Mixed Numbers & Improper Fractions Guide

M11Mixed Numbers

A mixed number is a whole number and a fraction together.

We can write improper fractions as mixed numbers and vice versa.

Convert between improper fractions and mixed numbers.

114

⇄

234

2 wholes and 3 quarters

Improper → Mixed: divide to find the whole number and the remainder.
Mixed → Improper: multiply the whole number by the denominator, then add the numerator.

Learn the 2 Methods

Improper Fraction → Mixed Number

Divide the numerator by the denominator. The answer is the whole number.

The remainder becomes the numerator. Keep the same denominator.

Write as a mixed number.

114 : 11 ÷ 4 = 2 remainder 3 → 234

Mixed Number → Improper Fraction

Multiply the whole number by the denominator.

Add the numerator.

Keep the same denominator. Write as an improper fraction.

234 : 2 × 4 = 8, 8 + 3 = 11 → 114

Worked Examples

A. Improper → Mixed

Example 1

7 ÷ 3 = 2 r 1

= 213

Example 2

175

17 ÷ 5 = 3 r 2

= 325

B. Mixed → Improper

Example 1

325

3 × 5 = 15, 15 + 2 = 17

= 175

Example 2

438

4 × 8 = 32, 32 + 3 = 35

= 358

Watch Out! Common Mistakes

Forgetting the remainder.

114 = 204 ✕

Wrong! The remainder is 3. Correct: 234

Only using the remainder.

114 = 34 ✕

Wrong! Don’t forget the whole number. Correct: 234

Wrong conversion (mixed → improper).

234 = 6 + 34 = 94 ✕

Wrong! You must multiply first: 2 × 4 = 8, then 8 + 3 = 11. Correct: 114

⬇ Cheat Sheet

MIXED NUMBERS

Improper → Mixed: divide numerator by denominator; whole number = quotient; remainder over denominator.
Mixed → Improper: multiply whole number by denominator; add the numerator; keep the denominator.

Example: 114 = 234 · 234 = 114

📖 Continue Your Journey

✓ M1 What Are Fractions?✓ M2 Equivalent Fractions ✓ M3 Simplifying Fractions ✓ M4 Comparing Fractions ✓ M5 Ordering Fractions ✓ M6 Adding Fractions (Same Denominator)✓ M7 Adding Fractions (Different Denominator)✓ M8 Subtracting Fractions (Same Denominator)✓ M9 Multiplying Fractions ✓ M10 Dividing Fractions M11 Mixed Numbers M12 Fraction of an Amount M13 Percentage

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Next Lesson: M12 Fraction of an AmountFractions show parts of shapes… and of amounts!

📄 Free printable: Download the Mixed Numbers cheat sheet (PDF) — keep it by your child's desk.

Quick summary

A mixed number combines a whole number and a fraction: 2 3/4.
An improper fraction has a top number bigger than (or equal to) its bottom number: 11/4.
Improper → mixed: divide the numerator by the denominator; the remainder goes over the same denominator (11 ÷ 4 = 2 r 3, so 11/4 = 2 3/4).
Mixed → improper: multiply the whole number by the denominator, then add the numerator (2 × 4 + 3 = 11, so 2 3/4 = 11/4).

Frequently asked questions

What is a mixed number?

A mixed number is a whole number and a fraction written together, such as 2 3/4 — meaning two wholes and three quarters.

What is an improper fraction?

An improper (or top-heavy) fraction has a numerator bigger than or equal to its denominator, such as 11/4. It represents more than one whole.

How do you convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The whole-number answer is the whole part, and the remainder becomes the new numerator over the same denominator: 17/5 = 3 r 2 = 3 2/5.

How do you convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and keep the denominator: 4 3/8 → 4 × 8 + 3 = 35, so 35/8.

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