Bits and Pieces II

ADDING AND SUBTRACTING

FRACTIONS AND MIXED NUMBERS

Like fractions are fractions with the same denominator. You can add like fractions easily by adding the numerators and writing the sum over the common denominator. NEVER add the denominators!

Example: 1/5 + 2/5 = 3/5

Now try to add 4/10 + 2/10. Remember to simplify if possible!

ADDING FRACTIONS

Before you can add or subtract fractions with diff erent denominators, you must fi rst write the fractions as equivalent fractions with the same denominator. To find the least common denominator: Find the least common multiple (LCM) of both numbers. Rewrite the fractions as equivalent fractions with the LCM

as the denominator.

Let’s rewrite 3/4 and 1/3 so that they have the same denominator. Then, let’s add the two fractions.

ADDING FRACTIONS (CONT.)

To subtract like fractions, keep the denominator and subtract the numerators. NEVER subtract the denominators!

Let’s practice. 5/8- 1/8

Remember to simplify!

SUBTRACTING FRACTIONS

To subtract fractions with diff erent denominators, rewrite the fractions as equivalent fractions with the same denominator. Remember, to find the least common denominator, you look for the least common multiple of the numbers.

Let’s practice. 11/20- 1/5

SUBTRACTING FRACTIONS (CONT.)

To add mixed numbers: Find the least common denominator.

Rewrite the fractions. Add the fractions. Add the whole numbers. Write your answer in lowest terms. Remember to make sure that the fraction is not improper.

Let’s practice. 3 1/6 + 2 5/12

ADDING MIXED NUMBERS

To subtract mixed numbers: Find the least common denominator. Rewrite the fractions. Subtract the fractions. Subtract the whole numbers. Write your answer in lowest terms.

Let’s practice. 44/5 – 31/3

SUBTRACTING MIXED NUMBERS

Sometimes you have to subtract a mixed number that has a greater fraction from a mixed number with a smaller fraction.

Ex: 3 1/8 – 1 3/8

What do you do in this case? There are two options. You can either change both mixed numbers to improper fractions to subtract, or you can borrow a whole from the 3, and add the

whole to the 1/8 as 8/8. Now you have 2 9/8 – 1 3/8. Let’s try.

SUBTRACTING MIXED NUMBERS (CONT.)