1. Operations with Fractions REVIEW CONCEPTS

2. Fractions A number in the form Numerator Denominator Or N D

3. Fractions The denominator can never be equal to 0. 0 12 = Does not exist!

4. Fractions A fraction with a numerator of 0 equals 0. 156 0 =0 4 0 =0

5. 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

6. Math with Fractions Four basic functions Multiply Divide Add Subtract

7. Multiplication Multiply the numerators and put in the numerator of the result. Multiply the denominators and put in the denominator of the result. 89 8 x 972 47 7 x 428 == x

8. Multiplication - Let’s Try It! 92 17 = x 53 17 = x 711 94 = x 414 730 = x 18 7 15 7 77 36 56 210

9. These numbers get pretty big! 56 210 Let’s make the fraction more simple, so it will be easier to use in the future.

10. Simplification Divide by the Greatest Common Factor 72 28 But what is a Common Factor?

11. Factors A factor is a number that can be divided into another number with no remainder ◦8’s factors are: ◦1(8 ÷ 1 =8) ◦2(8 ÷ 2 = 4) ◦4(8 ÷ 4 = 2) ◦8(8 ÷ 8 = 1) ◦3 is NOT a factor of 8, because 8 is not evenly divisible by 3 (8 ÷ 3 = 2 with R=3)

12. Common Factors A common factor is a factor that two numbers have in common ◦For example, 7 is a factor of both 21 and 105, so it is a common factor of the two. ◦The greatest common factor is the largest factor that the two number share So let’s go back to our simplification problem from before…

13. Simplification Divide both numerator and denominator by the Greatest Common Factor 72 28 Factors are 1, 2, 4, 7, 14, 28 Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72 Greatest Common Factor is 4 28 72÷ ÷ 4 4 = = 7 18 So 72 28 = 7 18

14. Simplification - Let’s Try It! 3 1 7 2 3 1 63 18 = 5 2 114 78 = 7 2 19 13 9 3 = 84 24 = 21 7 = 15 6 =

15. Division Just like multiplication with one more step Invert the second fraction and multiply 82 13 = ÷ 81 23 x = 8 6

16. Division - Let’s Try It! 92 17 =÷ = 53 17 ÷ 711 94 =÷ = 410 720 ÷ 9 14 5 21 63 44 7 50

17. Addition To add two fractions, you must make sure they have a Common Denominator 8 3 16 5 + What is a Common Denominator?

18. 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. So let’s go back to our addition problem from before…

19. 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? 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 16 6 8 3 2 2 x = 5 5 1 1 x = 6 5 += 11 Once you have a common denominator, add the numerators.

20. Addition - Let’s Try It! 42 11 =+ = 83 26 + 16 8 24 =+ = 4 3 13 + 4 3 12 17 2 1 16 25

21. 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 16 6 = 8 3 2 2 x 5 = 5 1 1 x 6 5 - = 1 Once you have a common denominator, subtract the numerators.

22. Subtraction - Let’s Try It! = 82 17 - 82 16 = - = 168 39 - 4 75 = - 8 3 4 1 3 13

23. Review A fraction has a numerator and a denominator The denominator can never be 0 You can multiply, divide, add and subtract fractions A common factor is a number that both denominators are evenly divisible by A common denominator is a number that both denominators share a factor with

24. Putting it All Together