1. Fractions Shelby Ferreira

2. Group Activity Write an inequality that compares each group of fractions 3 1 3 2 5 7 4 2 8 3 8 12 3 1 3 7 2 3 5 2 4 10 5 10 1 1 1 1 1 2 3 4 5 6

3. Vocabulary Numerator Denominator Proper fraction Improper fraction Mixed number

4. Converting Improper to Mixed Number 1. Divide the numerator by the denominator. (Do division with remainders, not division with decimals.) 2. The quotient is the whole number. 3. The remainder is the numerator. 4. The divisor is the denominator Ex: Convert 13/6 to a mixed number

5. Converting Mixed Number to Improper “Check mark method” 1. Multiply the whole number by the denominator. 2. Add the numerator to the product. 3. Keep the denominator the same. Ex: Convert 2 1/6 to an improper fraction

6. Equivalent Fractions You can arrive at an equivalent fraction by multiplying or dividing both the numerator and the denominator by the SAME number Ex: Find three equivalent fractions for 5/10

7. Reducing to Lowest Terms Making the numerator and the denominator the lowest numbers possible by dividing until you reach the smallest number possible 1. Find a common factor. 2. Divide both the numerator and the denominator by the SAME factor. 3. Continue to find common factors until the numerator and denominator have no more factors in common. Ex: What is 50/100 in lowest terms?

8. Greatest Common Factor 1. List common factors 2. Find the greatest This will make the reduction process quicker Ex: 56/80

9. Converting Decimals to Fractions By reading the decimal properly, you “say” the fraction form immediately. Ex: 0.5 is what fraction? (You may have to reduce to lowest terms)

10. Converting Fractions to Decimals The fraction bar functions as a division symbol. Divide the numerator by the denominator to covert a fraction to a decimal. Ex: ¾

11. Non-terminating Decimals Some fractions, when converted decimals, result in non-terminating decimals. Ex: 1/3

12. Converting Percents to Fractions 1. Put the percent over a fraction bar. 2. 100 in the denominator (You may have to reduce to lowest terms) Ex: 5%= what fraction?

13. Converting Fractions to Percents 1. Multiply the fraction by 100/1 2. Divide the numerator by the denominator Ex: 3/5=what percent?

14. Multiplying Fractions 1. Multiply numerator by numerator 2. Multiply denominator by denominator Ex: ½ x 2/3=? Ex: 1/3 x 6=? (2/5) 2 =?

15. Dividing Fractions 1. Find the reciprocal of the second fraction 2. Multiply the first fraction by the reciprocal of the second Ex: a/b ÷ c/d =?

16. Adding or Subtracting Like Fractions 1. Add the numerators 2. Keep the denominators the same Ex: a/c + b/c =?

17. Adding or Subtracting Unlike Fractions Find the least common denominator by finding the least common multiple (the smallest number that is a multiple of both denominators) Ex: 1/3 + 1/4

18. Adding or Subtracting Mixed Numbers Sometimes it’s best to first convert to improper fractions Ex: 3 1/5 + 1 4/5 =? Ex: 3 1/5 - 1 4/5 =?

19. Group Activity 1: Theo wants to use a cookie recipe that makes 36 cookies but he wants to reduce the number of cookies to 24. If the recipe specifies using 2 cups of sugar, how much sugar should he use? 2: Rita traveled 1,250 miles in the first 3 days of her trip. At this rate, how long will it take her to travel 1,875 miles? 3: An architect built a model of a 220-foot tall building he is designing. The model is 25 inches tall and 10 inches wide. How wide is the actual building? 4: Last month, Hao’s dog ate 40 cans of dog food in 31 days. How many cans should Hao buy to feed his dog for the next 6 days?

20. Ratios Comparison between two numbers Fractions = ratios Colon or fraction bar

21. Relationship of Ratios and Fractions Lowest terms, same as fractions Leave as improper fraction Ex: Donna processed 68 patient records in a 4-hour shift. Write this quantity as a unit rate (unit rate= ratio reduced to lowest terms).

22. Analogy Comparison that involves 4 items man : boy :: woman : girl Examples: father : mother :: man : ________________ eagle : ________________ :: beagle : doghouse water : liquid :: ________________ : solid ________________ : foot :: finger : hand

23. Proportion Analogy in number form Colon or fraction bar Cross multiplying must reveal equivalency Ex: Is this following proportion true? Why or why not? 18:3 :: 72:12 Ex: 39/x = 13/14. Solve for x. Ex: If the trip from Boston to Chicago is 1000 miles, how long will it take to drive at 55mph?