1. Fraction Review

2. What is a Fraction?
A fraction is formed by dividing a whole into a number of parts
I’m the NUMERATOR. I tell you the number of parts
I’m the DENOMINATOR. I tell you the name of part

3. Mixed numbers to improper fractions
Convert whole numbers to thirds
Mixed number
Improper fraction

4. Another Way to change Mixed Numbers to improper fractions
In short
5x3+2=17
Since 5/5=1 there are 5 fifths in each whole.
So 3 wholes will have 3x5=15 fifths.
Plus the 2 fifths already there makes a total of
15+2=17 fifths

5. Equivalent fractions
An equivalent fraction is one that has the same value and position on the number line but has a different denominator
Equivalent fractions can be found by multiplying by a special form of 1

6. Multiplying By a Special Form of One
Why does it work?
Multiplying any number by 1 does not change the value 4x1=4, 9x1=9 ……….
Any number divided by itself =1.
Multiplying a fraction by a special form of one changes the numerator and the denominator but
DOES NOT CHANGE THE VALUE

7. 1

8. Finding equivalent fractions
Convert 5ths to 20ths
That’s 4 so I must multiply by
What do we multiply 5 by to get a product of 20?
Special form of 1

9. Simplifying Fractions: Cancelling
Simplifying means finding an equivalent fraction with the LOWEST denominator by making a special form of 1 equal to 1 1
Another way of doing this

10. Adding and Subtracting Fractions

11. Adding Fractions with common denominators

12. 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

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

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

15. Lowest common denominator is 10 so make all fractions tenths

16. Turn both fractions into twelfths

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

18. Adding Mixed Numbers
Separate the fraction and the whole number sections, add them separately and recombine at the end