fractions, mixed numbers, common denominators

1. Unit 8 Fractions and Ratios

5. Try It Out…. 3/5 _____ 4/5 < = >

6. You Rock! 3/5 < 4/5

7. 3/5 is < 4/5 In these two fractions, the denominators are the same. Therefore, the pieces are the same size. Three of these pieces are less than four.

8. Try It Out…. 7/8 _____ 6/7 < = >

9. BEAUTIFUL! 7/8 > 6/7

10. 7/8 is > 6/7 In each of these two fractions, there is all but one piece. However, because 8ths are smaller than 7ths, the remaining 1/8 is smaller than the remaining 1/7.

11. Try It Out…. 3/5 _____ 10/15 < = >

12. Looking Good! 3/5 < 10/15

13. 3/5 is < 10/15 If you change 3/5 into an equivalent fraction, it would be equal to 9/15. 9 out of 15 is less than 10 out of 15.

15. Find an equivalent fraction: For example, 30% = 30/100. If I wanted to know what 30% of 150 was, I would need to find the numerator of an equivalent fraction of 30/100 that has a denominator of 150. 30/100 = n/150 To get from 100 to 150, I need to multiply by 1.5. To be fair, 30 x 1.5 gives me a numerator of 45. So, 30% of 150 is 45. Strategies for finding a percent of a number….

16. More strategies for finding a percent of a number… Change the percent into a decimal by dividing it by 100 and multiply that decimal by the number you are trying to find a percentage of. For example, 30% of 150 would be found by multiplying .3 x 150= 45 Another way to find a percent of a number is to multiply the equivalent fraction of the percent by the number you are trying to find the percentage of. For example, 30% of 150 = 30/100 x 150/1 4500/100 = 45

17. Try It Out…. 75% of 120 30 90 40 100

18. You Rock! 90 is 75% of 120

19. 90 is 75% of 120 75 is ¾ of 100 120 / 4 = 30 3 x 30 = 90 30 30 30 30

20. Try It Out…. 30% of 200 30 90 60 120

21. Far Out! 60 is 30% of 200

22. 60 is 30% of 200 10% of 200 is 20. 10% + 10% + 10% = 30% 3 x 20 = 60 20 20 20 20 20 20 20 20 20 20

23. Try It Out…. 75% of 600 75 400 150 450

24. Looking Good! 75% of 600 = 450

25. 75% of 600 = 450 50% (half) of 600 = 300 Half of 300 (25%) = 150 75% of 600 would then = 450 300 150 150

27. Examples… 3/20 = 15/100 = .15, or 3 divided by 20 = .15 35% = 35/100 = .35 .65 = 65/100 = 65% 1.25 = 125/100 = 125% A number that is greater than 1 will have a percentage greater than 100% Try an online quiz

28. Try It Out…. 5/25 = 20% .2 .25 .5

29. 5/25 = 20% 5/25 x 4/4 = 20/100 20/100 = 20% OR 5/25 = .2; .2 x 100 = 20%

30. Way to Groove! 5/25 = 20%

31. Try It Out…. 135% = 1.35 135 13.5 100 13.5

32. Far Out! 135% = 1.35

33. 135% = 1.35 135 / 100 = 1 35/100 OR 1.35 Remember that decimal hundredths and fraction hundredths refer to the same amounts. 5/100 is 5 hundredths .05 is 5 hundredths

34. Try It Out…. .02 = 1/50 20/100 20% 2/10

35. Awesome! .02 = 1/50

36. .02 = 1/50 .02 = 2/100 2/100 divided by 2/2 = 1/50 Remember that decimal hundredths and fraction hundredths refer to the same amounts. 2/100 is 2 hundredths .02 is 2 hundredths

38. To convert between improper fractions and mixed numbers, think about it like filling in pieces. 1 3/5 = 5/5 (1 whole) + 3/5 = 8/5 The denominator represents the total number of pieces in one whole. The numerator tells how many pieces you have.

39. Try It Out… Click on the links below for more practice: Take a quiz Play a game See it and try it Interactive demonstration (click skip intro, lesson 2)

40. Find common denominators * A “common denominator” is a denominator that two or more fractions have in common (or are the same).

41. Try It Out… Click on the links below for more practice: Find the least common denominator (the smallest denominator fractions have in common) Read more about it See it and try it

43. Step by step Try this site for a demonstration and opportunities to practice! Try It Out…

44. Use an algorithm to multiply fractions and mixed numbers. Multiplying fractions is easy! You don’t even have to have a common denominator. Just multiply the numerator by the numerator and the denominator by the denominator . Multiplying mixed numbers is a little trickier. When you multiply those, you need to convert any mixed numbers into improper fractions. Click here to see a demonstration and try it out!