Mixed Numbers Examples in Math

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

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

Concept Recap

A number consisting of a whole number and a proper fraction combined, such as 2\frac{3}{4}.

You ate 2 whole pizzas and \frac{3}{4} of a third pizza—that's 2\frac{3}{4} pizzas.

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: Mixed numbers express quantities greater than one in a way that shows how many wholes and how much extra.

Common stuck point: Students add the whole number and denominator, writing 2\frac{3}{4} as \frac{2+3}{4}.

Sense of Study hint: Write a plus sign between the whole number and the fraction part to remind yourself it means addition, not a single fraction.

Worked Examples

Example 1

easy
Add 1\frac{2}{5} + 2\frac{1}{5}.

Solution

  1. 1
    Add the whole number parts: 1 + 2 = 3.
  2. 2
    Add the fraction parts (same denominator): \frac{2}{5} + \frac{1}{5} = \frac{3}{5}.
  3. 3
    Combine: 3 + \frac{3}{5} = 3\frac{3}{5}.

Answer

3\frac{3}{5}
When adding mixed numbers with like denominators, add the whole numbers and the fractions separately, then combine the results. This works because a mixed number is simply a whole number plus a fraction.

Example 2

medium
Subtract 4\frac{1}{3} - 1\frac{3}{4}.

Example 3

medium
Multiply 2\frac{1}{3} \times 1\frac{1}{2}.

Practice Problems

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

Example 1

easy
A recipe needs 2\frac{3}{4} cups of flour and 1\frac{1}{4} cups of sugar. How many cups of dry ingredients are needed in total?

Example 2

hard
Add 3\frac{5}{6} + 2\frac{3}{4}.
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Background Knowledge

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

fractions