Transcript fraction addition 2

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Fraction Addition &
Subtraction
(w/ different denominators)
Copyright © 1999 Lynda Greene
Find the Least Common Denominator (LCD)
3
4
2
+
5
1) Find the multiples of each denominator
4, 8, 12, 16, 20, 24, ...
5, 10, 15, 20, 25, 30, ...
2) Pick the smallest number
both lists have in common
LCD = 20
Copyright © 1999 Lynda Greene
Now that we can find the LCD, we are able to add
& subtract fractions with different denominators
1) Find the LCD (20)
2) Rewrite each
fraction with the
LCD on the
bottom.
3) Now figure out
(for each fraction)
what number
changes the old
bottom number
into the new LCD
3 x5
4 x5
=
15
20
Ask yourself: 4 x ? = 20
Multiply the top and bottom
by this number
x4
2 =
+
5 x4
8
20
Ask yourself: 5 x ? = 20
Multiply the top and bottom
by this number
Copyright © 1999 Lynda Greene
15
8
+
20 20
Now that the two fractions
have a Common
Denominator we can:
1) Add the tops
2) Keep the bottom
3) Reduce if possible
15 + 8 = 23
20
20
This fraction can’t be reduced
Copyright © 1999 Lynda Greene
Another Example:
1) Find the LCD
multiples of 4: 4, 8, 12, 16, 20, 24,
multiples of 8: 8, 16, 24, 32,
2) Re-write the fractions with
the LCD on the bottom
3
5
+
8
4
8
+
LCD = 8
8
Copyright © 1999 Lynda Greene
3) The first fraction:
the bottom
number didn’t
change, so leave
the top the same.
3
5
+
8
4 x2
4) The second fraction:
We changed a 4
into an 8,
so 4 x ? = 8 (2)
x2
5) Multiply the top
and bottom of the
second fraction by 2
3
10
+
8
8
6) Now that the
denominators
(bottoms) are
the same, we
can add the tops.
3  10
8
ADD THE TOPS
13
=
8
ALWAYS REDUCE
IF POSSIBLE
KEEP THE BOTTOMS
Copyright © 1999 Lynda Greene
More than two fractions:
5 x3
1 x2 7
+
+
6
2 x3
3 x2
x1
x1
LCD = 6
multiples of 2: 2, 4, 6, 8, 10, 12,...
multiples of 3: 3, 6, 9, 12, 15,...
multiples of 6: 6, 12, 18, 24, 30,...
Rewrite all
three fractions
with a 6 on the
bottom
Multiply the tops by the correct numbers
15 + 2 + 7
6
6
6
Fraction 1: 2 x ? = 6 (3)
Fraction 2: 3 x ? = 6 (2)
Fraction 3: 6 x ? = 6 (1)
Copyright © 1999 Lynda Greene
Now that the three fractions have
a Common Denominator we can:
* Add (or subtract) the tops
* Keep the bottom
* Reduce if possible
15 + 2 + 7
6
6 6
ADD/SUBTRACT THE TOPS
REDUCE
15 + 2 + 7 = 24  6
6 6
6
=3

3
1
KEEP THE BOTTOM
Copyright © 1999 Lynda Greene
9
7

4
3
We need a common denominator
Find the LCM’s:
4,8, 12, 20,…
3, 6, 9, 12, 15, …
4 and 3 have “12” in common
12

Create 2 fractions with
This denominator
12
9 3 7 4

4 3 3 4
27
12
28

12
Now multiply each fraction
(top and bottom) by the number
that will make them into 12’s.
Now that they have the same
denominators, we can subtract
the tops(numerators).
27  28
1

12
12
This can’t be reduced
Addition & Subtraction Practice:
Press enter to see answers
7 3 10 5
1)  

8 8 8 4
3 9
2)  
10 5
5 2
3)  
6 9
21
10
11
18
3 7 3 37
4)   
4 2 8 8
1
2 3
5)  
35
5 7
11 5 38 19

6)  
6 3
2 6
1
3 104
7) 2  4 
3
5
15
7 2 5
8)  
3
3 3
Copyright © 1999 Lynda Greene