Example 1: Two proper fractions
Calculate 3/4 ÷ 1/2.
- 1Keep 3/4 as it is.
- 2Change ÷ to ×.
- 3Flip 1/2 to 2/1.
- 4Multiply: (3 × 2) / (4 × 1) = 6/4 = 3/2.
Answer: 3/2 or 1½
Arithmetic · Grades 5–7
Dividing Fractions: Method, Examples and Printable Test
To divide by a fraction, multiply by its reciprocal. The method takes one line, but it is worth understanding why it works, because dividing by a fraction usually makes the answer bigger and that surprises students every year.
Dividing Fractions formula
a/b ÷ c/d = a/b × d/c
Keep the first fraction, change the division to multiplication, and flip the second fraction. The flipped fraction is called the reciprocal. Once the question is a multiplication, the usual rules apply: multiply across and simplify.
- a/b
- The dividend, the fraction being divided
- c/d
- The divisor, the fraction you are dividing by
- d/c
- The reciprocal of the divisor
- ÷ → ×
- The operation changes when the second fraction is flipped
Worked examples
Example 2: Dividing by a whole number
Calculate 2/3 ÷ 4.
- 1Write 4 as 4/1.
- 2Flip it to 1/4 and change the operation to multiplication.
- 3Multiply: (2 × 1) / (3 × 4) = 2/12.
- 4Simplify: 2/12 = 1/6.
Answer: 1/6
Example 3: Understanding the result
How many quarter-cups are in 2 cups?
- 1This asks 2 ÷ 1/4.
- 2Write 2 as 2/1 and flip the quarter to 4/1.
- 3Multiply: 2 × 4 = 8.
- 4The answer is larger than 2 because you are counting small pieces inside a bigger amount.
Answer: 8 quarter-cups
Dividing Fractions practice questions with answers
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
- Question 1easy
Calculate: 1/2 ÷ 1/4
Show answer and worked solution
Answer: 2
Flip and multiply: 1/2 × 4/1 = 4/2 = 2.
- Question 2easy
Calculate: 3/5 ÷ 1/5
Show answer and worked solution
Answer: 3
3/5 × 5/1 = 15/5 = 3.
- Question 3easy
Calculate: 1/3 ÷ 2
Show answer and worked solution
Answer: 1/6
1/3 × 1/2 = 1/6.
- Question 4easy
Calculate: 4/5 ÷ 2/5
Show answer and worked solution
Answer: 2
4/5 × 5/2 = 20/10 = 2.
- Question 5medium
Calculate: 2/3 ÷ 3/4
Show answer and worked solution
Answer: 8/9
2/3 × 4/3 = 8/9.
- Question 6medium
Calculate: 5/8 ÷ 5/6
Show answer and worked solution
Answer: 3/4
5/8 × 6/5 = 30/40 = 3/4. Cancelling the 5s first is faster.
- Question 7medium
How many 1/3 cups are in 2 cups?
Show answer and worked solution
Answer: 6
2 ÷ 1/3 = 2 × 3 = 6 one-third cups.
- Question 8hard
Calculate: 1½ ÷ 3/4
Show answer and worked solution
Answer: 2
1½ = 3/2. Then 3/2 × 4/3 = 12/6 = 2.
- Question 9hard
A 3/4 metre ribbon is cut into 1/8 metre pieces. How many pieces?
Show answer and worked solution
Answer: 6 pieces
3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6.
- Question 10hard
Calculate: 2¼ ÷ 1½
Show answer and worked solution
Answer: 3/2 or 1½
9/4 ÷ 3/2 = 9/4 × 2/3 = 18/12 = 3/2.
Turn this into a printable test
Generate a dividing fractions test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
Prefer free practice first? free fraction worksheets with answers
Why flipping works
Dividing by 1/2 asks how many halves fit into the amount, and there are twice as many halves as wholes, so the answer doubles. Dividing by 1/4 quadruples it. Read that way, multiplying by the reciprocal is not a trick but a restatement of the question, and students who see this stop flipping the wrong fraction because they can sanity-check the size of their answer.
The measuring-cup framing is the fastest route to this understanding. Ask how many quarter-cups are in two cups before showing any algorithm, and the answer of eight is obvious. The formal method then arrives as a shortcut for something already understood rather than as a rule to trust blindly.
Estimating before calculating
Because dividing by a fraction less than 1 increases the value, students can predict roughly what the answer should be before doing any arithmetic. In 2/3 ÷ 3/4 the divisor is close to 1, so the answer should be close to 2/3, and 8/9 is plausible. In 3/4 ÷ 1/8 the divisor is tiny, so the answer should be several times larger, and 6 is plausible.
This estimate catches the flip-the-wrong-fraction error immediately, since that mistake usually produces an answer of obviously the wrong size. Building the habit costs one extra sentence per question and removes most of the marks lost in this topic.
Common mistakes with dividing fractions
✗ Flipping the first fraction instead of the second.
✓ Only the divisor, the fraction after the division sign, is flipped. The first one is kept unchanged.
✗ Flipping the second fraction but leaving the division sign.
✓ The operation must change to multiplication at the same moment the fraction is flipped.
✗ Assuming division always makes the answer smaller.
✓ Dividing by a fraction less than 1 gives a larger answer, because you are counting how many small pieces fit inside.
✗ Dividing mixed numbers without converting them.
✓ Convert both to improper fractions before flipping. 1½ must become 3/2 first.
Dividing Fractions FAQ
How do you divide fractions?
Keep the first fraction, change the division to multiplication, and flip the second fraction. Then multiply across and simplify.
What is a reciprocal?
The reciprocal of a fraction is that fraction turned upside down. The reciprocal of 3/4 is 4/3, and the reciprocal of 5 is 1/5.
Why does dividing by a fraction make the answer bigger?
Because you are counting how many small pieces fit inside the amount. There are eight quarter-cups in two cups, so 2 ÷ 1/4 = 8.
How do you divide a fraction by a whole number?
Write the whole number over 1, flip it, and multiply. For example, 2/3 ÷ 4 = 2/3 × 1/4 = 1/6.
How do you divide mixed numbers?
Convert both mixed numbers to improper fractions first, then keep, change and flip as usual.