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1. Fractions Review: How to add, subtract, multiply and divide fractions and mixed numbers Compiled and adapted by Lauren McCluskey from several power points by Monica Yuskaitis

2. Parts of a Fraction 3 = numerator = denominator 4 By Monica Yuskaitis

3. Parts of a Fraction 3 = numerator = denominator 4 = dividend 3 = divisor 4 Which means…3÷4 By Monica Yuskaitis

4. ¾ looks like Or 75% of the whole 1/4 1/4 1/4 If you think about money, ¾ of a dollar equals \$0.75 or 75 cents. By Monica Yuskaitis

5. Or ¾ might look like: 1/4 0.25ft. 1/4 0.25ft 75% of the whole 1/4 0.25ft 0.25ft If the rectangle is 1 foot high, then each section is 0.25 ft. By Monica Yuskaitis

6. How much of 4 is 3? • To find how big a portion you have, divide the numerator by the denominator. 3÷4 = 0.75 or 75% So ¾ = 75%

7. How many quarters are in a whole? 4 ? 1/4 1/4 1/4 1/4 1÷4 = 1/4 1÷ ¼ = 4 By Monica Yuskaitis

8. 4 1= 4/4 1/4 1/4 1/4 1/4 1÷4 = 1/4 1÷ ¼ = 4 By Monica Yuskaitis

9. How many quarters are in a half? 1/4 2 1/4 ½ ÷1/4 = 2 Or: 2 quarters equals ½ dollar. By Monica Yuskaitis

10. Equivalent Fractions • Name the same amount but have different numerators and denominators. • Or: Half a dollar = 2 quarters. 1 2 1 1 = 4 2 4 2 1 4 By Monica Yuskaitis

11. Equivalent Fraction Models ¼=2/8 1/8 1/8 1/4 1/4 1/8 1/8 1/8 1/4 1/8 1/4 1/8 So if you have 3 times as much, you have… 3 6 = 4 8 By M.Yuskaitis

12. To Find Equivalent Fractions • Multiply the numerator and the denominator by the same number. • Or… 1 3 3 x = 3 3 9 By Monica Yuskaitis

13. To Find Equivalent Fractions • Divide the numerator and the denominator by the same number. 4 4 1 ÷ = 12 4 3 By Monica Yuskaitis

14. Adding Like Denominators Only add the numerators 1/4 1/4 3 1 4 + = 4 4 4 1/4 1/4 By Monica Yuskaitis

15. Subtracting Like Denominators Only subtract the numerators 1/4 1/4 4 1 3 - = 4 4 4 1/4 1/4 By Monica Yuskaitis

16. To Add or Subtract Fractions with Unlike Denominators: • 1/3 + 1/6 = ? • 1/3 + 1/9 = ? • Rewrite each fraction using the least common multiple.

17. Common Multiple • A number that is a multiple of two or more numbers. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42 By Monica Yuskaitis

18. Shortcut for Finding the Least Common Denominator or Least Common Multiple Check to see if the smaller denominator divides evenly into the larger denominator. 1 3 1 3 will divide evenly into 9, so 9 is your LCD or LCM. + 9 By Monica Yuskaitis

19. To Add or Subtract Fractions With Unlike Denominators • Rewrite the fractions using the least common denominator or least common multiple. 1 = 5 1 = + 10 By Monica Yuskaitis

20. To Add or Subtract Fractions With Unlike Denominators • Now just add the numerators. 1 x 2 = 5 10 x 2 = Remember when adding fractions you never add the denominators. 1 1 + 10 10 10 By Monica Yuskaitis

21. Subtract these Fractions Use the short cut to find the Least Common Denominator (LCD). 1 2 1 - 8 By Monica Yuskaitis

22. Mixed Numbers • Mixed numbers are whole numbers and fractions together. 1 3 1 1 1 = ½ 2 By Monica Yuskaitis

23. Shortcut for Finding the Least Common Denominator Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD. By Monica Yuskaitis

24. Shortcut for Finding the Least Common Denominator 2 will divide evenly into 8, so 8 is your LCD or LCM. 1 3 2 1 1 + 8 By Monica Yuskaitis

25. To Add Mixed Numbers With Unlike Denominators • Find the multiples of each denominator. 1 3 4 = 4, 8, 12, 16, 20, 30 1 1 + 10 = 10, 20, 30, 40, 50 By Monica Yuskaitis

26. Compare the lists of multiples. Circle the common multiples between the two lists. 1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + = 10, 20, 30, 40, 50 10 By Monica Yuskaitis

27. Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. Ask yourself what you multiply 4 by to get 20. 1 3 4 20 x 5 = 1 1 + 10 20 By Monica Yuskaitis

28. To Subtract Two Mixed Numbers with Unlike Denominators • Borrow 1 whole. Rename. Add to what you already had, then subtract. 2 answer= 1 / 1 5 20 25 = = + 20 20 20 4 - 8 1 8 4 = 20 10 20 17 20

29. Try it! 1 3 - 1 • Answer= ? 2 3 5

30. Answer= 1 9/10 How did you do?

31. When would you multiply a fraction by a fraction? • Your family eats 1/8 of 1/2 of a left-over wedding cake. 1/8 of 1/2 or 1/8 x 1/2 By Monica Yuskaitis

32. Jose had already read 1/2 of his novel. Today he read 1/12 of the 1/2 left. How much of the book has he read? 1/12 of 1/2= 1/24 or 1/12 x 1/2 = 1/24 By Monica Yuskaitis

33. Multiplying Fractions • When you multiply two fractions that are between 0 and 1 the product is smaller than both fractions. By Monica Yuskaitis

34. Multiplying Fractions ½ x ¾ = 3/8 Look at the diagram on the next slide to understand why. By Monica Yuskaitis

35. Multiplying Fractions ½ x ¾ = 3/8 ½ of ¼ = 1/8 ¼ ¼ ¼ ¼ 1/8 1/8 1/8 By Monica Yuskaitis

36. How to Find a Fraction of a Fraction: • When you see a fraction problem with the word “of”, multiply. 1 4 x of 2 9 By Monica Yuskaitis

37. Multiply your numerators straight across. 1 x 4 4 = 2 9 By Monica Yuskaitis

38. Then multiply your denominators straight across. 1 x 4 4 = 2 9 18 By Monica Yuskaitis

39. Simplify your answer. In this case we reduce. 1 x 4 4 2 2 ÷ = = 2 9 18 2 9 ÷ By Monica Yuskaitis

40. When would you multiply a fraction and a whole number? • You walk a 4 mile route halfway. ½ of 4 or ½ x 4 • You walk a ¾ mile route twice. 2 x ¾ By Monica Yuskaitis

41. A \$12 ticket to the magic show is on sale for 2/3 of the original price. 2/3 of \$12 or 2/3 x 12 By Monica Yuskaitis

42. How to Find the Fraction of a Whole Number • The first thing to remember is “of” means multiply in mathematics. of = X (times) By M. Yuskaitis

43. Multiply. 1 x of 46 2 By Monica Yuskaitis

44. Change your whole number to a fraction by adding a one underneath. 1 x 46 2 1 By Monica Yuskaitis

45. Multiply your numerators straight across. 1 x 46 46 = 2 1 By Monica Yuskaitis

46. Multiply your denominators straight across. 1 x 46 46 = 2 1 2 By Monica Yuskaitis

47. Simplify your answer. In this case we change an improper fraction to a mixed number or a whole number. 23 1 x 46 46 2) = 46 2 1 2 By Monica Yuskaitis

48. Cross Simplifying: • Sometimes you can cross simplify before you multiply instead of afterwards.

49. Cross Simplifying: 46 1 = X 1 2 23 1 X 46 46÷2= 23 = 1 2 X 1 2÷2 = 1