Dividing fractions
Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions
What a learner can do afterwards
- Divide a fraction by a fraction using the reciprocal method
- Use visual fraction models to represent and explain fraction division
- Create story contexts for fraction division problems and solve them
1 · Read
You already know two skills: multiplying fractions, and dividing a fraction by a unit fraction like 1/4. Dividing a fraction by any fraction uses those same skills plus one new trick, called keep-change-flip. Keep the first fraction as it is. Change the divide sign to a multiply sign. Flip the second fraction upside down, so it becomes its reciprocal. Then multiply like you already know how.
Nina has 5/6 of a bag of rice. She pours it into cups that hold 5/12 of the bag each. Keep 5/6, change divide to multiply, flip 5/12 to 12/5. 5/6 x 12/5 = 60/30 = 2. She fills 2 cups.
Only flip the second fraction, the one right after the divide sign. If you flip the first fraction instead, or forget to flip at all, the answer will be wrong.
To divide a fraction by a fraction: keep the first fraction, change divide to multiply, and flip the second fraction upside down.
More to read
How to Divide a Fraction by a Fraction
Dividing a fraction by a fraction is easier than it looks. You only need three little moves called keep, change, flip.
Say you want to solve 1/2 ÷ 1/4.
1. Keep the first fraction just as it is. That is 1/2. 2. Change the division sign to a multiplication sign. 3. Flip the second fraction upside down. So 1/4 becomes 4/1.
Now your problem is 1/2 × 4/1. Multiply the top numbers: 1 × 4 = 4. Multiply the bottom numbers: 2 × 1 = 2. You get 4/2, which simplifies to 2. So 1/2 ÷ 1/4 = 2. That makes sense, because two quarter pieces fit inside a half.
Always check your answer by asking: does this many small pieces really fit in the bigger amount? If your answer is smaller than 1 but the pieces should fit more than once, flip back and try again.
How to Divide a Fraction by a Whole Number
Dividing a fraction by a whole number is not as tricky as it sounds. The secret is to turn the whole number into a fraction first.
Take the problem 2/3 ÷ 4.
1. Give the whole number a bottom of 1, so 4 becomes 4/1. 2. Now use keep, change, flip. Keep 2/3. Change ÷ to ×. Flip 4/1 to 1/4. 3. Multiply: 2/3 × 1/4. Top times top is 2 × 1 = 2. Bottom times bottom is 3 × 4 = 12.
The answer is 2/12, which simplifies to 1/6.
Imagine a pan of brownies cut into 3 rows, and you shade 2 of the rows, which is 2/3. Now cut every brownie into 4 smaller strips. The shaded part is now split into smaller pieces, and each small piece is 1/6 of the whole pan. Dividing by 4 made each piece four times smaller.
How to Divide a Whole Number by a Fraction
When you divide a whole number by a fraction, you are counting how many fraction pieces fit inside the whole.
Try 3 ÷ 1/2.
1. Turn the whole number into a fraction by giving it a bottom of 1. So 3 becomes 3/1. 2. Use keep, change, flip. Keep 3/1. Change ÷ to ×. Flip 1/2 to 2/1. 3. Multiply: 3/1 × 2/1 = 6/1, which is just 6.
So 3 ÷ 1/2 = 6. Picture a pizza cut into halves. How many half slices make 3 whole pizzas? Six! That matches your answer.
Dividing by a fraction like 1/2 does not make things smaller. It asks how many pieces fit, and pieces of 1/2 fit twice in every whole, so 3 wholes hold 6 halves.
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2 · Watch
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.