Any time we divide a number by a second number, we’re really just trying to answer the question: how many times does the second number go into the first number?

Question

Meaning

Answer

$6÷2=?$

How many$2$'s are in $6$?

$3$

We can see that to divide, we actually just multiply the first number by the second number flipped.$6÷2 =6×21 =1×26×1 =26 =3 $This works for all numbers, including fractions:

Question

Meaning

Answer

$4÷21 =?$

How many$21 $'s are in $4$?

$8$

$4÷21 =4×2=8 $

What is a reciprocal? 🤔

The reciprocal of a number is equal to the original number flipped. For example, the reciprocal of $21 $ is $2$ and the reciprocal of $32 $ is $23 $.

Dividing Fractions Calculator

$÷$

Step 1. Make sure both numbers are fractions.

Both of our numbers are already fractions, so we can skip to Step 2.$ ÷ $

Step 2. Flip both the sign and the second fraction.

$÷ $$= $$× $

Step 3. Multiply across the top.

$ × =×0 $

Step 4. Multiply across the bottom.

$×0 =00 $

Step 5. Simplify (if needed).

Looks like the result is already in simplest form, so the final answer is $00 $.

Key Steps 🗝 How to Divide Fractions

Step 1. Make sure both numbers are fractions.

If multiplying a fraction by a whole number, convert the whole number to a fraction by placing it over $1$. Otherwise, move onto Step 2.

Step 2. Flip both the sign and the second fraction.

$ba $$÷dc $$=ba $$×cd $

Step 3. Multiply across the top.

$ba ×cd =b×ca×d $

Step 4. Multiply across the bottom.

$ba ×cd =b×ca×d $

Step 5. Simplify (if needed).

Walk through example problems and practice dividing fractions!You can also use the Quick Links menu to jump to the section you’d like to explore!

Dividing Fractions

Division is all about finding how many times a number goes into another number.

We can solve division problems that include fractions by remembering that a numberdivided by a second number is equal to the first numbermultiplied by the reciprocal of the second number.

Question

Meaning

Answer

$21 ÷41 =?$

How many$41 $'s are in $21 $?

$2$

$21 ÷41 =21 ×4=2 $

We can notice a few things:

As the gets bigger, our answer gets bigger.

Smaller

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Bigger

Question

Meaning

Answer

$1÷21 =?$

How many$21 $'s are in $1$?

$2$

$1÷21 =1×2=2 $

If the first number is than the second number, our answer will always be bigger than 1.

Question

Meaning

Answer

$2÷41 =?$

How many$41 $'s are in $2$?

$8$

$21 ÷41 =21 ×4=2 $

Now that we know what to expect when we divide fractions, let’s check out some examples of how to divide fractions!

Let's start by finding the answer to $43 ÷21 $.

Step 1. Make sure both numbers are fractions.

Both of our numbers are already fractions, so we can skip to Step 2.$43 ÷21 $

Step 2. Flip both the sign and the second fraction.

$43 $$÷21 $$=43 $$×12 $

Step 3. Multiply across the top.

$43 ×12 =4×16 $

Step 4. Multiply across the bottom.

$4×16 =46 $

Step 5. Simplify (if needed).

$46 =23 $The final answer is $23 $.

Nice work! Now, let's find the answer to $32 ÷4$.

Step 1. Make sure both numbers are fractions.

Our second number is not a fraction, but we can make it one by putting it over $1$.$32 ÷14 $

Step 2. Flip both the sign and the second fraction.

$32 $$÷14 $$=32 $$×41 $

Step 3. Multiply across the top.

$32 ×41 =3×42 $

Step 4. Multiply across the bottom.

$3×42 =122 $

Step 5. Simplify (if needed).

$122 =61 $The final answer is $61 $.

Amazing job! Last one - let's find the answer to $54 ÷4−1 $.

Step 1. Make sure both numbers are fractions.

Both of our numbers are already fractions, so we can skip to Step 2.$54 ÷4−1 $

Step 2. Flip both the sign and the second fraction.

$54 $$÷4−1 $$=54 $$×−14 $

Step 3. Multiply across the top.

$54 ×−14 =5×−116 $

Step 4. Multiply across the bottom.

$5×−116 =−516 $

Step 5. Simplify (if needed).

$−516 =−516 $The final answer is $−516 $.

Incredible work! If you’d like additional practice with dividing fractions, take a moment to complete the quick practice below before closing out this lesson! ⚡

Practice: Dividing Fractions

Question 1 of 10: $65 ÷32 =?$

Step 1. Make sure both numbers are fractions.

Since both numbers are already fractions, we can just move on to Step 2.$65 ÷32 $

Turn the whole number into a fraction:

$5÷32 =$

$÷32 $

$65 ÷2=65 ÷$

Step 2. Flip both the sign and the second fraction.

The division ($÷$) sign becomes a multiplication ($×$) sign, and the top and bottom numbers of the fraction swap positions.

$5$$6$

$÷$

$2$$3$

$=$

$5$$6$

Step 3. Multiply across the top.

$5$$6$

$×$

$3$$2$

$=$

$6×2$

Step 4. Multiply across the bottom.

$15$$6×2$

$=$

$15$

Step 5. Simplify (if needed).

$15$$12$

$=$

Great work! Our answer is $65 ÷32 =45 $.

When you feel like you've mastered this lesson, click for a celebration ⬇️!

Incredible job, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?