Workshop: Numeracy 2
Topics Covered:
• Fractions.
• Percentages.
• Ratios.
by Dr.I.Namestnikova
namestnikova@brunel.ac.uk
Question
Write
Write
Write
Solution
7 17
,
10 10
7
2
3
4
0.7,
7
=
2
3
=
4
as a decimal
as a decimal
as a decimal
Write 1.3,
0.9,
0.01,
Write 1.234 as a fraction.
Calculate
7
8
×
3
6
7
8
Calculate ÷
3
6
3
Subtract from 2.5
4
0.15 as a fraction.
1.7
7×5
35
=
= 3.5
2×5
10
3 × 25
75
=
= 0.75
2 × 25
100
9
13
,
1
,
10
10
100
1234
617
=
1000
500
7
8
×
=
7×8
15
,
=
100
=
7×4
3
20
=
28
3
6
3×6
3×3
9
7
8
7
6
7×6
7
÷ = × =
=
3
6
3
8
3×8
4
3
2.5 − = 2.5 − 0.75 = 1.75
4
Percentages
A percentage is a fraction whose denominator is
Symbol % presents a percentage.
• Convert 48% to vulgar fraction and decimal fraction.
12
48
=
Vulgar fraction 48% =
100
25
48
= 0.48
Decimal fraction 48% =
100
• Convert 7.5% to vulgar fraction and decimal fraction.
15
15
3
Vulgar fraction 7.5% = 2 =
=
100
200
40
7.5
Decimal fraction 7.5% =
= 0.075
100
100
N Express
2
5
as a percentage.
2
5
=
2
5
20
×
20
=
40
100
= 40%
N Express 38% as a decimal.
38% =
38
100
= 0.38
1
N Convert 5 % to vulgar fraction and decimal fraction.
3
5 13
16
4
1
Vulgar fraction 5 % =
=
=
3
100
300
75
1
16
Decimal fraction 5 % =
= 0.05333...
3
300
N Calculate 27% of 90.
27
27
× 90 =
× 9 = 24.3
100
10
13
N Express
as a percentage. (65%)
20
9
as a percentage (90%)
N Express
10
N Calculate 23% of 124 (28.52)
N Express 35.6% as a decimal. (0.356)
Discount and prise increases are often expressed as percentages.
price change
Step 1. Construct a fraction
old price
Step 2. Convert to a percentage.
• If the price of an item goes up from £400 to £492 what is the percentage increase
price change
× 100% =
old price
492 − 400
92
× 100% =
× 100% = 23%
400
400
• If the price of an item is £100 and it goes down by 32% discount, what is the new price?
discount
new price£100
− £32 = £68
= 32% of old price
32
× old price
=
100
= £32
• If an item which usually sells for £300 is on sale at 32% discount, what is the sale price?
discount
sale price
= 32% of old price
32
=
× old price
100
= £96
= £300 − £96
32% discount ⇒
Sale price is 100% − 32% = 68%
or
sale price
= 68% of old price
68
=
× 300
100
= £204
= £204
• A person earns £500 a week, then received 5% increase. Calculate the new weekly wage.
• A person earns £300 a week, then received 3% increase. Calculate the new weekly wage.
Ratio
Ratio is a fundamental concept that has to be understood to use mathematics in science, engineering,
economics and almost any mathematics in upper secondary school and above.
A ratio is a fraction e.g.
7:3=7÷3≡
7
3
N Divide 170 in the ratio 3 : 2.
170
= 34.
5
Three of these make up a value of 3 × 34 = 102 and two of them make up a value of 2 × 34 = 68.
We may consider that 170 is made up of 3 + 2
3
2
=
= 5 parts. Therefore each part is of value
3 × 34
2 × 34
=
102
68
Examples
N Divide 180 in the ratio 6 : 2 : 1.
We may consider that 180 is made up of 6
+ 2 + 1 = 9 parts.
180
= 20.
9
Six of these make up a value of 6×20 = 120 and two of them make up a value of 2×20 = 40..
Therefore each part is of value
120 : 40 : 20 = 6 : 2 : 1
N The ratio of girls to boys in a junior tennis club is 3 : 2. If there are 30 girls, how many boys are
there? (20)
N One carton of apple juice holds 8 cups of juice. How many cups can be filled from 73 cartons?
N The product of three numbers is 210. What is the third number if two of the numbers are 5 and 7?
(6)
N My uncle was born in 1969. In what year will he be 75 yeas old? (2044)
N Buses leave a bus station every 10 minutes from 9.30 a.m. At what time will the fourth bus leave?
(10 a.m.)