How to Add, Subtract, Multiply, and Divide Fractions: The Complete Guide

Solve complex fraction equations instantly, complete with step-by-step simplification, using our Fractions Calculator, or read our guide below to master the manual methods.

Fractions represent a part of a whole. Every fraction consists of two numbers:

• Numerator (Top Number): Represents how many parts you have.
• Denominator (Bottom Number): Represents how many total parts make up the whole.

While decimals are often easier to work with, fractions are strictly required in many fields like carpentry, cooking, and higher-level algebra because they represent exact values (e.g., 1/3 is exact, while 0.333... is an approximation).

Adding and Subtracting Fractions

To add or subtract fractions, you must have a Common Denominator (the bottom numbers must be the same). You cannot add apples and oranges; similarly, you cannot add halves and thirds directly.

Step 1: Find a Common Denominator Example: 1/2 + 1/3 The lowest common multiple of 2 and 3 is 6.

Step 2: Convert the Fractions Multiply the top and bottom of each fraction to reach the denominator of 6.

• 1/2 becomes (1*3)/(2*3) = 3/6
• 1/3 becomes (1*2)/(3*2) = 2/6

Step 3: Add the Numerators Now that the bottoms match, simply add the tops together. Do not add the bottoms.

• 3/6 + 2/6 = 5/6

(The exact same rules apply for subtraction).

Multiplying Fractions

Multiplying fractions is actually much easier than adding them because you do not need a common denominator!

Rule: Multiply straight across. Multiply the numerators together, then multiply the denominators together.

Example: 3/4 × 2/5

• Top: 3 × 2 = 6
• Bottom: 4 × 5 = 20
• Result: 6/20

Always remember to simplify your final answer. Both 6 and 20 can be divided by 2, so the final simplified answer is 3/10.

Dividing Fractions (Keep-Change-Flip)

Dividing fractions uses a famous mental shortcut known as "Keep-Change-Flip."

1. Keep the first fraction exactly as it is.
2. Change the division sign (÷) to a multiplication sign (×).
3. Flip the second fraction upside down (this is called finding the reciprocal).

Example: 1/2 ÷ 3/4

• Keep: 1/2
• Change: ×
• Flip: 4/3
• New Equation: 1/2 × 4/3

Now, just follow the multiplication rule (multiply straight across):

• (1 × 4) / (2 × 3) = 4/6
• Simplified result: 2/3

FAQ

What is an Improper Fraction? An improper fraction is a fraction where the numerator is greater than or equal to the denominator (e.g., 5/4). This means the value is greater than 1.

How do I convert a Mixed Number to an Improper Fraction? A mixed number consists of a whole number and a fraction (e.g., 1 3/4). To convert it:

1. Multiply the whole number by the denominator (1 × 4 = 4).
2. Add the numerator to that result (4 + 3 = 7).
3. Place that new number over the original denominator: 7/4.

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