Bell Work:Write each decimal as a percent.

1.3 0.875 0.002

Answer:

1.3 = 130%

0.875 = 87.5%

0.002 = 0.2%

Lesson 13: Adding and Subtracting Fractions and Mixed Numbers

Leftover from the pizza party were 3/8 of a ham and pineapple pizza and 2/8 of a vegetarian pizza. What fraction of a whole pizza was left?

We can add 3/8 and 2/8 to find the fraction of a whole pizza remaining.

3/8 + 2/8 = 5/8

If McKenzie eats two of the slices of ham and pineapple pizza, what fraction of the ham and pineapple pizza will be left?

We can subtract 2/8 from 3/8 to find how much ham and pineapple pizza will be left if McKenzie eats two slices.

3/8 – 2/8 = 1/8

Equal parts of a circle, like slices of pizza, is one model for fractions. Another model for fractions is a number line.

Notice that the fractions have common denominators. To add or subtract fractions that have common denominators, we add or subtract the numerators and leave the denominators unchanged.

Practice:Simplify

¾ + ¾ 3/5 – 3/5

Answer:

¾ + ¾ = 6/4 = 3/2 = 1 ½

3/5 – 3/5 = 0/5 = 0

We often need to add or subtract fractions that do not have common denominators. We can do this by first renaming one or more of the fractions so that they have common denominators. Recall from Lesson 11 that we use the Identity Property of Multiplication to rename a fraction by multiplying the fraction by a fraction equal to 1.

Forming equivalent fractions enables us to add or subtract fractions that have different denominators.

½ x 2/2 = 2/4 ½ x 3/3 = 3/6

Practice:Simplify

2/3 + ¾ ¾ - 1/6

Answer:

2/3 + ¾ = 8/12 + 9/12 = 17/12 = 1 5/12

¾ - 1/6 = 9/12 – 2/12 = 7/12

Using the least common denominator often makes the arithmetic easier and often avoids the need to reduce the answer.

When adding and subtracting mixed numbers it is sometimes necessary to regroup.

Example:Simplify

3 ½ + 1 ¾ 3 ½ - 1 ¾

Answer:

3 ½ + 1 ¾ = 3 2/4 + 1 ¾ = 4 5/4 = 5 ¼

3 ½ - 1 ¾ = 3 2/4 – 1 ¾ = 2 6/4 – 1 ¾ = 1 ¾

Adding and Subtracting Fractions and Mixed Numbers

1. Write fractions with common denominators.

2. Add or subtract numerators as indicated, regrouping if necessary.

3. Simplify the answer if possible by reducing.

Example:The end of a 2 inch by 4 inch piece of lumber is actually about 1 ½ by 3 ½ inches. If one 2 by 4 is nailed on top of another 2 by 4, what will the dimensions of the combined ends be?

Answer:The width of the ends is not changed. We add 1 ½ inch and 1 ½ inch to find the boards combined thickness.

1 ½ + 1 ½ = 2 2/2 = 3The combined boards will be about 3 inches thick and 3 ½ inches wide.

Example:The carpenter cut 15 ½ inches from a 2 by 4 that was 92 5/8 inches long. How long was the resulting 2 by 4?

Answer:We subtract 15 ½ from 92 5/8 after writing the fractions with common denominators.

92 5/8 – 15 4/8 = 77 1/8The resulting 2 by 4 is 77 1/8 inches long.

HW: Lesson 13 # 1-30Due Tomorrow