fractions

Index Fractions Simplest form of a fraction Operations Exercises

Fractions

Matematicas 2o E.S.O.Alberto Pardo Milanes

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1 Fractions

2 Simplest form of a fraction

3 Operations

4 Exercises

Alberto Pardo Milanes Fractions


Fractions



Fractions

Parts of a fraction

A fraction is a number that represents a part of something.

Fractions are written in the forma

b, where a and b are integers,

and the number b is not zero. Reada

ba over b.

The number a is called numerator, and the number b is calleddenominator.

Example:13

25, 13 is the numerator and 25 is the denominator.

A proper fraction is a fraction that is less than one. A fractiongreater than one is called an improper fraction.

Examples:12

17is a proper fraction.

23

15is an improper fraction.



Fractions

Equivalent fractions

Equivalent fractions are different fractions that name the sameamount.

Example:

3

7=

6

14because they represent the same amount.

To find if two fractions are equivalent you have to check that thecross-products are equal.



Fractions

Amplify and reduce fractions

To find equivalent fractions, multiply or divide the numerator andthe denominator by the same number. If you multiply by the samenumber, you will amplify thefraction. If you divide by the same factor, you will reduce the fraction.

Examples:

• To amplify6

9we multiply the numerator and the denominator

by 10:6

9=

60

90.

• To reduce6

9we divide the numerator and the denomina-

tor by 3:6

9=

2

3.



Simplest form of a fraction




A lowest terms fraction is a fraction that can not be reducedanymore. To write a fraction in the simplest form find the lowestterms fraction. To reduce a fraction to the lowest terms fraction,we can use two methods:

• Divide the numerator and the denominator by the GreatestCommon Factor.

• Divide the numerator and the denominator by any commonfactor and keep dividing until they are relatively prime.




Examples:

To obtain the lowest terms fraction of70

105we can divide 70 and

105 by GCD(70, 105) = 35, so70

105=

2

3.

To reduce70

105to the lowest terms fraction we can divide by 5 and

keep dividing until there are no common factors but one70

105=

14

21=

2

3, (note 2 and 3 are relatively prime ).



Operations



Operations

Add and subtract

To add or subtract fractions with like denominators, add thenumerators and keep the same denominator. To add or subtractfractions with unlike denominators, first amplify these fractions toobtain like denominators (using the LCM or any multiple).Simplify, if possible.

Examples:4

15+

8

15=

12

15=

4

5.

To add3

15+1

6using the LCM:

3

15+1

6=

6

30+

5

30=

11

30. Because

LCM(15, 6) = 30.Using another common multiple of 15 and 6, for example 60:3

15+

1

6=

12

60+

10

60=

22

60=

11

30.



Operations

Multiply and divide

To multiply fractions, multiply the numerators and multiply thedenominators then simplify.

Example:12

5· 3

14=

12 · 35 · 14

=36

70=

18

35.

You can get the reciprocal of a fraction by switching its numeratorand denominator.

Example: The reciprocal of14

21is

21

14.

Todivide by a fraction, multiply by its reciprocal and simplify, if possible.

Examples:2

8:4

17=

2

8· 174

=2 · 178 · 4

=34

32=

17

16.



Exercises



Exercises

Exercise 1

Complete:

A half=

5

2=

Two thirds=

1

3=

A quarter=

3

4=

Three fifths=

1

5=

Two quarters=

1

7=

An/one eighth=

3

6=

One and a half=

41

3=

Two and a quarter=

42

5=

Two and four tenths=

11

12=



Exercises

Exercise 2

Write a fraction in the simplest form beside each of the followingsentences: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:



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?



Exercises

Exercise 4

George swims seven eighths miles and Mat swims ten twelfthsmiles. Who swims farther?



Exercises

Exercise 5

Compare these fractions using the least common denominator:2

−6,3

4,

9

15,7

5,−1

−3,−2

10,13

12.



Exercises

Exercise 6

Lance and Frank ate seven twelfths of a pizza. If Frank ate a thirdof the pizza, how much of the pizza did Lance eat?



Exercises

Exercise 7

Out of the 20 students, a quarter wear jeans, a fifth wear shortsand a tenth wear a skirt. How many students wear something else?



Exercises

Exercise 8

Tangram means seven boards of skill.The Tangram is a Chinesepuzzle consisting of seven flatpieces (called tans) which areput together to form differentshapes. Study the tans to theright that form a square. Theside of the square is 1 cm, sothe area is 1 cm2. Find thefractional value of each piece.



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 moneyis this fraction of the tank?



Exercises

Exercise 10

Peter cut six apples into quarters. How many pieces of apple did hehave?



Exercises

Exercise 11

Mike cleaned1

4of the yard that is 24 m2 in total . How many

square meters are left?



Exercises

Exercise 12

Thomas drunk3

5cup of milk, and now he has 24 cl left. How

many ml did the cup have originally?



Exercises

Exercise 13

Eric is reading a book with 195 pages. He read2

5of the pages

today. How many pages are left?



Exercises

Exercise 14

Of Paul’s stone collection1

5are white stones. He has a total of 75

stones. How many of them are not white?



Exercises

Exercise 15

Mom baked cookies and gave1

2of them to Beth. Of the remaining

ones she gave2

3to Seth. The rest, which was 4 cookies, she ate

herself. How many did she bake originally?



Exercises

Exercise 16

This time Mom baked cookies again, and gave1

2of them to Beth.

Of the remaining ones she gave1

3to Seth. There were 2 cookies

left. How many did she bake this time?


fractions

Technology

indexfractions simplest

improper fraction

fraction greater

simplest form nd

lowest terms fraction

dierent fractions

nd equivalent fractions

aalberto pardo milans