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Cambridge University Press978-1-107-67401-1 - CambridgeMaths: NSW Syllabus for the Australian Curriculum: Year 10: State 5.1/5.2Stuart Palmer, David Greenwood, Jenny Goodman, Jennifer Vaughan, Sara Woolley and Margaret PowellExcerptMore information

www.cambridge.org© in this web service Cambridge University Press

http://www.cambridge.org/9781107674011

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Chapter 1 Financial mathematics2

Chapter

Financial Mathematics1What you will learn

1A Review of percentages REVISION

1B Applying percentages REVISION

1C Income 1D The PAYG income tax system 1E Using a budget to manage income and expenditure FRINGE

1F Simple interest 1G Compound interest and depreciation 1H Investments and loans 1I Comparing interest using technology






Number and Algebra 3

Saving and borrowing money for expensive items

NSW Syllabus for the Australian CurriculumStrand: Number and Algebra

Substrand: FiNANCiAl MAtHEMAtiCS

Outcomes

A student solves fi nancial problems involving earning, spending and investing money.

(MA5.1–4NA)

A student solves fi nancial problems involving compound interest.

(MA5.2–4NA)

3

For many people, a car is the fi rst expensive item that involves long-term saving and borrowing. There is also a need to budget for the ongoing costs of petrol, insurance and repairs, as well as the hidden costs, such as interest on the loan and depreciation.






Chapter 1 Financial mathematics4 Chapter 1 Financial mathematics4

1 Find the following totals.

a $15.92 + $27.50 + $56.20 b $134 + $457 + $1021 c $457 × 6

d $56.34 × 11

2 e $87 560 ÷ 52 (to the nearest cent)

2 Write each of the following fractions as decimals.

a 1

2 b 1

4 c 1

5 d

7

25 e 1

3

3 Express the following fractions with denominators of 100.

a 1

2 b

3

4 c

1

5 d

17

25 e

9

20

4 Round the following decimals to 2 decimal places.

a 16.7893 b 7.347 c 45.3444 d 6.8389 e 102.8999

5 Copy and complete the following table.

Gross income ($) Deductions ($) Net income ($)4976 456.72 a

72 156 21 646.80 b92 411 c 62 839

156 794 d 101 916

e 18 472.10 79 431.36

6 Calculate the following annual incomes for each of these people.

a Tom: $1256 per week

b Viviana: $15 600 per month

c Anthony: $1911 per fortnight

d Crystal: $17.90 per hour, for 40 hours per week, for 50 weeks per year

7 Without a calculator, fi nd:

a 10% of $400 b 5% of $5000 c 2% of $100

d 25% of $844 e 20% of $12.80 f 75% of $1000

8 Find the simple interest earned on the following amounts.

a $400 at 5% p.a. for 1 year b $5000 at 6% p.a. for 1 year

c $800 at 4% p.a. for 2 years

9 Complete the following table.

Cost price Deduction Sale price $34 $16 a

$460 $137 b$500 c $236

d $45 $67

e $12.65 $45.27

10 The following amounts include the 10% GST. By dividing each one by 1.1, fi nd the original

costs before the GST was added to each.

a $55 b $61.60 c $605

Net income = gross income - deductions

Simple interest I = PRN

pre-

test

d $45 $67

e $12.65 $45.27

10 The following amounts include the 10% GST. By dividing each one by 1.1, fi nd the original

costs before the GST was added to each.

a $55 b $61.60 c $605







Review of percentagesIt is important that we are able to work with percentages

in our everyday lives. Banks, retailers and governments

use percentages every day to work out fees, prices

and interest.

let’s start: Which option should Jamie choose?Jamie currently earns $38 460 p.a. (per year) and is given a choice

of two different pay rises. Which should she choose and why?

1A

Choice A

Increase of $20 a week

Choice B

Increase of 2% on p.a. salary

■ A percentage means ‘out of 100’. It can be written using the symbol %, or as

a fraction or a decimal.

For example: 75 per cent = 75% = 75

100 or

3

4 = 0.75

■ To convert a fraction or a decimal to a percentage, multiply by 100%, or 100%

1.

■ To convert a percentage to a fraction, write it with

a denominator of 100 and simplify.

For example: 15% = 15

100 = 3

20

■ To convert a percentage to a decimal, divide by 100%.

For example: 15% = 15 ÷ 100 = 0.15

■ To fi nd a percentage of a quantity, write the percentage

as a fraction or a decimal, then multiply by the quantity.

x% of P = x

100 × P

Fraction

×100%

÷100%

%

Decimal

×100%

÷100%

%

Key

idea

s Percentage A convenient way of writing fractions with denominators of 100

Denominator The part of a fraction that sits below the dividing line

REVISION

Stage

5.3#5.35.3§

5.25.2◊5.14







1 Write the following with denominators of 100.

a 2

5 b

17

20 c

49

50

d 7

25 e

9

10

2 Complete the following.

a 7% = 7 b 0.9 = % c 3

5 = %

3 Use mental strategies to fi nd:

a 10% of $7.50 b 20% of $400 c 50% of $98

d 75% of $668 e 25% of $412 f 2% of $60

g 5% of $750 h 331

3% of $1200 i 30% of $15

Make sure you have an equivalent

fraction: =25 100

.

Example 1 Converting to a percentage

Write each of the following as a percentage.

a 19

20 b 3

8 c 0.07

SolutioN ExplANAtioN

a 19

20

19 5

20 5

95

10095

= ××

=

= %

Write using a denominator of 100.

Alternatively, multiply the fraction by 100%.

× = × =19

20

100

1% 19 5% 95%1

5

b = ×3

8

3

8

100

1%

2

25

=

=

75

2%

37.5%

Multiply the fraction by 100%.

Cancel common factors, then simplify.

c 0.07 = 0.07 × 100%

= 7%

Multiply the decimal by 100%.

Move the decimal point two places to the right.

WORKING

MATHE M ATICALL

Y

U F

R PSC

10% = 10

100‘Of’ means times.

Exercise 1AWORKING

MATHE M ATICALL

Y

U F

R PSC

R E V I S I O N







4 Convert each fraction to a percentage.

a 1

2 b 1

5 c 1

4

d 1

10 e 1

100 f 7

25

g 15

50 h 3

4 i 5

8

j 19

25 k 99

100 l 47

50

5 Write these decimals as percentages.

a 0.17 b 0.73 c 0.48 d 0.09

e 0.06 f 0.13 g 1.13 h 1.01

i 0.8 j 0.9 k 0.99 l 0.175

First, write using a denominator of 100 or alternatively multiply by 100%.

To multiply by 100%, move the decimal point two places to the right.

WORKING

MATHE M ATICALL

Y

U F

R PSC

6 Write each percentage as a simple fraction.

a 71% b 80% c 25% d 55%

e 40% f 88% g 15% h 161

2%

i 171

2% j 2

1

4% k 5

1

4% l 52

1

2%

Write with a denominator of 100, then simplify if possible.

Example 2 Writing percentages as simple fractions

Write each of the following percentages as a simple fraction.

a 37% b 58% c 61

2%


a =37%37

100Write the percentage with a denominator of 100.

b =

=

58%58

10029

50

Write the percentage with a denominator of 100.

Simplify 58

100 by cancelling, using the HCF of 58 and 100, which is 2.

=58

100

29

50

29

50

c =

=

61

2%

612

10013

200

Write the percentage with a denominator of 100.

Double the numerator

6

1

2 and the denominator (100) so that the

numerator is a whole number.







Example 3 Writing a percentage as a decimal

Convert these percentages to decimals.

a 93% b 7% c 30%


a 93% = 0.93 Divide the percentage by 100. This is the same as moving the decimal

point two places to the left.

93 ÷ 100 = 0.93

b 7% = 0.07 Divide the percentage by 100.

7 ÷ 100 = 0.07

c 30% = 0.3 Divide the percentage by 100.

30 ÷ 100 = 0.30

Write 0.30 as 0.3.

7 Convert to decimals.

a 61% b 83% c 75% d 45%

e 9% f 90% g 50% h 16.5%

i 7.3% j 200% k 430% l 0.5%

WORKING

MATHE M ATICALL

Y

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Example 4 Finding a percentage of a quantity

Find 42% of $1800.


42% of $1800

= 0.42 × 1800

= $756

Remember that ‘of ’ means multiply.

Write 42% as a decimal or a fraction: = =42%42

1000.42

Then multiply by the amount.

If using a calculator, type 0.42 × 1800.

Without a calculator: × = ×42

1001800 42 18

8 Use a calculator to fi nd:

a 10% of $250 b 50% of $300 c 75% of $80

d 12% of $750 e 9% of $240 f 43% of 800 grams

g 90% of $56 h 110% of $98 i 171

2% of 2000 m

1A







9 A 300 g pie contains 15 g of saturated fat.

a What fraction of the pie is saturated fat?

b What percentage of the pie is saturated fat?

10 About 80% of the mass of a human body is water. If Hugo

is 85 kg, how many kilograms of water are in his body?

11 Rema spends 12% of the 6.6 hour school day in Maths.

How many minutes are spent in the Maths classroom?

12 In a cricket match, Brett spent 35 minutes bowling.

His team’s total fi elding time was 31

2 hours.

What percentage of the fi elding time, correct to

2 decimal places, did Brett spend bowling?

13 Malcolm lost 8 kg, and now weighs 64 kg. What percentage of his original weight did he lose?

14 47.9% of a local council’s budget is spent on garbage collection. If a rate payer pays $107.50

per quarter in total rate charges, how much do they contribute in a year to garbage collection?

15 g out of 300 g.

First convert hours to minutes, and then write a fraction comparing times.

WORKING

MATHE M ATICALL

Y

U F

R PSC







Enrichment: Australia’s statistics

15 Below is the preliminary data on Australia’s population growth, as gathered by the Australian Bureau

of Statistics for September 2012.

population at end September quarter 2012

(’000)Change over

previous year (’000)

Change over previous year

(%, 1 decimal place)

New South Wales 7314.1 86.0

Victoria 5649.1 94.8

Queensland 4584.6 91.4

South Australia 1658.1 16.4

Western Australia 2451.4 81.7

Tasmania 512.2 0.5

Northern Territory 236.3 4.2

Australian Capital Territory 376.5 7.4

Australia 22 782.3 382.4

a Calculate the percentage change for each State and Territory shown

using the previous year’s population, and complete the table.

b What percentage of Australia’s overall population, correct to

1 decimal place, is living in:

i NSW?

ii Victoria?

iii WA?

c Use a spreadsheet to draw a pie chart (sector graph) showing the populations of the eight States

and Territories in the table. What percentage of the total is represented by each State/Territory?

d In your pie chart in part c, what is the angle size of the sector representing Victoria?

You will need to calculate the previous year’s population; e.g. for NSW, 7314.1 - 86.0.

1A






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