Math Basics: Fractions Explained Simply

What Is a Fraction?

A fraction represents a part of a whole. When you cut a pizza into 4 equal slices and eat 1 of them, you have eaten 1 out of 4 slices. That is written as 1/4.

Every fraction has two parts:

Numerator - the top number. It tells you how many parts you have.
Denominator - the bottom number. It tells you how many equal parts the whole is divided into.

    1   <-- Numerator   (parts you have)
   ---
    4   <-- Denominator (total equal parts)

Types of Fractions

Proper Fractions

The numerator is smaller than the denominator. The fraction is less than 1.

Examples: 1/2, 3/4, 5/8

Improper Fractions

The numerator is bigger than or equal to the denominator. The fraction is 1 or more.

Examples: 5/4, 7/3, 9/9

Mixed Numbers

A whole number plus a proper fraction combined.

Example: 2 and 1/4 means two whole things plus one quarter of another.

Quick Tip You can convert an improper fraction to a mixed number by dividing. 7 divided by 3 equals 2 remainder 1, so 7/3 = 2 and 1/3.

Adding Fractions

Same Denominator

When denominators match, just add the numerators. Keep the denominator.

Example

2/5 + 1/5 = 3/5

You have 2 parts and you add 1 more part. Total: 3 parts out of 5.

Different Denominators

You need to find a common denominator first. A common denominator is a number that both denominators divide into evenly.

Example: 1/3 + 1/4

Find a common denominator. Both 3 and 4 go into 12.
Convert: 1/3 = 4/12 and 1/4 = 3/12
Add: 4/12 + 3/12 = 7/12

  1/3 + 1/4

  Step 1: Find LCM of 3 and 4 = 12

  Step 2: 1/3 = 4/12    (multiply top & bottom by 4)
          1/4 = 3/12    (multiply top & bottom by 3)

  Step 3: 4/12 + 3/12 = 7/12

Subtracting Fractions

The same rules apply. Match the denominators, then subtract the numerators.

Example: 3/4 - 1/4

Same denominator, so: 3/4 - 1/4 = 2/4

Simplify: 2/4 = 1/2 (divide both by 2)

Example: 5/6 - 1/4

LCM of 6 and 4 is 12.
5/6 = 10/12 and 1/4 = 3/12
10/12 - 3/12 = 7/12

Multiplying Fractions

This is actually easier than adding. Multiply the numerators together, then multiply the denominators together.

Example: 2/3 x 3/5

Numerators: 2 x 3 = 6

Denominators: 3 x 5 = 15

Answer: 6/15 - simplify to 2/5 (divide both by 3)

  2   3     2 x 3     6     2
  - x - = ------- = -- = --
  3   5     3 x 5    15     5

Dividing Fractions

Flip the second fraction upside down (called the reciprocal), then multiply.

Example: 3/4 divided by 2/5

Flip the second fraction: 2/5 becomes 5/2
Multiply: 3/4 x 5/2 = 15/8
That is an improper fraction: 15/8 = 1 and 7/8

Remember "Keep, Change, Flip" - Keep the first fraction. Change the division sign to multiplication. Flip the second fraction. Then multiply normally.

Simplifying Fractions

A fraction is simplified (or in lowest terms) when no number other than 1 divides evenly into both the numerator and denominator.

Example: Simplify 8/12

Both 8 and 12 are divisible by 4. So: 8 / 4 = 2 and 12 / 4 = 3

Simplified: 8/12 = 2/3

Real-Life Uses of Fractions

Cooking - a recipe calls for 3/4 cup of flour
Time - a quarter of an hour is 1/4 of 60 minutes = 15 minutes
Sharing - splitting a bill or dividing something equally
Measurements - rulers use fractions like 1/2 inch, 1/4 inch

Summary

A fraction = numerator (top) over denominator (bottom)
Adding and subtracting: match the denominators first
Multiplying: multiply straight across
Dividing: keep the first, flip the second, then multiply
Simplify by dividing both parts by their greatest common factor

Frequently Asked Questions

What is the difference between a numerator and a denominator?

The numerator is the top number - it says how many parts you have. The denominator is the bottom number - it says how many equal parts the whole is split into. In 3/8, you have 3 parts out of 8 total.

Why do I need a common denominator to add fractions?

Because you can only add parts that are the same size. Adding 1/3 and 1/4 directly would be like adding apples to oranges. Converting to a common denominator (like 12ths) makes both fractions use the same size parts, so addition makes sense.

How do I turn a mixed number into an improper fraction?

Multiply the whole number by the denominator, then add the numerator. For example, 2 and 3/4: multiply 2 x 4 = 8, then add 3 = 11. So 2 and 3/4 = 11/4.

What does it mean to simplify a fraction?

Simplifying means writing the fraction in its smallest form. You divide both the numerator and denominator by the same number until no further division is possible. For example, 6/9 simplifies to 2/3 because both 6 and 9 divide by 3.

When would I use fractions in everyday life?

Fractions are everywhere: measuring ingredients in cooking, reading a ruler, splitting costs with friends, understanding sports statistics, and calculating discounts when shopping.

Quick Quiz

Check your understanding. Click an answer to see if you got it right.

← Algebra Percentages →