Fractions trip up a lot of people — but once you know the four simple rules, they’re easy. This guide walks through how to add, subtract, multiply, and divide fractions, how to simplify them, and how to handle mixed numbers, with clear examples for each. For instant answers that show every step, use our free Fraction Calculator.

Fraction Basics

A fraction has two parts: the numerator (top) and the denominator (bottom). The denominator tells you how many equal parts make a whole; the numerator tells you how many you have. So 3/4 means three of four equal parts. A proper fraction is less than 1 (like 2/5), an improper fraction is 1 or more (like 7/4), and a mixed number combines a whole number and a fraction (like 1¾).

How to Add Fractions

You can only add fractions that share the same denominator. If they’re different, give them a common denominator first:

a/b + c/d = (a·d + c·b) ÷ (b·d), then simplify.

Example: 1/2 + 1/3. The common denominator is 6, so rewrite as 3/6 + 2/6 = 5/6. Same-denominator fractions are easy — just add the tops: 1/5 + 2/5 = 3/5.

How to Subtract Fractions

Subtraction works exactly like addition — get a common denominator, then subtract the numerators:

Example: 3/4 − 1/3 = 9/12 − 4/12 = 5/12.

How to Multiply Fractions

Multiplying is the simplest — no common denominator needed. Multiply straight across:

a/b × c/d = (a·c) ÷ (b·d), then simplify.

Example: 2/3 × 3/4 = 6/12 = 1/2. Tip: you can cancel common factors before multiplying to keep the numbers small.

How to Divide Fractions

To divide, use “keep, change, flip” — keep the first fraction, change ÷ to ×, and flip (invert) the second:

a/b ÷ c/d = a/b × d/c

Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Dividing by a fraction smaller than 1 makes the answer bigger, which surprises people at first — but it’s correct.

How to Simplify Fractions

Simplifying means reducing a fraction to its smallest equivalent form by dividing the top and bottom by their greatest common divisor (GCD). For 8/12, the GCD is 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2/3. Always simplify your final answer — 2/3 is much cleaner than 8/12, even though they’re equal.

Mixed Numbers and Improper Fractions

To turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator: 1¾ = (1 × 4 + 3)/4 = 7/4. To go back, divide: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1¾. Do your calculations as improper fractions, then convert the answer back to a mixed number if you prefer — which the calculator does automatically.

Converting Fractions to Decimals

To convert any fraction to a decimal, just divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Some common ones worth knowing: 1/2 = 0.5, 1/4 = 0.25, 1/3 = 0.333…, 1/8 = 0.125. The calculator shows the decimal alongside every answer.

Where You’ll Actually Use Fractions

• Cooking & baking: halving or doubling a recipe (¾ cup × 2 = 1½ cups).
• Woodworking & DIY: measurements in inches are full of fractions.
• Sewing & crafts: seam allowances and pattern scaling.
• School & exams: the foundation for algebra, ratios, and probability.