Fractions Made Easy
Fractions trip people up more than almost any other area of basic maths. Most of the difficulty is not the arithmetic itself but the rules. The rules for adding fractions are different from the rules for multiplying them, and mixing them up is a very easy mistake to make.
This guide covers all four operations on fractions in a logical sequence. Each section explains the rule, shows why it works and walks through a clear example.
The Parts of a Fraction
| Term | Meaning |
|---|---|
| Numerator | The top number. How many parts you have. |
| Denominator | The bottom number. How many equal parts the whole is divided into. |
| Proper fraction | Numerator is smaller than denominator. Example: 3/4. |
| Improper fraction | Numerator is larger than or equal to denominator. Example: 7/4. |
| Mixed number | A whole number combined with a proper fraction. Example: 1 and 3/4. |
How to Add Fractions
Fractions can only be added when they share the same denominator. If the denominators are already the same, just add the numerators. If they are different, find the lowest common denominator first.
Adding Fractions: Same Denominator
Example: 1/5 plus 2/5
Step 1: Denominators are the same (both 5). No conversion needed.
Step 2: Add the numerators: 1 plus 2 = 3
Answer: 3/5
Adding Fractions: Different Denominators
Example: 1/3 plus 1/4
Step 1: Find the lowest common denominator (LCD). The LCD of 3 and 4 is 12.
Step 2: Convert each fraction. 1/3 = 4/12 1/4 = 3/12
Step 3: Add the numerators: 4 plus 3 = 7
Answer: 7/12
How to Subtract Fractions
Subtraction follows the same rules as addition. Match the denominators first, then subtract the numerators.
Subtracting Fractions
Example: 5/6 minus 1/4
Step 1: Find the LCD of 6 and 4. The LCD is 12.
Step 2: Convert each fraction. 5/6 = 10/12 1/4 = 3/12
Step 3: Subtract the numerators: 10 minus 3 = 7
Answer: 7/12
How to Multiply Fractions
Multiplying fractions is actually simpler than adding or subtracting them. You do not need a common denominator. Just multiply the numerators together and multiply the denominators together.
Multiplying Fractions
Example: 2/3 multiplied by 3/5
Step 1: Multiply the numerators: 2 multiplied by 3 = 6
Step 2: Multiply the denominators: 3 multiplied by 5 = 15
Answer: 6/15
Step 3: Simplify if possible. Both 6 and 15 are divisible by 3.
6/15 simplified = 2/5
A useful shortcut called cross-cancellation lets you simplify before multiplying rather than after. This keeps the numbers smaller and the arithmetic easier.
How to Divide Fractions
Dividing fractions uses a simple trick: multiply by the reciprocal. The reciprocal of a fraction is that fraction flipped upside down. The reciprocal of 3/4 is 4/3.
Dividing Fractions
Example: 3/4 divided by 2/5
Step 1: Keep the first fraction as it is: 3/4
Step 2: Change division to multiplication
Step 3: Flip the second fraction (find the reciprocal): 5/2
Step 4: Multiply: (3 multiplied by 5) divided by (4 multiplied by 2) = 15/8
Answer: 15/8, or as a mixed number: 1 and 7/8
How to Simplify a Fraction
A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. Find the greatest common factor (GCF) of both numbers and divide both by it.
Simplifying a Fraction
Example: Simplify 18/24.
GCF of 18 and 24 = 6
18 divided by 6 = 3
24 divided by 6 = 4
Simplified fraction: 3/4
Working With Mixed Numbers
When your calculation involves mixed numbers like 2 and 3/4, convert them to improper fractions first, do the calculation and then convert back.
Converting a mixed number to an improper fraction: 2 and 3/4. Multiply the whole number by the denominator: 2 × 4 = 8. Add the numerator: 8 + 3 = 11. Answer: 11/4.
Use the Mixed Number Calculator to handle these automatically.
Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator by the denominator.
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/3 | 0.333 (repeating) |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
Use the Fraction to Decimal Calculator for instant conversions.
Free Fraction Tools on CalConvs
- Fraction Calculator for all four operations on fractions
- Mixed Number Calculator for operations on numbers like 2 and 3/4
- Simplify Fraction Calculator for reducing fractions to lowest terms
- Fraction to Decimal Calculator for instant decimal conversions
- All Math Tools browse the full calculator collection
Frequently Asked Questions
Why do I need a common denominator to add fractions but not to multiply them?
When you add fractions you are combining parts of the same whole, so the parts must be the same size (same denominator). When you multiply fractions you are finding a fraction of a fraction, which is a completely different operation that works directly on numerators and denominators separately.
What is the fastest way to find the lowest common denominator?
Multiply the two denominators together — the result is always a common denominator, though not always the lowest one. For 3 and 4, multiply to get 12. For cleaner results with larger numbers, use the LCM of the two denominators instead.
How do I add a whole number and a fraction?
Convert the whole number to a fraction with the same denominator as the other fraction. For example, 2 + 3/4 becomes 8/4 + 3/4 = 11/4, which as a mixed number is 2 and 3/4.
What is cross-cancellation and does it always work?
Cross-cancellation divides a numerator from one fraction and a denominator from the other fraction by their GCF before multiplying. It always gives the same final answer as simplifying after multiplying — it just keeps the numbers smaller throughout the calculation.