How to Add, Subtract & Multiply Fractions ā Step-by-Step Guide
Fractions are everywhere ā from school homework and engineering blueprints to cooking measurements and financial ratios. If you have ever felt confused by common denominators, improper fractions, or cross-multiplication, this clear step-by-step tutorial will make fraction arithmetic second nature.
Step-by-Step Addition & Subtraction
To add or subtract fractions with different denominators:
Step 1: Find the Least Common Denominator (LCD) using LCM.
Step 2: Multiply the numerator and denominator of each fraction by the factor required to match the LCD.
Step 3: Add or subtract the numerators while keeping the common denominator identical.
Step 4: Reduce the final fraction by dividing by the Greatest Common Factor (GCF).
Multiplying & Dividing Fractions: The Keep-Change-Flip Rule
Multiplication of fractions is straightforward: simply multiply numerators together and denominators together: (a/b) Ć (c/d) = (a Ć c) / (b Ć d).
For division, follow the classic "Keep-Change-Flip" method:
1. Keep the first fraction unchanged.
2. Change the division symbol (Ć·) into multiplication (Ć).
3. Flip the divisor fraction upside down to take its reciprocal.
Example: (3/4) Ć· (2/5) becomes (3/4) Ć (5/2) = 15/8 = 1 7/8.
| Operation | Rule / Formula | Worked Example | Simplified Output |
|---|---|---|---|
| Addition | Find LCD, add numerators | 1/3 + 1/6 = 2/6 + 1/6 | 3/6 = 1/2 |
| Subtraction | Find LCD, subtract numerators | 3/4 - 1/2 = 3/4 - 2/4 | 1/4 |
| Multiplication | Multiply straight across | (2/3) Ć (3/5) = 6/15 | 2/5 |
| Division | Keep-Change-Flip to reciprocal | (1/2) Ć· (1/4) = 1/2 Ć 4/1 | 4/2 = 2 |
Converting Mixed Numbers & Improper Fractions
An improper fraction is one where the numerator is greater than or equal to the denominator (e.g. 7/4). A mixed number combines an integer and a proper fraction (e.g. 1 Ā¾).
To convert Mixed to Improper: Multiply the integer by the denominator, add the numerator, and divide by the original denominator: (1 Ć 4 + 3) / 4 = 7/4.
To convert Improper to Mixed: Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays identical.
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Frequently Asked Questions (10 Answers)
Q1: What is a fraction?+
A fraction represents a numerical part of a whole, written as a/b, where "a" is the numerator and "b" is the non-zero denominator.
Q2: How do you add fractions with different denominators?+
Find the Least Common Multiple (LCM) of the denominators to establish a common base. Convert both fractions to equivalent fractions with this denominator, add the numerators, and reduce to simplest form.
Q3: What is the Keep-Change-Flip rule for dividing fractions?+
Keep the first fraction, Change the division sign to multiplication, and Flip the second fraction to its reciprocal. Then multiply numerators and denominators.
Q4: How do you convert a mixed fraction to an improper fraction?+
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For 2 Ā¾: (2 Ć 4 + 3) / 4 = 11/4.
Q5: What is a reciprocal of a fraction?+
The reciprocal (or multiplicative inverse) of a fraction a/b is b/a. Multiplying a fraction by its reciprocal always equals 1.
Q6: Can the denominator of a fraction ever be zero?+
No. Division by zero is mathematically undefined. A fraction with denominator zero has no valid numerical value.
Q7: How do you reduce a fraction to lowest terms?+
Divide both the numerator and the denominator by their Greatest Common Factor (GCF). For example, 12/18 divided by GCF 6 simplifies to 2/3.
Q8: How do you multiply two fractions?+
Multiply the two numerators together to get the new numerator, and multiply the two denominators together to get the new denominator: (a/b) Ć (c/d) = (aĆc) / (bĆd).
Q9: How do you convert a fraction to a percentage?+
Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/4 = 0.75 Ć 100 = 75%.
Q10: What are like and unlike fractions?+
Fractions with identical denominators are called like fractions (e.g. 2/7 and 5/7). Fractions with different denominators are unlike fractions (e.g. 1/3 and 2/5).
Written by Mr. Chandan Yadav
Software Engineer & Founder, Digitac Solution ā¢ Saidpur, Ghazipur, Uttar Pradesh, India
Chandan is passionate about building accessible, fast, and transparent computational tools for students, homeowners, and investors across India. All calculations on this platform adhere strictly to official Indian regulatory frameworks including the Reserve Bank of India, Income Tax Department, and Postal Savings norms.