Dividing Fractions Calculator

Introduction

This Dividing Fractions Calculator divides one fraction by another and shows you how it works. Type in two fractions, press Calculate, and you get the answer as a simplified fraction, a mixed number, and a decimal.

You can enter plain fractions like 3/4, mixed numbers like 2 1/3, whole numbers like 5, and negative numbers like -3/4. The calculator handles all of them.

The step-by-step solution walks you through the "keep, change, flip" method: keep the first fraction, flip the second one, and multiply. You will also see how to check the sign and how to simplify using the greatest common divisor. A number line and a bar chart show how big your answer is, so it is more than just numbers on a page.

There is also a check box where you can type your own answer and see if it is right. That makes this tool useful for homework, test practice, and teaching fraction division in class.

How to use our Dividing Fractions Calculator

Type in two numbers: the fraction you want to divide and the fraction you want to divide by. The calculator gives you the answer as a simplified fraction, a mixed number, and a decimal, plus the full step-by-step work.

Dividend (first fraction): Enter the fraction you are dividing. You can type a simple fraction like 3/4, a mixed number like 2 1/3, a whole number like 5, or a negative value like -3/4.

Divisor (second fraction): Enter the fraction you are dividing by. It takes the same formats, but it cannot be zero, since you cannot divide by zero.

Math Input Pad (optional): Click "Show Math Input Pad" to tap the digits, slash, space, and minus sign instead of typing. Use the arrow buttons to pick which box you are filling in.

Examples (optional): Click any example to load both fractions at once and see how the steps work.

Check your answer (optional): Type the answer you got on paper, then click Verify. The calculator tells you if it matches, and shows the correct answer if it does not.

Press Calculate (or the = button) to solve. You will see the result, each step of the "keep, flip, multiply" method, the answer on a number line, and a bar chart comparing the decimal values. Click Reset to start over.

Dividing Fractions

Dividing fractions means finding how many times one fraction fits inside another. For example, 3/4 ÷ 1/8 asks: how many eighths fit into three fourths? The answer is 6.

The Keep, Change, Flip Rule

You never divide fractions directly. Instead, you turn the problem into multiplication using three moves:

Keep the first fraction (the dividend) the same.
Change the division sign (÷) to a multiplication sign (×).
Flip the second fraction (the divisor) upside down. This flipped fraction is called the reciprocal.

Then multiply straight across: top times top, bottom times bottom. Last, simplify the answer.

Example: 3/4 ÷ 2/5

Flip 2/5 to get 5/2.
Multiply: 3/4 × 5/2 = (3 × 5) / (4 × 2) = 15/8.
15/8 is already in lowest terms. As a mixed number it is 1 7/8, or 1.875 as a decimal.

Why Flipping Works

A reciprocal is the number you multiply by to get 1. Since 2/5 × 5/2 = 1, dividing by 2/5 does the same job as multiplying by 5/2. Dividing by a number and multiplying by its reciprocal always give the same result.

Whole Numbers and Mixed Numbers

Every whole number is a fraction with 1 on the bottom, so 5 becomes 5/1 and its reciprocal is 1/5. A mixed number must first be changed into an improper fraction. To do that, multiply the whole number by the denominator, add the numerator, and keep the same bottom number. So 2 1/3 becomes (2 × 3 + 1)/3 = 7/3.

Signs and Simplifying

The sign rules match regular division. Two positives or two negatives make a positive answer. One negative and one positive make a negative answer. To simplify at the end, divide the top and bottom by their greatest common divisor (GCD). If the top number is bigger than the bottom, you can also write the answer as a mixed number.

Things to Watch For

You can never divide by zero, so the divisor must not equal 0.
Dividing by a fraction smaller than 1 makes the answer bigger, not smaller.
Only flip the second fraction, never the first one.
Any number divided by itself equals 1, such as 7/8 ÷ 7/8 = 1.

Formulas used

Divide fractions (multiply by the reciprocal)

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}

Reciprocal of the divisor

\left(\frac{c}{d}\right)^{-1} = \frac{d}{c}, \quad c \neq 0

Simplify to lowest terms

\frac{N}{D} = \frac{N \div g}{D \div g}, \quad g = \gcd(|N|,\, D)

Mixed number to improper fraction

w\frac{n}{d} = \frac{w \times d + n}{d}

Improper fraction to mixed number

\frac{N}{D} = \left\lfloor \frac{|N|}{D} \right\rfloor \frac{|N| \bmod D}{D}

Decimal value of the result

x = \frac{N}{D}

Decimal input to fraction

0.d_1 d_2 \ldots d_k = \frac{d_1 d_2 \ldots d_k}{10^k}

Answer check (cross multiplication)

\frac{p}{q} = \frac{N}{D} \iff p \times D = N \times q

Frequently asked questions

What is the keep, change, flip rule for dividing fractions?

It is a three-step trick that turns division into multiplication:

Keep the first fraction as it is.
Change the ÷ sign to a × sign.
Flip the second fraction upside down.

Then multiply the top numbers together and the bottom numbers together. Example: 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6.

Do you need a common denominator to divide fractions?

No. Common denominators are needed for adding and subtracting, not for dividing. To divide, just flip the second fraction and multiply.

There is a common denominator method, though. If you give both fractions the same bottom number, you can divide the top numbers. Example: 3/4 ÷ 1/8 becomes 6/8 ÷ 1/8 = 6 ÷ 1 = 6. It gives the same answer, but flipping is faster.

Why does dividing by a fraction make the answer bigger?

Because you are asking how many small pieces fit inside a number. Small pieces fit many times.

Think of 3 ÷ 1/2. How many halves fit in 3 wholes? Six. The answer 6 is larger than 3. This happens any time you divide by a fraction less than 1. If you divide by a number bigger than 1, the answer gets smaller.

How do you divide a fraction by a whole number?

Write the whole number as a fraction over 1, then flip it and multiply.

Example: 3/5 ÷ 4. Write 4 as 4/1. Flip it to 1/4. Now 3/5 × 1/4 = 3/20.

Shortcut: multiply the bottom number by the whole number and keep the top the same.

How do you divide a whole number by a fraction?

Put the whole number over 1, flip the fraction, and multiply.

Example: 5 ÷ 2/3. Write 5 as 5/1. Flip 2/3 to 3/2. Then 5/1 × 3/2 = 15/2, which is 7 1/2.

The answer is bigger than 5 because two-thirds is smaller than one whole.

How do you divide mixed numbers?

Change both mixed numbers into improper fractions first. Multiply the whole number by the denominator, add the numerator, and keep the same bottom number.

Example: 2 1/2 ÷ 1 1/4.

2 1/2 = 5/2 and 1 1/4 = 5/4
Flip the second: 5/2 × 4/5 = 20/10
Simplify: 20/10 = 2

Never divide the whole parts and the fraction parts separately. That gives the wrong answer.

What is the reciprocal of a fraction?

The reciprocal is the fraction flipped upside down. The reciprocal of 3/8 is 8/3.

A number times its reciprocal always equals 1. For example, 3/8 × 8/3 = 24/24 = 1.

The reciprocal of a whole number like 6 is 1/6. Zero has no reciprocal, because 1/0 is undefined.

Why can't you divide a fraction by zero?

Dividing asks how many times one number fits into another. Zero fits into a number an endless number of times, so there is no single answer.

Also, dividing by zero means multiplying by the reciprocal of zero, which is 1/0. That is not a real number. So the divisor can never be 0 or 0/5 or any fraction equal to zero.

How do you divide negative fractions?

Divide the numbers like normal, then decide the sign:

Negative ÷ negative = positive
Negative ÷ positive = negative
Positive ÷ negative = negative

Example: -3/4 ÷ 2/5 = -3/4 × 5/2 = -15/8, or -1 7/8. Example: -5/6 ÷ -2/3 = 15/12 = 5/4.

How do you turn an improper fraction answer into a mixed number?

Divide the top number by the bottom number. The whole part of the answer goes in front, and the leftover becomes the new top number.

Example: 15/8. Since 15 ÷ 8 = 1 with 7 left over, the mixed number is 1 7/8.

If nothing is left over, the answer is just a whole number. 20/5 = 4.

How do you check if your fraction division answer is correct?

Multiply your answer by the divisor. You should get the dividend back.

Example: 3/4 ÷ 2/5 = 15/8. Check it: 15/8 × 2/5 = 30/40 = 3/4. It matches, so the answer is right.

You can also change both fractions to decimals and divide them to see if the numbers agree.

How do you divide three or more fractions?

Work from left to right, two fractions at a time. Flip each divisor and multiply.

Example: 1/2 ÷ 1/4 ÷ 2/3.

First: 1/2 × 4/1 = 4/2 = 2
Then: 2 × 3/2 = 6/2 = 3

You can also flip every fraction after the first one and multiply them all at once.

What is the difference between multiplying and dividing fractions?

Multiplying is one step: multiply the tops, then multiply the bottoms. Dividing adds one extra step: flip the second fraction first, then multiply.

Compare them: 1/2 × 1/4 = 1/8, but 1/2 ÷ 1/4 = 1/2 × 4/1 = 2. Multiplying by a small fraction makes the answer smaller. Dividing by a small fraction makes it bigger.

How do you divide a fraction by a decimal?

Turn the decimal into a fraction first, then flip and multiply.

Example: 3/4 ÷ 0.5. Write 0.5 as 5/10, which simplifies to 1/2. Then 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2.

Use the place value to build the fraction: 0.25 = 25/100 = 1/4, and 0.2 = 2/10 = 1/5.

When do you use fraction division in real life?

Any time you split something into equal parts or count how many small pieces fit inside a bigger amount.

Cutting a 3/4 yard ribbon into 1/8 yard pieces: 3/4 ÷ 1/8 = 6 pieces.
Sharing 1/2 a pizza among 3 people: 1/2 ÷ 3 = 1/6 each.
Splitting a 2 1/2 cup recipe into 1/2 cup servings: 2 1/2 ÷ 1/2 = 5 servings.

What happens when you divide a fraction by itself?

The answer is always 1. Flipping the second fraction makes the tops and bottoms cancel out.

Example: 7/8 ÷ 7/8 = 7/8 × 8/7 = 56/56 = 1.

This works for any number except zero.