How to Divide Fractions? Explained With Examples

Dividing fractions is quite different from simple division in mathematics. Division means splitting a whole number or amount into equal-sized groups. Whereas, division of fractions means dividing one fraction by the other into further parts. That’s why it requires an extra step to solve.

In this blog, we will guide you about the division of different types of fractions with examples. So, keep reading to learn more!

What is meant by division of Fractions?

While dividing fractions, we are asking, "How many times does one fraction fit into another?" It is a bit like asking how many quarter slices of pizza you can get from a half-pizza.

To divide two fractions, we multiply one fraction by the reciprocal of the second one. Instead of directly dividing, the fraction is inverted and multiplied. This means we flip the second fraction (the one we're dividing by) upside down and then multiply the two fractions together.

Think of it this way:

• Division is the opposite of multiplication.
• Inverting a fraction (finding its reciprocal) is like swapping the place of numerator and denominator.

Simple Steps to Divide Fractions

To further simplify the division process of two fractions, we have divided them into easy steps. We will explain each step with an example too.

Let’s say we have a problem, 34 ÷ 26. To solve it, follow the below instructions.

• Find the reciprocal of the second fraction. This means you flip the fraction so the numerator becomes the denominator, and vice versa. It will become 62.
• Change the division sign to multiply. We will get something like 34 × 62. 
• Multiply the numerators together, which is 3 x 6. The answer is 18.
• Then, multiply the denominators: 4 x 2 = 8.
• We will get 188 the answer.
• Now, we can further simplify the fraction if needed. For example, we can represent the resulting fraction as 94.

Formula for dividing Fractions

For dividing fractions, we keep the first one the same, flip the second one, and then change the symbol to multiplication. So, we can refer to this as KFC. This formula of dividing fractions is an easy way to remember. Let's break it down.

K = Keep the first fraction the same

F = Flip the other fraction

C = Change the sign to multiply

How to Divide Fractions by Fractions?

We have discussed the division method with reciprocal. Now, we will learn it through the formula. Let’s suppose our fractions are ab and cd.

ab ÷ cd

To solve this, the invert and multiply rule will remain the same.

⇒ ab x dc (the inverted version of cd is dc)

⇒ adbc

Now, if we need to divide 12 by 14, we must add the values according to the given numerator and denominator.

12 ÷ 14

⇒ 12 x 41 (the inverted version of 14 is 41)

⇒ 42 ⇒ 2

So, 12 divided by 14 equals 2.

How to Divide Fractions with Whole Numbers?

To divide a fraction by a whole number, you need to turn the whole number into a fraction first. Remember that any whole number can be written as itself over 1.

• Turn the whole number into a fraction by placing it over 1.
• Invert the whole number fraction.
• Multiply the fractions.
• Simplify the result, if possible.

Let’s clarify this concept with an example. Here are the steps to solve 110 divided by 5.

1. Turn 5 into 51.
2. Invert 51 to get 15.
3. Multiply: (110) x (15) = 150.
4. The result 150 is already simplified. So, we do not need to process it further.

So, 110 divided by 5 equals 150.

How to Do Division of Fractions with Mixed Numbers?

Dividing mixed numbers requires an extra step to convert them into improper fractions. 

• Convert any mixed numbers into improper fractions. To do this, multiply the whole number by the denominator and add the numerator. Keep the same denominator.
• Follow the same "invert and multiply" rule as before.
• Multiply the fractions.
• Simplify the result, if possible. If the result is an improper fraction, convert it back to a mixed number.

For instance, let's divide 112 by 214.

1. Convert 112  to an improper fraction: (1 x 2) + 1 = 3, so it's 32.
2. Convert 214 to an improper fraction: (2 x 4) + 1 = 9, so it's 94.
3. Invert 94 to get 32.
4. Multiply: (32) x (94) = 1218.
5. Convert 1218 to its simplified form, 23.

So, 112 divided by 214 equals 23.

Division of Fractions Examples

Here are more instances of dividing fractions.

Whole Number Divided by a Fraction

Problem: You have 4 pizzas, and you want to divide them into pieces that are each 2/5 of a whole pizza. How many pieces will you have?

Mathematical Representation: 4 ÷ 2/5

Solution: 

• Turn 4 into 4/1
• Invert 2/5 to get 5/2
• Multiply: (4/1) x (5/2) = 20/2
• Simplify: 20/2 = 10

Answer: You will have 10 pieces.

Mixed Number Divided by a Whole Number

Problem: You have 1 1/4 cups of flour, and you need to divide it equally into 2 bowls. How much flour will be in each bowl?

Mathematical Representation: 1 1/4 ÷ 2

Solution: 

• Convert 1 1/4 to 5/4
• Turn 2 into 2/1
• Invert 2/1 to get 1/2
• Multiply: (5/4) x (1/2) = 5/8

Answer: Each bowl will have 5/8 cup of flour.

Fraction Divided by a Fraction

Problem: You have 3/4 of a yard of ribbon, and you need to cut it into pieces that are each 1/8 of a yard long. How many pieces can you cut?

Mathematical Representation: 3/4 ÷ 1/8

Solution: 

• Invert 1/8 to get 8/1
• Multiply: (3/4) x (8/1) = 24/4
• Simplify: 24/4 = 6

Answer: You can cut 6 pieces.

Mixed Number Divided by a Mixed Number

Problem: A recipe calls for 2 1/2 cups of sugar, and you have 1 1/4 cups of sugar. How many times can you make a half recipe?

Mathematical Representation: 1 1/4 ÷ 2 1/2

Solution: 

• Convert 1 1/4 to 5/4
• Convert 2 1/2 to 5/2
• Invert 5/2 to get 2/5
• Multiply: (5/4) x (2/5) = 10/20
• Simplify: 10/20 = 1/2

Answer: You can make the half recipe 1/2 of a time, or you have enough sugar for half of a half recipe.

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