How to Work with Fractions
Fractions represent parts of a whole and are one of the most important building blocks in math. This guide covers the four basic operations along with tips for converting between fractions and decimals.
What Is a Fraction?
A fraction is written as two numbers separated by a line: a/b. The top number is the numerator (how many parts you have) and the bottom number is the denominator (how many equal parts make up the whole).
For example, 3/4 means you have 3 out of 4 equal parts. If a pizza is cut into 4 slices and you eat 3, you have eaten 3/4 of the pizza.
Adding Fractions
Same denominator: Add the numerators and keep the denominator the same.
Example: 1/4 + 2/4
The denominators are the same, so add the numerators: 1 + 2 = 3
Result: 3/4
Different denominators: Find the Least Common Denominator (LCD), rewrite each fraction, then add.
Example: 1/3 + 1/4
The LCD of 3 and 4 is 12.
Rewrite: 1/3 = 4/12 and 1/4 = 3/12
Add: 4/12 + 3/12 = 7/12
Result: 7/12
Subtracting Fractions
The process is the same as addition — find a common denominator, then subtract the numerators. Always simplify the result if possible.
Example: 5/6 − 1/3
The LCD of 6 and 3 is 6.
Rewrite: 1/3 = 2/6
Subtract: 5/6 − 2/6 = 3/6
Simplify: 3/6 = 1/2
Result: 1/2
Multiplying Fractions
Multiply straight across — numerator times numerator, denominator times denominator. No common denominator needed.
Example: 2/3 × 4/5
Numerators: 2 × 4 = 8
Denominators: 3 × 5 = 15
Result: 8/15
Dividing Fractions
To divide by a fraction, flip the second fraction (take its reciprocal) and multiply.
Example: 3/4 ÷ 2/5
Flip the second fraction: 2/5 becomes 5/2
Multiply: 3/4 × 5/2 = 15/8
Result: 15/8 (or 1 7/8 as a mixed number)
Converting Between Fractions and Decimals
Fraction to decimal: Divide the numerator by the denominator.
Example: Convert 3/8 to a decimal
3 ÷ 8 = 0.375
Decimal to fraction: Identify the place value of the last digit, write the decimal as a fraction over that place value, and simplify.
Example: Convert 0.6 to a fraction
The 6 is in the tenths place, so 0.6 = 6/10.
Simplify: 6/10 = 3/5
Result: 3/5
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