Algebra 1 Common Core Student Edition, Grade 8-9

Adding and Subtracting Fractions

You can add an d subtract fractions w h en they have th e sam e denom inator.

Fractions with the sam e d en o m in ato r are called like fractions.

Ex a m p l e 1

a. Add | + 1.

4 I 3_ 4 + 3_7_ .2

5 5 5 5 5

b. Subtract | - 1.

Add or subtract the numerators and

keep the same denominator.

5-2

Fractions with unlike denom inators are called unlike fractions. To add or subtract unlike

fractions, find the least com m on denom inator (LCD) and write equivalent fractions with

the same denominator. Then add or subtract the like fractions.

Ex a m p l e 2

Add | + 1.

3 + 5 = JL , 10

46 12 12

9 + 10 19 , 7

12 = l 2' 0r l l 2

Find the LCD. The LCD is the least common m ultiple (LCM) o f the denominators.

The LCD o f 4 and 6 is 12. W rite equivalent fractions.

Add like fractions and simplify.

To add or subtract m ixed num bers, ad d or subtract th e fractions. Then ad d or
subtract th e w hole num bers. Som etim es w h en subtracting m ixed n u m b ers you
have to regroup so th at you can su b tract th e fractions.

Ex a m p l e 3

Subtract - 3§.

• 5— -3 - 6 -12 12
  i 15 08
  12 12

W rite equivalent fractions w ith the same denominator.

W rite 5 ^ as 4 j | so you can subtract the fractions.

Subtract the fractions. Then subtract the w hole numbers.

Ex e r c i se s

Add or subtract. Write each answer in sim plest form.

1 ^ i.?

16.

• 
  
  
  
  • -, -t- 7 2 a + z 8 8 3 - + -5 ^ 5 (^) 4 ^ 9 9 5.6§ + 3|
    1 + 2n 7 4 - + 1—/m 6 18 8. 2 | + 3y
    g 42 | jJ.
    3 A11 1°. 3 | + 5^;
    i + i | 1 2. s | + 3§ 13 i3. rig -r z1611-+ 2— 14 Z _ 3 8 8 15 — - — 10 10
    7 2
    5 5 17i /.^7?
    is 5____4
    1S- 11 11 19. s | - e j 2 0 3 - — 1 -Z U. Og l g
    1-4
    22 12 - — 4 -a s
    zz. rz4 23. 17| - 8 | 24 zh. r4 7- — 3- o8 25 4—— 1— 12 x12
    c
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