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# Fractions

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### Fractions

1. 1. Index Fractions Simplest form of a fraction Operations Exercises Fractions Matem´ticas 2o E.S.O. a Alberto Pardo Milan´s e -
2. 2. Index Fractions Simplest form of a fraction Operations Exercises 1 Fractions 2 Simplest form of a fraction 3 Operations 4 Exercises
3. 3. Index Fractions Simplest form of a fraction Operations Exercises FractionsAlberto Pardo Milan´s e Fractions
4. 4. Index Fractions Simplest form of a fraction Operations Exercises Fractions Parts of a fraction A fraction is a number that represents a part of something. a Fractions are written in the form , where a and b are integers, b a and the number b is not zero. Read a over b. b The number a is called numerator, and the number b is called denominator. 13 Example: , 13 is the numerator and 25 is the denominator. 25 A proper fraction is a fraction that is less than one. A fraction greater than one is called an improper fraction. 12 23 Examples: is a proper fraction. is an improper fraction. 17 15Alberto Pardo Milan´s e Fractions
5. 5. Index Fractions Simplest form of a fraction Operations Exercises Fractions Equivalent fractions Equivalent fractions are diﬀerent fractions that name the same amount. Example: 3 6 = because they represent the same amount. 7 14 To ﬁnd if two fractions are equivalent you have to check that the cross-products are equal.Alberto Pardo Milan´s e Fractions
6. 6. Index Fractions Simplest form of a fraction Operations Exercises Fractions Amplify and reduce fractions To ﬁnd equivalent fractions, multiply or divide the numerator and the denominator by the same number. If you multiply by the same number, you will amplify the fraction. If you divide by the same factor, you will reduce the fraction. Examples: 6 • To amplify we multiply the numerator and the denominator 9 6 60 by 10: = . 9 90 6 • To reduce we divide the numerator and the denomina- 9 6 2 tor by 3: = . 9 3Alberto Pardo Milan´s e Fractions
7. 7. Index Fractions Simplest form of a fraction Operations Exercises Simplest form of a fractionAlberto Pardo Milan´s e Fractions
8. 8. Index Fractions Simplest form of a fraction Operations Exercises Simplest form of a fraction A lowest terms fraction is a fraction that can not be reduced anymore. To write a fraction in the simplest form ﬁnd the lowest terms fraction. To reduce a fraction to the lowest terms fraction, we can use two methods: • Divide the numerator and the denominator by the Greatest Common Factor. • Divide the numerator and the denominator by any common factor and keep dividing until they are relatively prime.Alberto Pardo Milan´s e Fractions
9. 9. Index Fractions Simplest form of a fraction Operations Exercises Simplest form of a fraction Examples: 70 To obtain the lowest terms fraction of we can divide 70 and 105 70 2 105 by GCD(70, 105) = 35, so = . 105 3 70 To reduce to the lowest terms fraction we can divide by 5 and 105 70 keep dividing until there are no common factors but one = 105 14 2 = , (note 2 and 3 are relatively prime ). 21 3Alberto Pardo Milan´s e Fractions
10. 10. Index Fractions Simplest form of a fraction Operations Exercises OperationsAlberto Pardo Milan´s e Fractions
11. 11. Index Fractions Simplest form of a fraction Operations Exercises Operations Add and subtract To add or subtract fractions with like denominators, add the numerators and keep the same denominator. To add or subtract fractions with unlike denominators, ﬁrst amplify these fractions to obtain like denominators (using the LCM or any multiple). Simplify, if possible. Examples: 4 8 12 4 + = = . 15 15 15 5 3 1 3 1 6 5 11 To add + using the LCM: + = + = . Because 15 6 15 6 30 30 30 LCM(15, 6) = 30. Using another common multiple of 15 and 6, for example 60: 3 1 12 10 22 11 + = + = = . 15 6 60 60 60 30Alberto Pardo Milan´s e Fractions
12. 12. Index Fractions Simplest form of a fraction Operations Exercises Operations Multiply and divide To multiply fractions, multiply the numerators and multiply the denominators then simplify. 12 3 12 · 3 36 18 Example: · = = = . 5 14 5 · 14 70 35 You can get the reciprocal of a fraction by switching its numerator and denominator. 14 21 Example: The reciprocal of is . 21 14 To divide by a fraction, multiply by its reciprocal and simplify, if possible. 2 4 2 17 2 · 17 34 17 Examples: : = · = = = . 8 17 8 4 8·4 32 16Alberto Pardo Milan´s e Fractions
13. 13. Index Fractions Simplest form of a fraction Operations Exercises ExercisesAlberto Pardo Milan´s e Fractions
14. 14. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 1 Complete: Three ﬁfths= A half= 1 = 1 5 5 = 4 = 2 3 Two quarters= Two thirds= Two and a quarter= 1 = 2 1 7 = 4 = 3 5 An/one eighth= A quarter= Two and four tenths= 3 = 1 3 6 = 1 = 4 12 One and a half=Alberto Pardo Milan´s e Fractions
15. 15. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 2 Write a fraction in the simplest form beside each of the following sentences: There are forty-two girls out of seventy-two people: The baby snake was just four and three quarters inches long: Fifteen out of the twenty students have dogs as pets: I walk ﬁve and a quarter miles a day:Alberto Pardo Milan´s e Fractions
16. 16. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 3 An orchard has 72 peach trees, 15 apple trees, and 23 lemon trees. In the simplest form, what fraction of the trees are peach trees?Alberto Pardo Milan´s e Fractions
17. 17. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 4 George swims seven eighths miles and Mat swims ten twelfths miles. Who swims farther?Alberto Pardo Milan´s e Fractions
18. 18. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 5 Compare these fractions using the least common denominator: 2 3 9 7 −1 −2 13 , , , , , , . −6 4 15 5 −3 10 12Alberto Pardo Milan´s e Fractions
19. 19. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 6 Lance and Frank ate seven twelfths of a pizza. If Frank ate a third of the pizza, how much of the pizza did Lance eat?Alberto Pardo Milan´s e Fractions
20. 20. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 7 Out of the 20 students, a quarter wear jeans, a ﬁfth wear shorts and a tenth wear a skirt. How many students wear something else?Alberto Pardo Milan´s e Fractions
21. 21. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 8 Tangram means seven boards of skill. The Tangram is a Chinese puzzle consisting of seven ﬂat pieces (called tans) which are put together to form diﬀerent shapes. Study the tans to the right that form a square. The side of the square is 1 cm, so the area is 1 cm2 . Find the fractional value of each piece.Alberto Pardo Milan´s e Fractions
22. 22. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 9 My car’s gas tank was empty. I paid forty euros and now It is full. To go to Marbella I need two ﬁfths of the tank. How much money is this fraction of the tank?Alberto Pardo Milan´s e Fractions
23. 23. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 10 Peter cut six apples into quarters. How many pieces of apple did he have?Alberto Pardo Milan´s e Fractions
24. 24. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 11 1 Mike cleaned of the yard that is 24 m2 in total . How many 4 square meters are left?Alberto Pardo Milan´s e Fractions
25. 25. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 12 3 Thomas drunk cup of milk, and now he has 24 cl left. How 5 many ml did the cup have originally?Alberto Pardo Milan´s e Fractions
26. 26. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 13 2 Eric is reading a book with 195 pages. He read of the pages 5 today. How many pages are left?Alberto Pardo Milan´s e Fractions
27. 27. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 14 1 Of Paul’s stone collection are white stones. He has a total of 75 5 stones. How many of them are not white?Alberto Pardo Milan´s e Fractions
28. 28. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 15 1 Mom baked cookies and gave of them to Beth. Of the remaining 2 2 ones she gave to Seth. The rest, which was 4 cookies, she ate 3 herself. How many did she bake originally?Alberto Pardo Milan´s e Fractions
29. 29. Index Fractions Simplest form of a fraction Operations Exercises Exercises Exercise 16 1 This time Mom baked cookies again, and gave of them to Beth. 2 1 Of the remaining ones she gave to Seth. There were 2 cookies 3 left. How many did she bake this time?Alberto Pardo Milan´s e Fractions