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

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.