Download Fractions Overview Fraction Definitions Equivalent fractions

Overview
This presentation will cover:
Fractions
The Learning Centre
Fraction Definitions
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A fraction represents a part of a whole or, more generally, any
number of equal parts.
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The denominator (the number on the bottom of the
fraction) tells us how many parts the object is divided into.
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The numerator (the part on the top of the fraction) tells us
how many of these parts we have.
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An improper fraction is a fraction where the numerator is
3
larger than the denominator, for example, .
2
A mixed number has a whole number with a fraction, for
1
example 1 .
2
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Fraction definitions;
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Equivalent fractions;
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Mixed numbers and improper fractions;
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Addition and subtraction of fractions;
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Multiplication of fractions; and
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Division of fractions.
Equivalent fractions
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Equivalent fractions have different names for the same
1
2
value, for example is equivalent to .
2
4
Equivalent fractions can be made by multiplying or dividing
both the numerator and the denominator by the same number.
The process of dividing the numerator and denominator by
the same number is called simplifying fractions, for example
6
1
is equalent to , which is in simplest form.
12
2
Equivalent fractions: Exercise
Equivalent fractions: Answers
1.
Write equivalent fraction for each of the following by making the
new denominator the number given in the brackets.
2
1. (9)
3
4
2. (20)
5
−3
3.
(8)
4
−2
4.
(28)
7
7
5.
(60)
12
Equivalent fractions: exercise
2.
4
4×4
16
=
=
.
5
5×4
20
3.
−3
−3 × 2
−6
=
=
.
4
4×2
8
4.
−2
−2 × 4
−8
=
=
.
7
7×4
28
5.
7
7×5
35
=
=
.
12
12 × 5
60
Equivalent fractions: Answers
1.
Simplify the following fractions, giving your answer in its simplest
form.
9
1.
15
−3
2.
18
8
3.
10
−12
4.
16
30
5.
40
2 000
6.
6 000
2
2×3
6
=
= .
3
3×3
9
2.
3.
4.
5.
9
9 3
3
=
= .
5
15 15
5
(Dividing by 3)
−1
−3 −3
−1
=
=
.
6
18
18
6
(Dividing by 3)
8
8 4
4
=
= .
5
10 10
5
(Dividing by 2)
−3
−12 −12
−3
=
=
.
4
16
16
4
30
30
3
=
=
40
40
4
(Dividing by 4)
(We are dividing by 10 but in practice we just cancel the zeros.)
6.
2, 000
2, 000
2 1
1
=
= 3 =
6, 000
6, 000
6
3
(Cancel three zeros on the top
and three zeros on the bottom.)
Mixed numbers and improper fractions
Mixed numbers and improper fractions
1.
Express these improper fractions as mixed numbers.
5
1.
3
45
2.
20
−16
3.
7
40
4.
25
−35
5.
14
Mixed numbers and improper fractions
5
2
=1 .
3
3
2.
9
45
9
1
= =2 .
4
20
4
4
3.
−16
2
= −2 .
7
7
4.
8
40
8
3
= =1 .
5
25
5
5
5.
−5
−35
−5
1
=
= −2 .
2
14
2
2
Mixed numbers and improper fractions
1.
Express these mixed numbers as improper fractions.
1
1. 3
4
2
2. 9
11
2
3. −5
3
5
4. 102
12
2
5. −21
5
2.
1
3×4+1
13
3 =
=
.
4
4
4
2
9 × 11 + 2
101
=
=
.
11
11
11
2
5×3+2
17
−5 = −
=− .
3
3
3
9
3.
4.
5
102 × 12 + 5
1, 229
=
=
.
12
12
12
2
21 × 5 + 2
107
−21 = −
=−
.
5
5
5
102
5.
Addition and Subtraction of Fractions
Adding fractions: Example
For example:
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To add or subtract fractions they need to have the same
denominator.
=
2×8 3×5
+
5×8 8×5
When adding mixed numbers (whole number with a fraction),
you add the whole numbers, then the fractions.
=
16 15
+
40 40
When subtracting mixed numbers, convert to improper
fractions, before doing the subtraction.
=
16 + 15
40
=
31
40
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Remember that fractions should always be left in lowest form.
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2 3
+
5 8
Addition of fraction: mixed number example
=
=
=
=
=
17 19
+
8 5
17 8
19 5
×
+
×
5
8
8
5
136 95
+
40
40
231
40
31
5 .
40
Remember to check if it is in simplest form.
Yes it is.
Subtraction of fractions: example
Calculate:
2
3
3 +2
5
8
find the common denominator: 5 × 8 = 40,
1 7
−
6 9
Find the lowest common denominator: 18.
Now calculate:
1 7
1 3
7 2
−
=
×
−
×
6 9
6 3
9 2
3
14
=
−
18 18
3 − 14
=
18
11
= −
.
18
Multiplication of Fractions
Fractions — Multiplication and division
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To multiply to fractions, multiply the numerators and the
denominators.
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Common factors can be cancelled either during the
multiplication or at the end to give answer in simplest form.
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To multiply mixed numbers, convert them to improper
fractions first.
Multiplication of fractions: example
Calculate:
7 16
1. × ;
8 21
1
1
2. −3 × −7 ;
3
2
Multiplication of fractions: example
For example:
7 16
×
8 21
=
=
=
=
7 × 16
8 × 21
2
7 1 × 16
3
8 1 × 21
1×2
1×3
2
.
3
1
1
−3 × −7
3
2
10
15
×−
3
2
5 × −
5
−
10
15
=
3 1 × 2 1
−5 × −5
=
1×1
= 25 .
= −
Division of Fractions
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Dividing by a fraction is the same as multiplying by its
reciprocal (fraction turned upside down)
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If dividing with mixed numbers, remember to convert to
improper fractions first.
Exercise
Evaluate the following without a calculator.
3
9
1. ÷
4 20
21 35
2. − ÷
25 30
2
7
3. 4 ÷ 2
5
10
5
1
4. 7 ÷ −3
8
2
1
3
5. −2 ÷ −
4
8
Check your answers on the calculator.
Division of fractions: example
3 2
÷
4 3
=
3
9
÷
4 20
=
3 3
×
4 2
3×3
=
4×2
9
=
8
1
= 1 .
8
Answers
1.
=
=
=
=
3 20
×
4
9
5
3 1 × 20
4 1 × 9 3
1×5
1×3
5
3
2
1 .
3
Answers (cont)
Answers (cont)
3.
2
7
4 ÷2
5
10
2.
−21 35
÷
25
30
=
=
−21 30
×
25
35
−3 × 6
−21
30
=
=
=
5 1
25 × 35
−3 × 6
=
25
18
= − .
25
=
=
=
Answers (cont)
22 27
÷
5
10
22 10
×
5
27
2
22 × 10
5 1 × 27
22 × 2
1 × 27
44
27
17
1 .
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Answers (cont)
4.
5
1
7 ÷ −3
8
2
=
=
=
=
=
=
61 −7
÷
8
2
61 −2
×
8
7
61 × −2 −1
8 4 × 7
61 × −1
4×7
−61
28
5
−2 .
28
5.
1 −3
−2 ÷
4
8
=
=
=
=
=
−9 −3
÷
4
8
−9 −8
×
4
3
−3
−2
−9
×
−8
4 1 × 3 1
−3 × −2
1×1
6.