How do you convert an improper fraction like $\frac{38}{3}$ into a mixed fraction?

The answer to convert $\frac{38}{3}$ into a mixed number is:

$$ \frac{38}{3} = 12\frac{2}{3} $$

What Is An Improper And A Mixed Fraction?

An improper fraction is a fraction where the numerator is larger than the denominator, such as:

$$ \frac{38}{3} $$

A mixed number (or mixed fraction) is a combination of a whole number and a fraction:

$$ 12\frac{2}{3} $$

How To Convert An Improper Fraction To A Mixed Number

To change an improper fraction into a mixed number:

  1. Check if the numerator and denominator share a common factor (they don’t in this case).
  2. Divide the numerator by the denominator:
    • The quotient becomes the whole number.
    • The remainder becomes the new numerator.
    • The denominator remains unchanged.

This formula shows the idea:

$$ \frac{\text{improper numerator}}{\text{denominator}} = \text{WHOLE NUMBER} , \frac{\text{remainder}}{\text{denominator}} $$

Subtraction Method

We subtract 3 repeatedly from 38 and count how many times:

  • $38 - 3 = 35 \Rightarrow 1$
  • $35 - 3 = 32 \Rightarrow 2$
  • $32 - 3 = 29 \Rightarrow 3$
  • $29 - 3 = 26 \Rightarrow 4$
  • $26 - 3 = 23 \Rightarrow 5$
  • $23 - 3 = 20 \Rightarrow 6$
  • $20 - 3 = 17 \Rightarrow 7$
  • $17 - 3 = 14 \Rightarrow 8$
  • $14 - 3 = 11 \Rightarrow 9$
  • $11 - 3 = 8 \Rightarrow 10$
  • $8 - 3 = 5 \Rightarrow 11$
  • $5 - 3 = 2 \Rightarrow 12$

You stop here because the remainder is now less than 3.

Result:

$$ \frac{38}{3} = 12\frac{2}{3} $$

Division Method

You can also perform short division:

$$ 38 \div 3 = 12 \text{ remainder } 2 $$

So:

  • Quotient = 12 → whole number
  • Remainder = 2 → new numerator
  • Denominator = 3 (unchanged)

Hence:

$$ \frac{38}{3} = 12\frac{2}{3} $$

Summary

To convert $\frac{38}{3}$ to a mixed number:

  • Divide 38 by 3: $38 \div 3 = 12$ remainder 2
  • So the mixed number is:

$$ 12\frac{2}{3} $$