How to Divide Fractions: A Step-by-Step Guide
Dividing fractions may appear complicated at first, but with the right techniques, it becomes an easy process. All it takes is to recall the basic rule—invert and multiply. In this comprehensive tutorial, we will divide fractions into what to do when dividing by another fraction, a whole number, and a mixed number. We will also discuss dividing decimals and give examples, practice exercises, and FAQs to guarantee complete understanding.
Table of Contents
What are Fractions?
A fraction is a part of a whole and has two parts:
- Numerator – The numerator is the top number showing how many parts are being taken.
- Denominator – The denominator is the bottom number showing the total number of equal parts.
Some examples of fractions are 1/2, 3/4, 5/8, etc. Fractions are utilized in daily life, ranging from the measurement of ingredients while cooking to the determination of probabilities in mathematics and science.
All the four fundamental arithmetic operations—addition, subtraction, multiplication, and division—are applicable on fractions. Let’s discuss how fractions can be divided in various cases.
What does Dividing Fractions Mean?
Dividing fractions is equivalent to multiplying the first fraction by the second fraction‘s reciprocal. The reciprocal of a fraction a/b is b/a, i.e., we interchange the numerator and the denominator.
The formula for division is:
This way, the division is made equivalent to multiplication, which simplifies the process.
How to Divide Fractions?
Dividing fractions can be categorized into three broad categories:
- Dividing a fraction by another fraction
- Dividing a fraction by a whole number
- Dividing a fraction by a mixed fraction
Let’s do these step by step.
Dividing a Fraction by Another Fraction
Do these three easy steps:
- Find the reciprocal of the second fraction.
- Change division to multiplication by multiplying the first fraction by the reciprocal.
- Simplify the fraction if necessary.
Example: Divide 2/3 by 4/5
Dividing a Fraction by a Whole Number
Steps:
- Change the whole number to a fraction by putting it over 1.
- Find the reciprocal of the whole number fraction.
- Multiply and simplify.
Example: Divide 6/5 by 10
- Convert 10 into a fraction: 10/1
- Take the reciprocal: 1/10
- Multiply: (6/5) × (1/10) = 6/50 = 3/25
Dividing a Fraction by a Mixed Fraction
Steps:
- Convert the mixed fraction into an improper fraction.
- Take the reciprocal of the improper fraction.
- Multiply and simplify.
Example: Divide 2/5 by 3½
- Convert 3½ into an improper fraction: 7/2
- Take the reciprocal: 2/7
- Multiply: (2/5) × (2/7) = 4/35
Dividing Decimals as Fractions
We can also divide decimals based on fraction division rules.
Example: Divide 0.5 by 0.2
- Convert decimals to fractions: 0.5 = 5/10, 0.2 = 2/10
- Use the division formula: (5/10) ÷ (2/10) = (5/10) × (10/2) = 50/20 = 5/2 = 2.5
Alternatively, use direct division:
Solved Examples
Example 1: Divide 1/4 by 1/2
- Find the reciprocal of 1/2 → 2/1
- Multiply: (1/4) × (2/1) = 2/4 = 1/2
Example 2: Divide 3/5 by 2/3
- Reciprocal of 2/3 is 3/2
- Multiply: (3/5) × (3/2) = 9/10
Practice Problems
Solve the following fraction division problems:
- 2/3 ÷ 1/3 = ?
- 3 ÷ 1/3 = ?
- 5 ¾ ÷ ¼ = ?
- 2/3 ÷ 1/6 = ?
- 5 ½ ÷ 4 ⅓ = ?
- 3/8 ÷ 7/8 = ?
- 1/4 ÷ 1/7 = ?
- 7/11 ÷ 1/6 = ?
- 2/5 ÷ 1/2 = ?
- 1/3 ÷ 6/9 = ?
Recommendation Reading:
Frequently Asked Questions (FAQs)
Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction.
Division is the opposite of multiplication. Through the use of reciprocals, we are able to make division a problem of multiplication.
Change the whole number to a fraction (with a denominator of 1), find its reciprocal, multiply, and simplify.
- Addition
- Subtraction
- Multiplication
- Division
Fraction division comes in handy while cooking, financing, engineering, and building, where measurements and portions are applied.
Final Thoughts
Learning how to divide fractions is a vital step in the mastery of math. With the flip and multiply technique, fraction division problems can be solved quite easily. Keep practicing, and you’ll soon be an expert at dividing fractions!
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