348 LearnersLast updated on June 11th, 2025
Division of Fractions
Division is the process of breaking down a number into equal parts. Division of fractions refers to the process of dividing two or more fractions. In this topic, we will learn more about the division of fractions and the steps involved.
How to Divide Fractions?
Division is the process of dividing the whole into equal parts. In division, we divide a number by the divisor to get the quotient. Here, we will learn the step-by-step process involved in dividing two fractions. For instance, 5/8 ÷ 1/6. Now let’s learn the division of fractions step by step.
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Steps for Division of Fractions
There are certain steps that need to be followed while dividing fractions. Let us learn about these steps here:
Step 1: Taking the inverse of the second fraction
Step 2: Simplify the fraction
Step 3: Multiply the first fraction with the inverse of the second fraction.
For example, 5/15 ÷ 6/12
Step 1: Taking the inverse of the second fraction
The inverse of the second fraction 6/12 is 12/6
Step 2: Simplifying the fractions
5/15 = 1/3
12/6 = 2
Step 3: Multiplying the fraction with the inverse of the second fraction.
1/3 × 2 = 2/3
Let’s learn about the different types of division of fractions like division of fraction with whole number, the division of fraction by fraction, the division of fraction with decimals, the division of fractions with mixed numbers.
Division of Fractions with Whole Numbers
To divide a fraction with whole numbers, we multiply the whole number with the denominator of the fraction.
Step 1: Taking the inverse of the whole number, that is, 1 by the whole number.
Step 2: Multiply the fraction with the new divisor
For example, 3/5 ÷ 4
Step 1: Replace the whole number (4) with its reciprocal
The reciprocal of 4 is 1/4
Step 2: Multiply the fraction with the new divisor
3/5 × 1/4 = 3/20
Dividing Fractions with Decimals
To divide a fraction by a decimal, we should first convert the decimal into fraction. Given below are the steps to divide a fraction by a decimal:
Step 1: Converting the decimal to fraction
Step 2: Taking the inverse of the divisor
Step 3: Simplify the fraction and multiply the fractions.
For example, 3/4 ÷ 0.5
Step 1: Converting the 0.5 to fraction
0.5 in fraction is 5/10 = 1/2
Step 2: Taking the inverse of the divisor
Dividing 3/4 ÷ 1/2
The inverse of ½ is 2/1
Step 3: Simplify the fraction and multiply the fractions.
3/4 × 2/1 = 6/4
= 3/2
Division of Fractions by a Mixed Fraction
To divide a fraction by a mixed fraction, we should first convert the mixed fraction into an improper fraction. Then, continue with the division process as usual.
For example: 2/3 ÷ 112
112 can be converted into an improper fraction as;
112 = 1 × 2 + 1 / 2 = 3/2
So, 2/3 ÷ 3/2 = 2/3 × 2/3
=4/9
Common Mistakes and How to Avoid Them in Division of Fractions
It is common for students to make mistakes while working with fractions. The mistakes given below will help us to avoid some of the most frequent mistakes:
Mistake 1
Incorrectly reciprocating the fraction
When doing division of fractions, students tend to invert the dividend (first fraction) instead of the divisor (second fractions) which is wrong. So, when dividing the fraction, it is important to inverse the divisor before multiplying the fraction. For example, 5/4 ÷ 4/3 = 5/4 × 3/4 = 15/16
Mistake 2
Dividing the fraction after the reciprocal
Students sometimes tend to multiply the fraction first and then inverse the fraction, which is wrong. When dividing a fraction, we should inverse the divisor and then multiply the fraction.
Mistake 3
Not simplifying the fraction correctly
After getting the result of division, it is important to simplify the fraction by cancelling out the common factors. Sometimes students tend to make errors while simplifying, so students should remember that we can only simplify the fraction when the numerator and denominator share the common factors.
Mistake 4
Dividing the numerator and denominator separately
Sometimes students divide the numerator and denominator separately, that is a/b ÷ c/d = a ÷ c/ b ÷ d, which is wrong. The division of fractions works like, a/b ÷ c/d = a/b × d/c.
Misunderstanding the word problems
Students when working on word problems make errors by misinterpretation and misidentify the values. So when doing the word problems, it is important to understand the question and identify the values.
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Real-world Applications of Division of Fractions
The division of fractions happens everyday and thus it has varied applications. We use it for cooking, time management, construction, and so on. Here are a few real-life applications of dividing fractions.
- In cooking, to find the amount of ingredients required for the recipe, we use the division of fractions. That is, if we require 3/4 cups of sugar for 1 cup of flour, then for 1/2 cup of flour the required amount of sugar is half of 3/4, which is 3/4 1/2 = 3/8 .
- To share any object among a group, we use division of fraction.
- In construction, to cut the wooden plank of 3/4 meter long into pieces of 1/8 meters, we need to divide. That is 3/4 ÷ 1/8 = 3/4 × 8/1 = 6 .
Solved Examples for Division of Fractions
Problem 1
A pizza is cut into 8 equal slices. Sarah ate 3 slices. If she wants to share the remaining slices equally among 2 friends, how many slices will each friend get?
The number of slices each friend will get is 5/2
Explanation
The total number of slices = 8
The number of slices Sarah ate = 3
So, the number of slices left = 8 - 3 = 5
The number of slices 2 friends shared = 5/2
Problem 2
A 5/6 liter bottle of juice is being poured into 1/4 liter cups. How many full cups can be filled?
The number of cups filled is 3
Explanation
To find how many cups can be filled = 5/6 ÷ 1/4
= 5/6 × 4/1 = 20/6
= 10/3 = 3.333
So, the number of cups filled is 3
Problem 3
A tank can hold 9/10 liters of water. If each bucket holds 3/5 liters, how many buckets are needed to fill the tank?
The number of buckets required to fill is 1.5 buckets .
Explanation
The amount of water the tank can hold = 9/10 liters
The amount of water the bucket can hold = 3/5 liters
The number of buckets required = 9/10 ÷ 3/5
= 9/10 × 5/3
= 45/30 = 1.5 buckets.
Problem 4
A farmer has 4/5 kg of apples and wants to pack them into bags, each holding 1/2 kg. How many bags can he fill?
The number of bags required is 1 full bag
Explanation
The total amount of apple = 4/5 kg
The amount of apple the bags can hold = 1/2 kg
The number of bags required = 4/5 ÷ 1/2
= 4/5 × 2/1
= 8/5 = 1.6
Problem 5
A recipe calls for 2/3 cup of sugar, but Sarah only has a 1/6 -cup measuring spoon. How many times does she need to use the spoon to measure the sugar?
The number of times Sarah required to measure sugar is 4 times.
Explanation
The amount of sugar required = 2/3 cups
The amount of sugar Sarah needs = 1/6 cups
The number of times Sarah needs sugar = 2/3 ÷ 1/6
= 2/3 × 6/1
= 12/3 = 4
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FAQs on Division of Fractions
1.What is a fraction?
2.What is the reciprocal of a fraction?
3.What is 2/3 ÷ 4/5?
4.How to check if the division is correct?
5.What are the real-life applications of division of fraction?
6.How can children in Australia use numbers in everyday life to understand Division of Fractions ?
7.What are some fun ways kids in Australia can practice Division of Fractions with numbers?
8.What role do numbers and Division of Fractions play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Division of Fractions skills?
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