all about fractions packet

8/13/2019 All about Fractions Packet

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Fractions Packe

Created by MLC @ 2009 page 2 of 42

Intro to Fractions

Reading FractionsFractions are parts. We use them to write and work with amounts that are lessthan a whole number (one) but more than zero. The form of a fraction is onenumber over another, separated by a fraction (divide) line.

i.e.95and,

43,

21

These are fractions. Each of the two numbers tells certain information aboutthe fraction (partial number). The bottom number (denominator) tells how manyparts the whole (one) was divided into. The top number (numerator) tells howmany of the parts to count.

2

1says, Count one of two equal ports.

4

3says, Count three of four equal parts.

9

5says, Count five of nine equal parts.

Fractions can be used to stand for information about wholes and their parts:EX. A class of 20 students had 6 people absent one day. 6 absentees are

part of a whole class of 20 people.20

6 represents the fraction of people

absent.EX. A Goodbar candy breaks up into 16 small sections. If someone ate 5

of those sections, that person ate16

5of the Goodbar.


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Fractions Packe


Exercise 1 Write fractions that tell the following information:(answers on page 39)

1. Count two of five equal parts2. Count one of four equal parts3. Count eleven of twelve equal parts4. Count three of five equal parts5. Count twenty of fifty equal parts6. Its 25 miles to Grammas. We have already driven 11 miles. What

fraction of the way have we driven?

7. A pizza was cut into twelve slices. Seven were eaten. What fraction ofthe pizza was eaten?

8. There are 24 students in a class. 8 have passed the fractions test.What fraction of the students have passed fractions?

The Fraction Form of OneBecause fractions show how many parts the whole has been divided into andhow many of the parts to count, the form also hints at the number of partsneeded to make up the whole thing. If the bottom number (denominator) is

five, we need 5 parts to make a whole: 15

5. If the denominator is 18, we

need 18 parts to make a whole of 18 parts: 118

18. Any fraction whose top

and bottom numbers are the same is equal to 1.

Example: 166,1

11111,

1001001,

44,1

22


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Fractions Packe


Complementary FractionsFractions tell us how many parts are in a whole and how many parts to count.The form also tells us how many parts have not been counted (the complement).The complement completes the whole and gives opposite information that canbe very useful.

4

3 says, Count 3 of 4 equal parts. That means 1 of the 4 was not counted and

is somehow different from the original 3.

4

3implies another

4

1(its complement). Together,

4

4make

4

1and

4

3, the whole

thing.

8

5 says, Count 5 of 8 equal parts. That means 3 of the 8 parts have not been

counted, which implies another8

3, the complement. Together,

8

5and

8

3make

8

8,

which is equal to one.

Complementary Situations

Its 8 miles to town, We have driven 5 miles. Thats8

5of the way, but we still

have 3 miles to go to get there or8

3of the way.

8

5+

8

3=

8

8= 1 (1 is all the way to town).

A pizza was cut into 12 pieces. 7 were eaten12

7. That means there are 5 slices

left or12

5of the pizza.

12

7+

12

5 =

12

12= 1 (the whole pizza).

Mary had 10 dollars. She spent 5 dollars on gas, 1 dollar on parking, and 3dollars on lunch. In fraction form, how much money does she have left?

Gas = 105

, parking = 101

, lunch = 103

10

5+

10

1+

10

3=

10

9;

10

1is the complement (the leftover money)

Altogether it totals10

10 or all of the money.


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Fractions Packe


Exercise 2 (answers on page 39)Write the complements to answer the following questions:

1. A cake had 16 slices. 5 were eaten. What fraction of the cake wasleft?

2. There are 20 people in our class. 11 are women. What part of the classare men?

3. It is 25 miles to grandmas house. We have driven 11 miles already.What fraction of the way do we have left to go?

4. There are 36 cookies in the jar. 10 are Oreos. What fraction of thecookies are not Oreos?

Reducing FractionsIf I had 20 dollars and spent 10 dollars on a CD, its easy to see Ive spent half

of my money. It must be that2

1

20

10. Whenever the number of the part (top)

and the number of the whole (bottom) have the same relationship betweenthem that a pair of smaller numbers have, you should always give the smaller

pair answer. 2 is half of 4. 5 is half of 10.2

1is the reduced form of

10

5and

4

2and 20

10and many other fractions.

A fraction should be reduced any time both the top and bottom number can bedivided by the same smaller number. This way you can be sure the fraction is assimple as it can be.

10

5 both 5 and 10 can be divided by 5

2

1

510

55

10

5

2

1describes the same number relationship that

10

5 did, but with smaller

numbers.2


10

5.

8

6 both 6 and 8 can be divided by 2.

4

3

28

26

8

6


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Fractions Packe


4


8

6.

When you divide both the top and bottom numbers of a fraction by the samenumber, you are dividing by a form of one so the value of the fraction doesntchange, only the size of the numbers used to express it.

8

6

216

212

16

12 These numbers are smaller but they can go lower

because both 6 and 8 can be divided by 2 again.4

3

28

26

8

6

4

3

312

39

12

9

224

218

24

18

7

3

963

927

63

27or

7

3

321

39

21

9

363

327

63

27

Exercise 3 (answers on page 39)

Try these. Keep dividing until you cant divide anymore.1.

8

6= 2.

15

12= 3.

18

14=

4.10

8= 5.

12

6= 6.

24

16=

Good knowledge of times tables will help you see the dividers you need to

reduce fractions.Here are some hints you can use that will help, too.Hint 1

If the top and bottom numbers are both even, use2

2.

Hint 2

If the sum of the digits is divisible by 3 then use3

3.

231

111 looks impossible but note that 111 (1+1+1) adds up to three and 231 (2+3+1)

adds up to 6. Both 3 and 6 divide by 3 and so will both these numbers:

77

37

3231

3111

231

111

The new fraction doesnt look too simple, but it is smaller than when we first started.


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Fractions Packe


Hint 3

If the 2 numbers of the fraction end in 0 and/or 5, you can divide by5

5.

14

9

570

545

70

45

Hint 4

If both numbers end in zeros, you can cancel the zeros in pairs, one from the

top and one from the bottom. This is the same as dividing them by10

10for each

cancelled pair.

25

2

250

24

50

4

50000

4000

50000

4000

Hint 5

If you have tried to cut the fraction by2

2,3

3,5

5and gotten nowhere, you

should try to see if the top number divides into the bottom one evenly. For

69

23, none of the other hints help here, but 69 23 = 3. This means you can

reduce by23

23.

3

1

2369

2323

69

23

For more help on reducing fractions, see page 13

Exercise 4 (answers on page 39)Directions: Reduce these fractions to lowest terms

1.18

14 2.

100

80 3.

36

18 4.

5000

400

5.2520 6.

3627 7.

4540 8.

8163

9.12

9 10.

85

60 11.

51

17 12.

75

50


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Fractions Packe


Higher EquivalentsThere are good reasons for knowing how to build fractions up to a larger form.It is exactly the opposite of what we do in reducing. If reducing is done bydivision, it makes sense that building up should be done by multiplication.

4

2

22

21

2

1

15

9

35

33

5

3

54

48

69

68

9

8

A fraction can be built up to an equivalent form by multiplying by any form of

one, any number over itself.

18

12

63

62

3

2

12

8

43

42

3

2

33

22

113

2

3

2 11

1510

5352

32

9

6

33

22

12

8

18

12

3

2 All are forms of

3

2; all will reduce to

3

2

Comparing FractionsSometimes it is necessary to compare the size of fractions to see which islarger or smaller, or if the two are equal. Sometimes several fractions must beplaced in order of size. Unless fractions have the same bottom number(denominator) and thus parts of the same size, you cant know for certain which

is larger or if they are equal.

Which is larger3

2or

6

5? Who knows? A ruler might help, but rulers arent

usually graduated in thirds or sixths. Did you notice that if 3 were doubled, itwould be 6?


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Fractions Packe


So build up3

2by

2

2 ;

6

4

23

22

3

2

Then its easy to see that6

5 is larger because it counts more sixth parts than

6

4, so

6

4

2.4

1 2.

20

9 2.

5

4 2.

5

4 2. >

3. 12

11

3. 25

14

3. 9

7

3. 2

1

3.


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Fractions Packe


Answer to Multiplication and Division of Fractions

Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5

1.12

1 1.

8

52 1.

5

4 1.

9

42 1. 12 boards

2.5

2 2.

5

312 2.

5

41 2.

9

13 2. 26 revolutions

3. 116

3. 81

8 3. 3

3. 1916

2 3. 41

41 turns

4.3

2 4.

16

11 4.

7

42 4.

28

9 4. 15 books

5.15

1 5.

32

272 5.

5

22 5.

5

313 5. 36 yards

6.28

15 6.

3

15 6.

3

2 6. 10 6. 8

527 pounds

7.72

35 7.

8

59 7.

2

13 7.

11

44 7.

4

12 pounds

8. 2 8. 14 8.5

11 8.

14

131 8. 250 sheets

9. 5 9. 60 9.3

2 9.

32

151 9. 520 pages

10. 5 10.54

253 10.

2

11 10. 1 10. 8 pizzas

11. 4 11. 60 11.9

7 11.

3

21

12.4

3 12.

3

210 12.

81

64 12.

79

211

13.26

21 13.

3

15

14.9

2 14. 12

15.8

3 15.

16

3

16.51

46

17.24

5

18.20

9


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Fractions Packe


Answers to Addition and Subtraction of Fractions

Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6

1) 6 1) 5 1)5

11 1)7

5 1)10

916 1)8

14 inches

2) 15 2) 10 2)4

11 2)7

5 2)21

22 2)8

71 inches

3) 8 3) 10 3)3

12 3)3

2 3)24

1317 3)4

33 teaspoons

4) 12 4) 9 4)3

21 4)20

17 4)5

116 4)12

118 feet

5) 35 5) 8 5) 2 5)6

11 5)

4

11 5)

8

5

6) 9 6) 156)

2

11 6)

10

31 6)

8

13 6)

60

721 miles

7) 4 7) 1 7) 5 7) 17)

6

52 7)

4

35 ounces

8) 40 8) 38)

3

21 8)

24

51 8)

8

312 8)

3

117 ounces

9) 30 9) 49)

4

34 9)

9

41 9)

5

38 9)

16

13104 feet

10) 15 10) 1 10)5

34 10)4

1 10)12

52 10)4

120 ft.

11) 6 11) 1 11) 6 11)15

4 11)21

103

12) 16 12) 1 12)5

23 12)24

5 12)7

5

13) 24 13) 10 13)9

14 13)6

1 13)2

114

14) 42 14) 1 14)2

13 14)22

7 14)9

811

15) 120 15) 2 15)9

25 15)12

1 15)5

1154

16) 3 16) 2126 16) 61 16) 326

17) 8 17)2

18 17)12

7 17)8

11

18) 10 18) 7 18)30

17 18)5

36

19) 1 19)5

116 19)5

3 19)3

27

20) 1 20)5

37 20)30

23 20)6

14

21) 1 21)3

117 21)56

11 21)8

595

22) 1

23)9

2

24)8

31

25)42

11

26)5

1

27)39

32


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Answer to Ordering Fractions

Exercise A

1.4

3,

3

2,

7

3

2.14

3,

7

1,

28

3

Exercise B

1.22

13,

11

8,

4

3

2.16

5,

64

35,

8

7

all about fractions packet

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