Adding Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Adding Fractions.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Adding fractions combines parts of a whole by rewriting both with a common denominator and then adding the numerators.

You can only add like-sized pieces directly — \frac{1}{4} and \frac{1}{3} must be converted to twelfths before adding.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Rewrite both fractions with a common denominator so the pieces are the same size, then add numerators only.

Common stuck point: Students mistakenly add both numerators and denominators directly: \frac{1}{3} + \frac{1}{3} \neq \frac{2}{6}.

Sense of Study hint: Draw both fractions on the same-sized whole before adding.

Worked Examples

Example 1

easy
Add \frac{1}{4} + \frac{3}{4}.

Solution

  1. 1
    Check that the denominators are the same: both fractions have denominator 4.
  2. 2
    Add the numerators: 1 + 3 = 4, giving \frac{4}{4}.
  3. 3
    Simplify: \frac{4}{4} = 1 (the two fractions together make a whole).

Answer

1
When two fractions with the same denominator sum to a value where numerator equals denominator, the result is exactly 1 whole. Recognising this shortcut avoids unnecessary simplification steps.

Example 2

medium
Add \frac{2}{3} + \frac{3}{8} + \frac{1}{4}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Add \frac{5}{12} + \frac{3}{12}.

Example 2

hard
Three tanks contain \frac{5}{8}, \frac{3}{4}, and \frac{1}{3} of their capacity in water. If each tank has a capacity of 120 litres, how many total litres of water are in all three tanks?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsequivalent fractionsleast common multiple