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Overview

Mixed Fractions

January 15, 2025
1 min read
mixed-fractions improper-fractions

Fractions Greater than One

If the numerator is smaller than the denominator (e.g., 12,34\frac{1}{2}, \frac{3}{4}), the fraction is less than 1. If the numerator is larger than the denominator (e.g., 32,54\frac{3}{2}, \frac{5}{4}), the fraction is greater than 1.

Example: 32\frac{3}{2} means 3 halves.

32=12+12+12=1+12\frac{3}{2} = \frac{1}{2} + \frac{1}{2} + \frac{1}{2} = 1 + \frac{1}{2}

Mixed Numbers

A mixed number (or mixed fraction) contains a whole number part and a fractional part. Instead of writing 92\frac{9}{2}, we can see how many whole units fit. 92\frac{9}{2} is 9 halves. Since 2 halves make a whole, 8 halves make 4 wholes. We have 1 half left.

92=412\frac{9}{2} = 4 \frac{1}{2}

This is read as “four and a half”.

Converting Mixed Numbers to Fractions

To write 3343 \frac{3}{4} as a regular fraction:

  1. Multiply the whole number by the denominator: 3×4=123 \times 4 = 12.
  2. Add the numerator: 12+3=1512 + 3 = 15.
  3. Keep the denominator: 154\frac{15}{4}.
334=(3×4)+34=1543 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4}