Post on 17-Jan-2015
description
Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Matematicas 2o E.S.O.Alberto Pardo Milanes
-
Index Fractions Simplest form of a fraction Operations Exercises
1 Fractions
2 Simplest form of a fraction
3 Operations
4 Exercises
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Alberto Pardo Milanes Fractions
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.
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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Simplest form of a fraction
Alberto Pardo Milanes Fractions
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 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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Simplest form of a fraction
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 ).
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Operations
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations 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=
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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:
Alberto Pardo Milanes Fractions
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 Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 4
George swims seven eighths miles and Mat swims ten twelfthsmiles. Who swims farther?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
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 thirdof the pizza, how much of the pizza did Lance eat?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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.
Alberto Pardo Milanes Fractions
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 moneyis this fraction of the tank?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 10
Peter cut six apples into quarters. How many pieces of apple did hehave?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 11
Mike cleaned1
4of the yard that is 24 m2 in total . How many
square meters are left?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 12
Thomas drunk3
5cup of milk, and now he has 24 cl left. How
many ml did the cup have originally?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 13
Eric is reading a book with 195 pages. He read2
5of the pages
today. How many pages are left?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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?
Alberto Pardo Milanes Fractions
Index Fractions Simplest form of a fraction Operations Exercises
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?
Alberto Pardo Milanes Fractions