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
3½+1¾
3½-1¾
Answer:
3 ½ + 1 ¾ = 3 2/4 + 1 ¾ = 4 5/4
=5¼
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.
1. Add or subtract numerators as
indicated, regrouping if necessary.
1. 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 = 3
The 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 1/8
The resulting 2 by 4 is 77 1/8
inches long.
HW: Lesson 13 # 1-30
Due Tomorrow