Mixed Numbers & Improper Fractions Builder

Build mixed numbers with stepper buttons and watch them decompose into improper fractions with animated fraction circles or bars. A number line shows both forms at the same point. Practice converting in both directions, then try adding and subtracting mixed numbers in Challenge mode.

Reference Guide

What Is a Mixed Number?

A mixed number has a whole-number part and a fraction part. It tells you how many full pieces plus how much of the next piece you have.

2 34=2 wholes and 342\,\frac{3}{4} = 2 \text{ wholes and } \frac{3}{4}

Think of it as 2 full pizzas and 3 out of 4 slices of a third pizza.

What Is an Improper Fraction?

An improper fraction has a numerator that is greater than or equal to the denominator. It represents a value of 1 or more.

114 means 11 quarter-pieces\frac{11}{4} \text{ means 11 quarter-pieces}

Both forms describe the same amount. The improper fraction just counts all the pieces without separating wholes.

Mixed to Improper

Multiply the whole number by the denominator, then add the numerator. Keep the same denominator.

2 34  ⇒  2×4+34=1142\,\frac{3}{4} \;\Rightarrow\; \frac{2 \times 4 + 3}{4} = \frac{11}{4}

This counts how many equal pieces are in all the whole parts, then adds the leftover fractional pieces.

Improper to Mixed

Divide the numerator by the denominator. The quotient is the whole-number part and the remainder is the new numerator.

114  ⇒  11÷4=2 R3  ⇒  2 34\frac{11}{4} \;\Rightarrow\; 11 \div 4 = 2 \text{ R}3 \;\Rightarrow\; 2\,\frac{3}{4}

This figures out how many complete groups (wholes) fit, with the leftover becoming the fraction.