Subtract Fractions and Mixed Numbers

**Subtract Fractions and Mixed Numbers**

**Fractions with Common Denominators**

Fractions with the same denominator are subtracted by placing the difference of the numerators over the common denominator. After subtracting, write the fraction in simplest form (if necessary).

**Fractions with Different Denominators**

Find the least common denominator (LCD) of the fractions.

- The common denominator is the least common multiple (LCM) of the original denominators.
- Rewrite the fractions as equivalent fractions with that LCM as their denominators.
- Subtract.
- Simplify your answer.

**Example**

The least common multiple of 10 and 20 is 20, then

and

The lowest common denominator (LCD) of the fractions is 20, then

Simplify the difference (not needed in this example)

**Mixed Numbers**

To subtract mixed numbers without borrowing, subtract the fractional parts and then subtract the whole numbers.

**Subtraction of mixed numbers may involve borrowing**

- To borrow "1" from a whole number, reduce the whole number by 1 and add 1 to the fractional part.
- Rewrite the borrowed "1" as a fraction with the same common denominator as the fractional part (
*to have a value of "1," that fraction needs the same numerator and denominator)*

**Example**

Find 5 − 1 ^{2}/_{3}.

Rename 5 as 4 + 1, and then rename 1 using 3 as a denominator (*Any fraction with the same numerator and denominator is equivalent to 1*)

Subtract the fractions

Subtract the whole numbers

4 − 1 = 3

The result is

**Example**

First, rename the fractions so they have common denominators:

Since we can't take 12 from 5, we clearly need to borrow. Rename 6 as 5 + 1, then rename 1 as ^{15}/_{15}. This gives us

Now we're ready to subtract.