Today we will solve simple problems involving the addition of fractions and mixed numbers.

1. Today we will solve simple problems involving the addition of fractions and mixed numbers. Solve=work out

2. In 3rd and 4th grade, you learned how to add fractions like: 1/3 +2/3= 3/3 1 5 6 6 6 6 = +

3. Fractions defined… • The top number is the numerator • The bottom number is the denominator • Example: 2 numerator 5 denominator A fraction can also look like this 2/5 with the 2 as the numerator and the 5 the denominator.

4. To add fractions with the same denominator • Keep the common denominator and add the numerator. • Example: 2/5 + 1/5= 3/5 • Example: 4/10 + 3/10= 7/10 • Notice that the denominator does not change, you only add the numerator!

5. Adding Fractions with common denominators + =

6. 1.) 1/3 + 1/3 = 2.) 3/8 + 4/8 = 3.) 1/10 + 6/10 = 4.) 1/5 + 2/5 = 5.) 24/50 + 20/50 = 6.) 6/13 + 6/13 = 7.) 2/45 + 12/45 = 8.) 8/90 + 15/90 = Try some!!! • 2/3 • 7/8 • 7/10 • 3/5 49/50 12/13 14/45 23/90

7. Adding fractions with different denominators is a little different • You must first change the fraction before you can add fractions. • The fractions must have the same denominators to add them.

8. 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

9. 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?

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

11. 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

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

13. Turn both fractions into twelfths

14. 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

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

16. It’s important to know how to add fractions because… It will be on the CST’s! How else will you know how to share your pizza with your techer? Why else is it important?

17. What did you learn? • Solve=to work it out • Adding fractions with the same denominator I just add the numerator and the denominator stays the same. • What happens when I want to add fractions with different denominators?