}\) meter per second. After 8 seconds, its vertical change is represented by \((-\dfrac{3}{4}) \times 8\). What is this value?

11A container holds \(\dfrac{3}{8}\) liter of juice. Each serving is \(\dfrac{1}{4}\) liter. How many full servings can you pour?

12You are checking products of signed fractions. Select all computations that give a negative result.

Select all that apply

13A board is \(3\dfrac{1}{2}\) meters long. Each small piece needs to be \(\dfrac{7}{8}\) meter long. How many small pieces can be cut from the board?

14You want to evaluate \(\dfrac{3}{4} \div \dfrac{1}{2}\). Select all expressions that correctly represent this calculation or its result.

Select all that apply

15Evaluate \(\bigl(\dfrac{3}{8} \times \dfrac{4}{3}\bigr) \div \dfrac{1}{2}\).

16Evaluate \(\dfrac{3}{4} \div \dfrac{3}{8} \div \dfrac{1}{2}\), working from left to right.

17Mia hikes \(1\dfrac{3}{4}\) miles each day for 4 days, then hikes only half that daily distance on the fifth day. How many miles does she hike in total over the five days?

18Arrange the steps in the correct order to compute \(\dfrac{3}{4} \div \dfrac{2}{3}\).

Put in order

1Flip \(\dfrac{2}{3}\) to its reciprocal \(\dfrac{3}{2}\).

2Change the operation from division to multiplication.

3Write the original expression \(\dfrac{3}{4} \div \dfrac{2}{3}\).

4Multiply \(\dfrac{3}{4}\) by \(\dfrac{3}{2}\).

5Simplify the product to get \(\dfrac{9}{8}\).

6Keep the first fraction \(\dfrac{3}{4}\).

Frequent Errors on Fraction Multiplication and Division with 1, 2, 3, 4, and 8

Why these fraction items cause trouble

Fraction questions that reuse 1, 2, 3, 4, and 8 look friendly. Many students rush and rely on intuition instead of the formal rules. The same small numbers appear in different places, which makes it easy to mix up operations or skip simplification opportunities.

Typical mistakes and how to avoid them

Treating multiplication like addition. Students add numerators and denominators, for example 1/2 × 3/4 becomes 4/6. Fix this by repeating the rule before you start: multiply across the top, multiply across the bottom.
Dividing without using the reciprocal. In problems like 3/4 ÷ 2/3, some students divide 3 by 2 and 4 by 3 directly. Use the pattern keep, change, flip. Keep the first fraction, change division to multiplication, flip the second fraction, then multiply.
Skipping simplification with 2, 4, and 8. Factors of 2 appear often. In a product such as 3/8 × 4/5, many students multiply to get 12/40, then simplify. It is easier to cancel the factor 4 with part of 8 first, then multiply smaller numbers.
Mishandling the number 1. Some learners think multiplying by 1/1 or 1 changes the size. Others think dividing by 1/2 always gives half. Recall that multiplying by 1 leaves the value unchanged, while dividing by 1/2 doubles the number.
Losing negative signs. In mixed sets, a single minus sign often disappears during cross cancellation. Track signs separately. Count negative factors. An odd number of negatives produces a negative result. An even number of negatives produces a positive result.
Forgetting to convert mixed numbers. Problems such as 1 3/4 × 2/3 often get treated as whole number times fraction. Always convert mixed numbers to improper fractions before any multiplication or division.

Quick Reference Sheet for Multiplying and Dividing Fractions with 1, 2, 3, 4, and 8

How to use this sheet

Keep this page beside you while you work on fraction multiplication and division problems. You can print it or save it as a PDF for offline practice and review.

Core rules for multiplying fractions

Rule 1: Multiply numerators to get the new numerator.
Rule 2: Multiply denominators to get the new denominator.
Rule 3: Simplify the result by dividing top and bottom by any common factor.
Shortcut with 2, 3, 4, and 8: Look for factors of 2, 3, 4, and 8 across a numerator and a denominator. Cancel them before you multiply to keep numbers small.

Core rules for dividing fractions

Step 1: Keep the first fraction.
Step 2: Change the division sign to multiplication.
Step 3: Flip the second fraction to its reciprocal.
Step 4: Multiply using the multiplication rules above.

Working with reciprocals and 1

Reciprocal: Swap numerator and denominator. For example, the reciprocal of 3/4 is 4/3.
Product with reciprocals: A fraction times its reciprocal is 1. For example, 3/8 × 8/3 = 1.
Multiplicative identity: Multiplying any fraction by 1 leaves the value unchanged.

Mixed numbers and improper fractions

Convert mixed numbers to improper fractions before multiplying or dividing.
Example conversion: 2 1/4 becomes 9/4 because 2 × 4 + 1 = 9.
After you finish the operation, you may convert improper fractions back to mixed numbers if needed.

Sign rules and quick checks

One negative factor gives a negative result. Two negative factors give a positive result.
Estimate first. For instance, 3/4 is about 1, so 3/4 × 2/3 should be a bit less than 1.
Use estimation to catch impossible answers, such as a product larger than both original fractions when both are less than 1.

Step-by-Step Worked Examples for Fraction Multiplication and Division

Example 1: Multiplying with 4 and 8

Compute 3/8 × 4/5.

Factor numbers to look for common factors. Here 8 = 2 × 4 and 4 appears in the other numerator.
Use cross cancellation. Cancel the 4 in the numerator with the factor 4 in 8. You get 3/2 × 1/5.
Multiply numerators. 3 × 1 = 3.
Multiply denominators. 2 × 5 = 10.
The final answer is 3/10. The simplification happened before multiplication, so no extra reducing is needed.

Example 2: Dividing fractions with reciprocal thinking

Compute 2/3 ÷ 1/4.

Keep the first fraction. It remains 2/3.
Change division to multiplication.
Flip the second fraction to its reciprocal. 1/4 becomes 4/1.
Now multiply: 2/3 × 4/1.
Use cross cancellation if possible. No cross factors other than 1 appear, so multiply directly. Numerator 2 × 4 = 8. Denominator 3 × 1 = 3.
The result is 8/3. You may also write this as the mixed number 2 2/3.

Example 3: Mixed number with a factor of 2

Compute 1 1/2 × 3/4.

Convert 1 1/2 to an improper fraction. The denominator is 2. Compute 1 × 2 + 1 = 3. So 1 1/2 becomes 3/2.
Write the product as 3/2 × 3/4.
Look for common factors. There is a factor of 3 in each numerator, but cross cancellation only works across a numerator and a denominator. Instead, use the common factor 2. Cancel the 2 in the first denominator with part of 4 in the second denominator. You get 3/1 × 3/2.
Multiply numerators. 3 × 3 = 9.
Multiply denominators. 1 × 2 = 2.
The result is 9/2, or 4 1/2 as a mixed number.

Multiplying and Dividing Fractions Quiz FAQ

Common questions about this fractions quiz

Why does this quiz focus on the numbers 1, 2, 3, 4, and 8 so often?

These numbers create rich patterns for multiplication and division. They share many common factors, especially powers of 2, which encourages cross cancellation and simplification. Practicing with them helps you see structure in numerators and denominators instead of treating each problem as random arithmetic.

What specific skills should I have before trying the standard quiz mode?

You should be comfortable multiplying whole numbers up to at least 12, simplifying basic fractions, and understanding what a reciprocal is. You should also know how to convert between mixed numbers and improper fractions. If any of these feel shaky, review the cheat sheet first.

How can I improve speed on multiplying fractions without making careless errors?

Train one habit at a time. First, slow down and write every step, including cross cancellation. Once accuracy is stable, start grouping easy factors such as repeated 2s in your head. Always estimate before you record a final answer so you can catch results that are too large or too small.

What is the best way to think about division of fractions during this quiz?

Treat every fraction division problem as a multiplication problem in disguise. Say the pattern out loud at first. Keep the first fraction, change the sign, flip the second fraction. After the flip, you are just multiplying. This reduces confusion, especially when 1, 2, 3, 4, and 8 reappear in both positions.

How should I review my mistakes after finishing a quiz attempt?

Sort your missed questions into categories. Examples include mixing up addition and multiplication, missing cross cancellation, incorrect reciprocal, or sign errors. Redo each problem slowly with full working shown. Then create two or three new problems of the same type and solve them correctly to lock in the fix.