Download UNIT 7: FRACTIONS I 7.1 What are fractions? *A fraction is used to e

UNIT 7: FRACTIONS I
7.1 What are fractions?
*A fraction is used to express part of a whole that has been divided into
equal parts.
5
Example:
Numerator: expresses the number of parts we take.
8
Denominator: expresses the number of equal parts in
the whole group.
Reading fractions
We use the cardinals to name the numerator and the ordinals for the
denominator with two exceptions when the denominators are 2 and 4, for
denominator larger than 10 we say “over” and do not use ordinal.
Examples: a)
1
one half
2
b)
Five thirds
c)
Three quarters
f)
Three eighths
d)
Two fifths
e)
Seven sixths
g)
Five ninths
h)
Two tenths
Exercise: Write down how these fractions are read:
3
1
3
6
3
1
1
a)
b)
c)
d)
e)
f)
g)
2
4
10
7
5
3
8
3
6
5
h)
i)
j)
14
37
129
* A Fraction is a division: a fraction can be expressed as a decimal number.
1
Example: = 0,5
2
It is very useful to compare fractions with different denominators.
Exercise: Divide and express each fraction as a decimal number. Then
compare them( > greater than or < less than).
3
5
7
4
7
a)
b)
c)
d)
e)
4
8
3
9
5
7.2. A fraction of an amount: Fraction as an operator
Fraction are operators that act on numbers and transform them. Example:
4
Finding of 50 consists of: Dividing 50 into five equal parts and taking 4 of
5
those parts.
Like this: 50: 5= 10 ( each part is 10)
10 X4= 40 ( we take 4 of these
parts)
4 x 50 200
4
of 50 

 40
Or like this
5
5
5
7.3 Equivalent fractions
Two fractions are equivalent when they express the same part of a whole.
Equivalent fractions have the same numeric value.
1
2
4
Example: = =
=
2
4
8
How to Know if two fractions are equivalent?
In order to know if two fractions are equivalent, you multiply:
The numerator of the first one by the denominator of the second one.
The denominator of the first one by the numerator of the second one.
If the products are the same, they are equivalent. If they aren’t, they are
not equivalent.
1
2
Example: and are equivalent, because 1x4= 2x2=4
2
4
2
3
Exercise: Are
and equivalent fractions?
3
4
Exercise: Find out the unknown number
1
2
x
a) =
b)
= 20
2
x
12
24
c)
3
= 21
x
14
How to find equivalent fractions?
To find fractions equivalent to another given fraction, the numerator and
the denominator must be multiplied( or divided) by the same number.
We can find an infinite number of equivalent fractions.
3
Example: List three fractions equivalent to
4
3x2 6
3 x3 9
3 x 4 12



4 x2 8
4 x3 12
4 x 4 16
so
3
= 6
4
8
=
9
= 12
12
16
Exercise : Write four fractions equivalent to
5
7
7.4. Simplification of fractions:
Simplifying a fraction means we replace it with another fraction that is
equivalent to it, expressing it in the lowest terms.
To simplify a fraction we divide the numerator and the denominator by the
same number.
A fraction that can’t be simplified is called an irreducible fraction.
3
3:3 1
1

Example: Simplify
is an irreducible fraction.
12
12 : 3 4
4
Exercise: Simplify until you have an irreducible fraction:
15
10
18
30
8
12
12
a)
b)
c)
d)
e)
f)
g)
20
24
60
60
20
30
36
h)
18
180
Exercises
1.
1. Change these fractions to decimal numbers:
3
8
a)
b)
1
2
c)
1
5
d)
2
5
e)
2
7
f)
5
6
g)
5
10
h)
3
100
2. Compare these pairs of fractions:
a)
6
7
and
11
13
b)
3
5
and
4
7
c)
2
4
and
3
6
d)
1
5
and
2
9
3. Write these fractions in order from least to greatest:
a)
2
5
3 3
5 7
2
7
1 4
3 6
b)
2
7
5
10
4. Francisco bought a television that had to be paid for in five instalments. He has paid
three. Alba bought a television that had to be paid for in eight instalments and she has
paid four. Who has paid more so far?
5.Calculate:
a)
3
of 20
5
b)
2
of 20
5
c)
1
of 40
8
c)
3
of 21
7
d)
5
of 40
8
d)
5
of 40
8
e)
1
2
of 12 f)
of 12
3
3
6.Calculate:
a)
2
of 15
5
b)
3
of 12
4
g)
4
de 30
5
h)
3
de 85
5
i)
3
de 24
8
j)
1
de 340
4
e)
2
2
of 30 f)
of 72
3
3
K)
3
2
de 715 l)
de 9
5
3
7. A kilo of steak fillets costs 12€. What is the price of three quarters of a kilo?
8. Of the twelve flowers in a vase, one sixth are pink. How many pink flowers are there
in the vase?
9. Of the 15 girls in the park one third are wearing a red skirt. How many girls in the c
park are wearing a red skirt?
10. A quarter kilo of ham costs 8€. How much does one kilo cost?
11. Three quarters of a kilo of salami cost 6 €. What’s the price of one kilo?
12. Cross multiply to find out if these fractions are equivalent:
2
6
4
6
and
b)
and
5
15
6
9
4
8
1
3
f)
and
g)
and
5
10
2
4
a)
1
5
and
2
9
c)
d)
6
9
and
8
11
e)
2
5
and
3
7
13. Write three equivalent fractions for each of the following:
1
4
a)
3
5
b)
15
20
c)
18
24
d)
21
49
e)
14. Search for couples of equivalent fractions:
2
5
1
3
5
9
6
8
5
15
9
12
5
7
10
18
15.Luis cut his pie into 6 pieces and ate 2. Raquel cut her pie into 9 pieces and ate 3.
Who has eaten a larger portion?
16. Find out the unknown number:
a)
2 4
=
5
x
b)
4
8
=
x 12
c)
x 5
=
6 10
d)
3
20
=
x
21
e)
12 16
=
x 20
f)
2 4
=
x 10
17. Simplify until you have an irreducible fraction:
a)
12
15
b)
10
30
c)
21
28
d)
6
8
e)
5
15
f)
9
12
g)
24
36
h)
10
4
i)
18
6
18. Simplify until you have an irreducible fraction:
a)
30
45
b)
56
80
c)
20
60
d)
165
e)
330
22
33
19. Victor spends 540 € to pay for his rent which is three tenths of his salary. How
much does he earn?
20. The library has 630 borrowed books which makes two fifths of the total.What’s
the total number of books in the library?
21. Marta has gone for walk and has covered three quarters of the route. If she still
has 2 km to walk, how long is the total route?
22. In one phase of a cycling race, a cyclist has covered
are 30 km left. How long is the total route?
3
of the total route. If there
5