Fractions Continued
Fractions
• If the numerator is larger than the denominator, it is called an improper fraction.
Find the improper fraction
11
7
12
10
73
56
9
4
8
10
Addition• To add two fractions, you must make
sure they have a Common Denominator
8
3
16
5+
What is a Common Denominator?
Common Denominator
• A common denominator is a number with which both of the denominators share at least one factor that is not the number 1
– For example, if the denominators are 4 and 7, then a common denominator is 28.
– 28 shares the factors 1, 2 and 4 with the number 4, and the factors 1 and 7 with the number 7.
Addition• To add two fractions, you must make sure
they have a Common Denominator• What can you multiply each fraction by to give the
smallest common denominator?
83
165+
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
166
83
22x = 16
5165
11x =
166
165+ =
1611
Once you have a common denominator, add the numerators.
Subtraction• To subtract two fractions, they also must
have a Common Denominator• What can you multiply each fraction by to
give the smallest common denominator?
8
3
16
5-
The smallest number that has both of these as factors is 16
8 goes into 16 two times 16 goes into 16 one time
166
=83
22x
165
=165
11x
166
165- =
161
Once you have a common denominator, subtract the numerators.
Multiplication
• Multiply the numerators and put in the numerator of the result
• Multiply the denominators and put in the denominator of the result
8 9 8 x 9 72
47 7 x 4 28= =x
56
210 These numbers get pretty big!
What if we needed to multiply again?
Let’s make the fraction more simple, so it will be easier to use in the future.
Division
• Just like multiplication with one more step• Invert the second fraction and multiply
8 2
13=÷
8 1
23x =
8
6