1. 3
8
Adding and Subtracting
Fractions

2. Adding Fractions with common
denominators
3 4 7
+ =
8 8 8

3. Adding Fractions with different
denominators
Problem:
You can’t add fractions with different denominators
without getting them ready first. They will be ready to
add when they have common denominators
Solution:
Turn fractions into equivalent fractions with a
common denominator that is find the Lowest
Common Multiple (LCM) of the two denominators

4. Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number in BOTH lists of multiples
1 1 Multiples of 2 are 2, 4, 6, 8, 10……
+ Multiples of 3 are 3, 6, 9, 12, ………
2 3
What is the lowest common
multiple?

5. Finding the
Lowest Common Denominator
• The lowest common multiple of two numbers is
the lowest number they will BOTH divide into
1 1 2 divides into 2, 4, 6, 8…..
+ 3 divides into 3, 6, 9….
2 3
What is the lowest number 2 and 3
both divide into?

6. 1 1
+ You can’t add fractions with
different denominators
2 3
+
The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths
1 3 1 2 3 2 5
× + × = + =
2 3 3 2 6 6 6
Special form of 1

7. 1 2
+
2 5
Lowest common denominator is 10 so make all fractions tenths
5 4 9
+ =
10 10 10

8. 1 1
+
3 4
Turn both fractions into twelfths
4 3 7
+ =
12 12 12

9. 3 3 2 7 ? ? 9 14 23 2
× + × = + = + = =1
3 7 3 7 21 21 21 21 21 21
Finally the fractions are READY to
It is 3/3 add. I just have to add the
It is 7/7
So I multiply What is special form 9+14=23
numerators
So I multiply What the lowest number
What special form
3/7 by 3/3
2/3 by 7/7 ofBOTH change 7 3 into?
will 3 and 7 divide
1 of 1 will change
to 21. 21. Hmmmm?
to Hmmmm?
It is 21. So that is my
Hmmmmm??????
common denominator
Now 3x3=9 and 2x7=14
Now I know the new
numerators

10. Adding Mixed Numbers
• Separate the fraction and the whole number sections,
add them separately and recombine at the end
1
2 +5
1
2 +5
1
1
3 = + + +
2
2 3
5
= 7+ 6
5
= 7 6