1. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Fractions
Matem´ticas 1o E.S.O.
a
Alberto Pardo Milan´s
e
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2. Indice Definition Proper fractions Equivalent fractions Operations Exercises
1 Definition
2 Proper fractions and improper fractions
3 Equivalent fractions
4 Operations
5 Exercises
Alberto Pardo Milan´s
e Fractions
3. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Definition
Alberto Pardo Milan´s
e Fractions
4. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Definition
What is 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 naturals,
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.
Example:
3
9
3 is the numerator,
9 is the denominator.
Alberto Pardo Milan´s
e Fractions
5. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Proper fractions and improper
fractions
Alberto Pardo Milan´s
e Fractions
6. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Proper fractions and improper fractions
Proper fraction
a
A proper fraction is a fraction such that< 1.
b
(The numerator is less than the denominator)
Improper fraction
a
A fraction > 1 is called an improper fraction.
b
(The numerator is greater than the denominator)
Examples:
2 9
is a proper fraction. is an improper fraction.
7 7
2 is less than 7 9 is greater than 7
Alberto Pardo Milan´s
e Fractions
7. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
Alberto Pardo Milan´s
e Fractions
8. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
Definition
Equivalent fractions are different fractions which represent the
same amount.
Example:
2 4
= because they represent the same amount.
7 14
2 4
7 14
Alberto Pardo Milan´s
e Fractions
9. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
Amplify and reduce fractions
To amplify a fraction we must multiply the numerator and the
denominator by any number.
To reduce a fraction we must divide the numerator and the
denominator by any common factor.
Examples:
2
To amplify we can multiply the numerator and the denominator
7
6
by 3 =⇒ .
21
15
To reduce we can divide the numerator and the denominator by
45
3
5 =⇒ .
9
Alberto Pardo Milan´s
e Fractions
10. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
Simplest form of a fraction
A lowest terms fraction is a fraction that can not be reduced
anymore. If you reduce a fraction to the lowest terms fraction you
find the simplest form of the fraction.
To reduce a fraction to the simplest form, we can use two
methods:
• Divide the numerator and the denominator by any common
factor and keep dividing until there are no common factors
(only 1).
• Divide the numerator and the denominator by their Greatest
Common Factor.
Alberto Pardo Milan´s
e Fractions
11. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
How to obtain the simplest form of a fraction
Method 1
• Divide the numerator and the denominator by any common
factor and keep dividing until there are no common factors
(only 1).
Example:
18
To reduce to the lowest terms fractions we can divide by 2 and
60
keep dividing until there are no common factors (only 1)
18 9 3
= = , and GCF (3, 10) = 1.
60 30 10
Alberto Pardo Milan´s
e Fractions
12. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Equivalent fractions
How to obtain the simplest form of a fraction
Method 2
• Divide the numerator and the denominator by their Greatest
Common Factor.
Example:
18
To reduce to the lowest terms fractions we can divide 18 and
60
18 3
60 by GCF (18, 60) = 6, so = .
60 10
Alberto Pardo Milan´s
e Fractions
13. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Operations
Alberto Pardo Milan´s
e Fractions
14. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Operations
Add and subtract
To add or subtract fractions with the same denominator, we have
to add the numerators and keep the same denominator.
2 1 3 4 2 2
Examples: + = . − = .
5 5 5 7 7 7
To add or subtract fractions with different denominators, first we
have to amplify these fractions changing the denominators to the
same number (using the LCM or any multiple of the
denominators).
3 1 11
Examples: + = , because
15 6 30
3 6 1 5
LCM (15, 6) = 30 = =
15 30 6 30
3 1 6 5 11
+ = + = .
15 6 30 30 30
Alberto Pardo Milan´s
e Fractions
15. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Operations
Multiply and divide
To multiply fractions, multiply the numerators and multiply the
denominators.
2 3 2·3 6 3
Example: · = = = .
5 4 5·4 20 10
You can get the reciprocal of a fraction by switching its numerator
and denominator.
4 7
Example: The reciprocal of is .
7 4
To divide by a fraction, multiply by its reciprocal.
1 4 1 7 1·7 7
Example: : = · = = .
8 7 8 4 8·4 32
Alberto Pardo Milan´s
e Fractions
16. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Alberto Pardo Milan´s
e Fractions
17. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
A half= =
5
2 An/one eighth=
=
2
1
A/one third= =
6
2 Three quarters=
=
3
3
A quarter= =
7
2 Forty over twenty-three=
=
4
35
Two fifths= =
75
Alberto Pardo Milan´s
e Fractions
18. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
19. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
20. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
21. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
22. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
23. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
24. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
25. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
1
A half=
2
2
=Two halves/ Two over two
2
1
A/one third=
3
2
=Two thirds / Two over three
3
1
A quarter=
4
2
=Two fourths / Two over four
4
2
Two fifths=
5
Alberto Pardo Milan´s
e Fractions
26. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
Alberto Pardo Milan´s
e Fractions
27. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
28. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
29. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
Alberto Pardo Milan´s
e Fractions
30. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
Alberto Pardo Milan´s
e Fractions
31. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
32. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
33. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 1
Complete:
4
=Four fifths / Four over five
5
1
An/one eighth=
8
1
=A sixth / One over six
6
3
Three quarters=
4
3
=Three sevenths / Three over seven
7
4
Forty over twenty-three=
23
35
=Thirty five over seventy-five
75
34. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 3 2 1
+ = − · =
5 5 20 4 5
2 5 1 3
+ = 2− : =
4 6 5 10
1 1 4 1 1 3
· + = + · =
3 5 15 2 3 5
Alberto Pardo Milan´s
e Fractions
35. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
Alberto Pardo Milan´s
e Fractions
36. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
Alberto Pardo Milan´s
e Fractions
37. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
Alberto Pardo Milan´s
e Fractions
38. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
Alberto Pardo Milan´s
e Fractions
39. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
40. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
41. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 2
Calculate the following and write down how we read the answer:
3 1 4
+ = four over five
5 5 5
2 5 6 10 16 4
+ = + = = four over three
4 6 12 12 12 3
1 1 4 1 3 4 1 7 7
· + = · + = · =
3 5 15 3 15 15 3 15 45
seven over forty-five
3 2 1 3 2 1
− · = − = one over twenty
20 4 5 20 20 20
1 3 10 1 3 9 3 90
2− : = − : = : = =6 six
5 10 5 5 10 5 10 15
1 1 3 3 2 3 5 3 15 1
+ · = + · = · = = A half
2 3 5 6 6 5 6 5 30 2
42. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 3
Fill in the blank with a number so the fractions are equivalent:
16
=
7 14
11
=
27 9
1
=
5 25
11
=
22 6
144 12
=
60
2 22
=
5
Alberto Pardo Milan´s
e Fractions
43. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 3
Fill in the blank with a number so the fractions are equivalent:
8 16
=
7 14
33 11
=
27 9
1 5
=
5 25
11 3
=
22 6
144 12
=
60 5
2 22
=
5 55
Alberto Pardo Milan´s
e Fractions
44. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 4
Order these fractions from least to greatest:
4 3 9 7 1 13
, , , , , .
6 2 15 5 3 6
Alberto Pardo Milan´s
e Fractions
48. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 60
= =
6 80
18 22
= =
45 44
Alberto Pardo Milan´s
e Fractions
49. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
50. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
51. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
52. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
53. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
54. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
55. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
56. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 5
Find the lowest terms fraction dividing the numerator and
denominator by common factors until the only common factor is 1:
14 7
= 60 30 3
6 6 = =
80 40 4
dividing by
dividing by
2
2 and 10
18 6 2
= = 22 11 1
45 15 5 = =
44 22 2
dividing by
dividing by
2 and 3
2 and 11
Alberto Pardo Milan´s
e Fractions
57. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 6
Find the lowest terms fraction using prime decomposition of the
numerator and denominator:
18
=
30
63
=
42
14
=
21
22
=
33
Alberto Pardo Milan´s
e Fractions
63. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10
=
6
30
=
60
18
=
24
23
=
46
Alberto Pardo Milan´s
e Fractions
64. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10 5
= dividing by GCF(10,6)=2
6 3
30 1
= dividing by GCF(30,60)=30
60 2
18 3
= dividing by GCF(18,24)=6
24 4
23 1
= dividing by GCF(23,46)=23
46 2
65. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10 5
= dividing by GCF(10,6)=2
6 3
30 1
= dividing by GCF(30,60)=30
60 2
18 3
= dividing by GCF(18,24)=6
24 4
23 1
= dividing by GCF(23,46)=23
46 2
66. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10 5
= dividing by GCF(10,6)=2
6 3
30 1
= dividing by GCF(30,60)=30
60 2
18 3
= dividing by GCF(18,24)=6
24 4
23 1
= dividing by GCF(23,46)=23
46 2
Alberto Pardo Milan´s
e Fractions
67. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10 5
= dividing by GCF(10,6)=2
6 3
30 1
= dividing by GCF(30,60)=30
60 2
18 3
= dividing by GCF(18,24)=6
24 4
23 1
= dividing by GCF(23,46)=23
46 2
Alberto Pardo Milan´s
e Fractions
68. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 7
Find the lowest terms fraction dividing the numerator and
denominator by the GCF:
10 5
= dividing by GCF(10,6)=2
6 3
30 1
= dividing by GCF(30,60)=30
60 2
18 3
= dividing by GCF(18,24)=6
24 4
23 1
= dividing by GCF(23,46)=23
46 2
Alberto Pardo Milan´s
e Fractions
69. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 8
12 11
Alice runs miles on Monday. On Wednesday, she runs miles.
5 6
How many miles does Alice run on both days?
Alberto Pardo Milan´s
e Fractions
70. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 8
12 11
Alice runs miles on Monday. On Wednesday, she runs miles.
5 6
How many miles does Alice run on both days?
Data: She runs:
12 11
m on Monday. m on Wednesday.
5 6
12 11 72 55
+ = + =
5 6 30 30
122 61
= =
30 15
Using: GCF (5, 6) = 30 and
GCF (30, 122) = 2 Answer: Alice
61
runs miles.
15
Alberto Pardo Milan´s
e Fractions
71. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 8
12 11
Alice runs miles on Monday. On Wednesday, she runs miles.
5 6
How many miles does Alice run on both days?
Data: She runs:
12 11
m on Monday. m on Wednesday.
5 6
12 11 72 55
+ = + =
5 6 30 30
122 61
= =
30 15
Using: GCF (5, 6) = 30 and
GCF (30, 122) = 2 Answer: Alice
61
runs miles.
15
Alberto Pardo Milan´s
e Fractions
72. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 8
12 11
Alice runs miles on Monday. On Wednesday, she runs miles.
5 6
How many miles does Alice run on both days?
Data: She runs:
12 11
m on Monday. m on Wednesday.
5 6
12 11 72 55
+ = + =
5 6 30 30
122 61
= =
30 15
Using: GCF (5, 6) = 30 and
GCF (30, 122) = 2 Answer: Alice
61
runs miles.
15
Alberto Pardo Milan´s
e Fractions
73. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 9
Find:
1 My soccer team wins 3 games and lost 5.
Write down a fraction of the games they win:
3
2 Tim sells of his cookies, and now he has 14 left.
5
How many did he have originally?
1
3 Of Tim’s stone collection are white stones. He has total of
5
75 stones.
How many of them are not white?
Alberto Pardo Milan´s
e Fractions
74. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 9
Find:
1 My soccer team wins 3 games and lost 5.
3
Write down a fraction of the games they win:
8
3
2 Tim sells of his cookies, and now he has 14 left.
5
How many did he have originally?
2 1
of them all is 14 , so of them all is 7, so He had
5 5
originally 35.
1
3 Of Tim’s stone collection are white stones. He has total of
5
75 stones. How many of them are not white?
1 1 75
of 75 = · 75 = = 15.
5 5 5
75 − 15 = 60 60 of the stones are not white.
75. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 9
Find:
1 My soccer team wins 3 games and lost 5.
3
Write down a fraction of the games they win:
8
3
2 Tim sells of his cookies, and now he has 14 left.
5
How many did he have originally?
2 1
of them all is 14 , so of them all is 7, so He had
5 5
originally 35.
1
3 Of Tim’s stone collection are white stones. He has total of
5
75 stones. How many of them are not white?
1 1 75
of 75 = · 75 = = 15.
5 5 5
75 − 15 = 60 60 of the stones are not white.
76. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 9
Find:
1 My soccer team wins 3 games and lost 5.
3
Write down a fraction of the games they win:
8
3
2 Tim sells of his cookies, and now he has 14 left.
5
How many did he have originally?
2 1
of them all is 14 , so of them all is 7, so He had
5 5
originally 35.
1
3 Of Tim’s stone collection are white stones. He has total of
5
75 stones. How many of them are not white?
1 1 75
of 75 = · 75 = = 15.
5 5 5
75 − 15 = 60 60 of the stones are not white.
77. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 9
Find:
1 My soccer team wins 3 games and lost 5.
3
Write down a fraction of the games they win:
8
3
2 Tim sells of his cookies, and now he has 14 left.
5
How many did he have originally?
2 1
of them all is 14 , so of them all is 7, so He had
5 5
originally 35.
1
3 Of Tim’s stone collection are white stones. He has total of
5
75 stones. How many of them are not white?
1 1 75
of 75 = · 75 = = 15.
5 5 5
75 − 15 = 60 60 of the stones are not white.
78. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 10
When you write music in the stave you must write signs called
notes, and you need to say how long a note is. The note value is a
code which determines the note‘s duration. The length of a whole
note is equal to four beats (in 4/4 time), half notes are played
for one half the duration of the whole note, crotchet are played
for one quarter the duration of the whole note, quavers are each
played for one eighth the duration of the whole note, semiquaver
are each played for one sixteenth the duration of the whole
note,...
In this piece from Tchaikovsky‘s The Nutcracker draw a vertical
line every two beats.
Alberto Pardo Milan´s
e Fractions
79. Indice Definition Proper fractions Equivalent fractions Operations Exercises
Exercises
Exercise 10
When you write music in the stave you must write signs called
notes, and you need to say how long a note is. The note value is a
code which determines the note‘s duration. The length of a whole
note is equal to four beats (in 4/4 time), half notes are played
for one half the duration of the whole note, crotchet are played
for one quarter the duration of the whole note, quavers are each
played for one eighth the duration of the whole note, semiquaver
are each played for one sixteenth the duration of the whole
note,...
In this piece from Tchaikovsky‘s The Nutcracker draw a vertical
line every two beats.
Alberto Pardo Milan´s
e Fractions