Dividing Fractions
Dividing fractions means keep the first, flip the second to its reciprocal, then multiply. The same rule handles a whole number (write it over 1) and a mixed number (make it improper).
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How to Divide a Fraction?
- Change the division sign into multiplication.
- Turn the second fraction upside down to get the reciprocal.
- Multiply the fractions and simplify to get the final answer.
How to Divide a Fraction by a Whole Number?
- Write the whole number as a fraction over 1.
- Flip it to its reciprocal, then multiply.
How to Handle Mixed Numbers in Division?
- First convert mixed numbers into improper fractions.
- To do so, multiply the whole number by the denominator, then add the numerator.
- Finally, use the same rule to divide: flip, multiply, and simplify.
Practice Questions
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What is ?
Correct! 🎉 +10 pointsNot quite right
Replace the division sign with multiplication and flip to . Cross-cancel the 2s. The answer is .
What is ?
Correct! 🎉 +10 pointsNot quite right
Replace the division sign with multiplication and flip to . Cross-cancel 4 and 8 to get 1 and 2. Multiply 5 × 1 and 2 × 1 to get .
What is ?
Correct! 🎉 +20 pointsNot quite right
Flip to . Multiply 3 × 7 and divide by 4 to get .
What is ?
Correct! 🎉 +20 pointsNot quite right
Replace the division sign with multiplication and flip to . Multiply and , giving .
What is ?
Correct! 🎉 +20 pointsNot quite right
Replace the division sign with multiplication and flip to . Cross-cancel 10 and 5 to get 2 and 1. Multiply 7 × 1 and 2 × 2 to get .
What is ?
Correct! 🎉 +30 pointsNot quite right
Convert to and flip to . Multiply 7 × 6 and 4 × 5 to get , then simplify to .
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Interactive Activity
How to divide fractions step-by-step
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Write the whole number as a fraction over 1, then divide as normal. Change the division sign to multiplication, flip the second fraction to its reciprocal, and multiply. For example, 6 becomes 6/1, and its reciprocal is 1/6. The method stays exactly the same.
Keep, change, flip is a way to remember how to divide fractions. Keep the first fraction the same, change the division sign to a multiplication sign, and flip the second fraction to its reciprocal. After that, multiply the fractions and simplify your answer.
To find the reciprocal of a fraction, swap its numerator and denominator, which turns the fraction upside down. For example, the reciprocal of 3/4 is 4/3. For a whole number, write it over 1 first, so the reciprocal of 6 is 1/6.
A mixed number is a whole number plus a fraction, not a multiplication. If you divide the fraction parts on their own, you get the wrong answer. Converting to an improper fraction first, such as 2 2/5 to 12/5, keeps the value correct so the division works.
Once you have switched to multiplication, look for a numerator and a denominator that share a common factor and divide both by it. This is called cancelling. For example, 9 and 6 share a factor of 3, becoming 3 and 2. Cancelling early keeps the numbers small.