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Master Mixed to Improper

Convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the denominator. Example: 1 3/4 = 7/4.

What is Mixed to Improper Conversion?

Writing mixed numbers as single fractions

A mixed number has a whole part and a fractional part. To convert to an improper fraction: (whole × denominator) + numerator, all over the denominator. Example: 1 3/4 = (1×4 + 3)/4 = 7/4.

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Whole × Denominator + Numerator

Multiply the whole number by the denominator, add the numerator, place over the denominator.

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Mixed to Improper Rules

Key steps for converting mixed numbers to improper fractions

Formula

a b/c = (a×c + b)/c. Multiply whole by denominator, add numerator, over denominator.

1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}
2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}

Single Fraction

The result is one fraction (numerator may be greater than or equal to denominator).

3 \frac{2}{3} = \times 3 + 2 = \frac{11}{3}

Mixed to Improper Examples

Worked examples

Basic Examples

1 \frac{3}{4}\frac{7}{4}
2 \frac{1}{5}\frac{11}{5}
3 \frac{2}{3}\frac{11}{3}

Why Mixed to Improper Matters

Many fraction operations (multiply, divide, add with different denominators) are easier with improper fractions. Converting is a useful skill.

Applications

Used before multiplying or dividing mixed numbers, and in algebra.

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Mixed to Improper Practice

Practice converting mixed numbers to improper fractions with easy, medium, and hard levels.

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