
Meaning and Models  Key
Ideas
 Percent Examples  Ratio
Examples  Rates Examples 
Meaning
and models quiz answers
1. 

a) 
95/100 or 19/20; 0.95

b) 
13.5/100 or 27/200; 0.135 
c) 
42/100
or 21/50; 0.42

d) 
1/100;
0.01 
e) 
1/1000; 0.001



2.


a)

37%

b) 
164% 
c) 
50%

d) 
70% 
e) 
64%



3. 

a)

1
%

b) 
83% 
c) 
0.5%

d) 
110% 
e) 
20%



4.


a) 
ratio of boys to girls is 3 : 5 
b) 
ratio of people who watch TV to people who don't is 9 : 1,
or we could also say,
ratio
of people who watch TV to total number of people is 9 : 10

c) 
ratio of left to right handedness in class is 3 : 22, or we
could also say, ratio of left handedness to the rest of the
class is 3 : 25

d) 
ratio of rice to water is 1:2 
e) 
ratio of the mass of rice to flour is 1 : 1



5. 

a)

10
: 20 = 1 : 2 = 2 : 4

b) 
30 : 50 = 3 : 5 = 60 : 100 
c) 
100
: 100 = 1 : 1 = 2 : 2

d) 
6 : 4 : 2 = 3 : 2 :1 = 30 : 20 : 10 
e) 
75
: 25 = 3 : 1 = 6 : 2



6. 

a)

3 : 3 : 4 = 3/10 : 3/10 : 4/10 = 0.3 : 0.3 : 0.4 =
30% : 30% : 40%

b) 
11 : 4 : 5 = 11/20 : 4/20 : 5/20 = 0.55 : 0.2 : 0.25 =
55% : 20% : 25%

c) 
4
: 1 = 4/5 : 1/5 = 0.8 : 0.2 = 80% : 20%

d) 
5 : 3 : 1 : 6 = 5/15 : 3/15 : 1/15 : 6/15 =
0.33
: 0.20 : 0.07 : 0.40 = 33% : 20% : 7% : 40%
(note
0.07 has been rounded from 0.0666 recurring)



7. 

a)

100 metres / 15 seconds = 6.67 m/s

b) 
850 kilometres / 10 hours = 85 km/h 
c) 
160
words / 2 minutes = 80 words per minute 
d) 
600 packets / 5 minutes = 120 packets per minute

Extra
questions:
1.
20% is 20 parts out of 100, so 20 rectangle out of 100 must be
shaded
2.
(a)
Percentage shaded = 9 rectangles out of 50, which equals 18 rectangles
out of 100 which equals 18%
(b)
Percentage not shaded = Total percent less the percent shaded = 100
 18 = 82%
3.
The ratio of pink to white = 2 : 6 This is the same as 1 : 3 For
every one pink there are 3 white.
4.
The order is important in ratio. Also, while the units must be the
same, there are no units in the answer.
(a)
ratio of biro length : ruler length = 23 : 30
(b)
ratio of ruler length : biro length = 30 : 23
5.
Percentage

Common
Fraction

Decimal
Fraction

32%


Thirty
two hundredths = 0.32

Six
hundredths = 6%


0.06



Forty
eight hundredths =0.48

6.
(a) Length of dog = 90 cm
The
dog is 3 times the length of the bird, so bird is 30 cm.
(b)
The ratio of dog : bird = 90 : 30. This is the same as 3 : 1. So,
for every 1 cm of the bird there are 3 cm of the dog.
7.
(a)
kilogram = 500 g. Hence, ratio of sugar to butter = 300 : 500. This
is the same as 3 : 5 For every 3 units of sugar
there are 5 of butter.
(b)
Ratio of butter to sugar = 500 : 300 this is the same as 5 : 3
Distance
is measured in km and time is measured in hours. Hence the two quantities
being measured are distance and time.
Key
Ideas quiz answers
1. 

a)

33
1/3% = 1/3 = 0.33

b) 
231% = 231/100 = 2.31 
c) 
0.03%
= 3/10000 = 0.0003

d) 
75%
= 75/100 = 3/4 = 0.75 
e) 
12.5%
= 12.5/100 = 0.125 


2. 
Two
methods have been used to calculate these answers. Either method
can be used for each question.
The
20% discounted prices are:

a)

$2.30 x 0.8 = $1.84

b) 
$1 900 x 0.8 = $1 520 
c) 
$6.50  (0.2 x $6.50) = $5.20

d) 
$11  (0.2 x $11) = $8.80 
e) 
$40 000 x 0.8 = $32000

f) 
$30
x 0.8 = $24 


3. 
Two
methods have been used to calculate these answers. Either method
can be used for each question.
The
prices including the 15% increase are:

a)

$2.30 x 1.15 = $2.65

b) 
$1
900 x 1.15 = $2 185 
c) 
$6.50 + (0.15 x $6.50) = $7.48

d) 
$11 + (0.15 x $11) = $12.65 
e) 
$40 000 x 1.15 = $46000

f) 
$30 x 1.15 = $34.50 


4.


a)

9% of 70 is nearly 10% so that is about 7 
b) 
48.5%
of 120 is nearly 50% so that is about 60 
c) 
24% of 200 is nearly 25% (which is one quarter) so that is about
50 
d) 
To find 0.5% of 100, I know 1% of 100 is 1, so 0.5% would be
0.5 exactly

e) 
98% of 163 is nearly 100% so that is about 160 (or we could about
say 163) 
f) 
19% of 5000 is nearly 20% (which is one fifth) so that is about
1000

g) 
47% of 820 is nearly 50% so that is about a half of 820 which
is 410 
h)

69%
of 8960 is a bit over two thirds or nearly 70% of 8960. If we
round up 8960 to 9000 and then find two thirds of it, that is
about 6000



5.


a)

6
: 12 = 1 : 2 = 18 : 36

b) 
1 : 3 = 2 : 6 = 5 : 15 
c) 
2 : 7 = 4 : 14 = 8 : 56 = 1 : 3.5

d) 
7 : 22 : 25 = 14 : 44 : 70 
e) 
3 : 9 : 24 : 36 = 1 : 3 : 8 : 12

f) 
5
: 10 : 26 = 10 : 20 :52 




a)

14
: 6 : 8 = 7 : 3 : 14

b) 
2 : 50 000 = 1 : 25 000 
c) 
4 : 12 : 48 = 1 : 3 : 12

d) 
30 000 : 3 = 10 000 : 1 
Extra
questions:
1.
Discount = 12%
of 864 =
x 864 = 0.125 x 864 = 108
Amount
paid for TV = Marked Price  Discount = 864  108 = 756
The
discounted price of the TV = $756
2.
(a) The units must be the same. 1 day = 24 hours
12
hours is to 1 day = 12 : 24 = 1 : 2 ( because 12 divides evenly into
12 and 24)
(b)
The units are the same. Multiply both fractions by 7 to remove the
denominator of the fractions. The answer is 3 : 5.
3.
The given ratio, 3 : 4, can be written as .
Since this fraction is less than 1, when we multiply it by 24 g the
number of grams will be less than 24.
Therefore
the amount of fat in light and healthy Brand A icecream is 18g.
4.
Total number of units = 7 + 3 = 10
Jane
receives
=
5.
The scale is 1 : 100 000, so multiply by 10,
10
x 1 : 10 x 100 000 = 10
: 1 000 000
The
towns are 1 000 000 cm apart
This
means the towns are 10 000 m apart. (There are 100 cm in a metre)
This
means the towns are 10 km apart. (There are 1000 m in a kilometre)
6.
20 beats in 5 seconds.
Divide
both the 20 and the 5 by 5
This
gives 4 beats in 1 second i.e. 4 beats/s
7.
The front width of the drawing of the house is 6 cm. The width
of the front of the real house is 6 x 200 = 1 200 cm = 12 m.
In one
year’s time the value of the investment =
At the
end of two years, the value of the investment =
Percent Examples quiz answers
1.


a) 
80% of 45 seats is 36 seats 
b) 
19 out of 45 seats is 42.2% 


2.

13
girls is 45% of the class.
13/b = 45/100
b = 1300/45 = 28.89
There
are 29 students in the class



3. 

a)

If
Georgie answered 35 out of 40 questions correctly she answered
87.5 % correctly.
35/40
= r /100
r
= 3500/40 = 87.5 %

b)

As
Georgie scored above 85% she did pass 
c) 
p/40 = 97/100
p
= (97 x 40)/100 = 38.8
Georgies
answered 39 questions correctly



4.

300
gs is 15% of the puppy's total body weight.
300
/ b = 15/100
b = 30 000 / 15
b=
2000
The
puppy's total body weight is 2000 grams (2 kg)



5.


a)

5
tickets out of 15 tickets is one third or 33.3% 
b) 
Ryan bought the tickets for $65 each and then increased the
cost by 10%.
$65
+ 0.10 x $65 = $71.50
Therefore
he is selling the tickets for $71.50

c) 
Ryan reduces the $65 tickets by 20%.
$65
x 0.8 = $52

d) 
Ryan finally sold 73% of 15 tickets
73/100
= p/15
p
= (73 x 15) / 100
p
= 10.95
(we
round 10.95 to 11 because 10.95 tickets does not make sense)
This
means Ryan sold 11 tickets.



6.

The
full price of the jeans was $79. They are now discounted by
25%
$79
x 0.75 = $59.25
The
jeans now cost $59.25


The
full price of the Tshirt was $35. It is now discounted by 25%.
$35
x 0.75 = 26.25
The
Tshirt now cost $26.25



7.


a)

8 workers out of 35 workers ride their bikes. This is 22.86%

b) 
14
workers out of 35 workers catch public transport. This is 40%

c) 
13 workers ride or walk to work. This is 37.14% of the 35
workers.

d) 
25 out of 35 workers do not use their car to get to work, This
is 71.43% 
e) 
Since the percents represent fractions out of 100 we can say;
bike=23 (rounded from 22.86%)
public transport =40
drive=29 (71%  rounded  do not use their car, so we can say
29% do use their car)
walk=8 (3 out of 35 is about 8%)



8.

The
440 g can has 35 parts out of 100 that contain fat. The 1 kg
can contains 20 parts out of 100 that contain fat. A bowl of
each contains the same parts out of 100 of fat as the cans,
so a bowl from the 440 g will contain more fat than a bowl from
the 1 kg can.



Extra
questions:
1. 
Fraction
of Australians who attended the 2000 Olympic Games =

and 

Percent
of Australians who attended the 2000 Olympic Games = 15%

2. 
Percent
of people who prefer skiing = 100  28 = 72%
Fraction
of people who prefer skiiing =

3. 
Fraction
who liked P.E. best =
Percent
who liked P.E. best = 20%

4. 

5. 

6. 

(a) 
Commission
= 15% commission of $1 700
10%
of 1 700 = 170
5
% of 1 700 = half of 10% = half of 170 = 85
15%
= 10% + 5% = 170 + 85 = 255
Commission
= $255

(b) 
Total
amount earned = 520 + 255 = $775 
7. 

(a) 
The
15% profit on $180 = the 15% loss on $180, so altogether she did
not make a profit or loss on the sale of the two racquets. 
(b) 
She
made $0 on the sale of the two racquets, because they cost her
$360 and she received $360 for them. 
8. 
No.
of boys in Mrs Smith's class = 13
No.
of boys in Mr. Jones' class = 30  3 = 27 (There are 10% of
30 girls = 3 girls)
Total
no. of boys in the two classes = 13 + 27 = 40
Total
no. of children in both classes = 20 + 30 = 50
Fraction
boys =
Percent
of boys = 80%

Ratio Examples quiz answers
1.

a)
baby : mug = 3 : 8


b)
baby : regular = 3 : 20 

c)
mug : regular = 8 : 20
= 2 : 5


d)
mug : baby = 8 : 3 


2.

a)
turtles : fish = 2 : 22 =
1 : 11


b)
ratio of orange fish to black fish is
7 : 12 

c)
ratio of turtles to black fish is
2 : 12 = 1 : 6


d)
mottly fish : total number of fish = 3 : 22 

e)
mottly fish : turtles = 3 : 2


f)
ratio of black fish to orange fish is 12 : 7 


3.

a)
ratio of number of lasagnas to number of pizzas is 5 : 13


b)
13 pizzas cut into 5 pieces means that there are 13 x 5 pieces
in total. Ratio of pieces of pizza to lasagnas is (13 x 5):
5. This is 13:1. You can check it by multiplying 13 x 5 to get
65 and then dividing by 5, but it is important to know this
important relationship.



4.

a)
1 : 1000


b)
1 : 300 

c)
1 : 100 000


d)
15 : 50 000 = 3 : 10 000 


5.

a)
smaller


b)
larger 

c)
smaller


d)
smaller 

e)
smaller


f)
larger

6.

The
1.25 litre bottle is cheaper than the 600 ml bottle since it
contains more than double the quantity but is less than double
the price.
Two
of the 1.25 litre bottles would contain 2.4 litres but would
only cost 15 cents more ($3.70) than the 2 litre bottle. Therefore
the 1.25 litre bottle is the best value.
You
could also solve this problem by working out the cost per litre
for each bottle of water. The
1.25 litre bottle is the best value at $1.48 per litre



Rates
Examples quiz answers
1.

a)
800 kilometres in 8 hours can be expressed as a rate of 100
km/h


b)
100 metres in 10 secs can be expressed as a rate of 10 m/s 

c)
7 hours for $84 can be expressed as a rate with the units of
$/hr.
84/7
= 12 $/h


d)
330 hamburgers in 2 hours is 165 hamburgers per hour 

e)
96 goals in 12 games can be expressed as a rate with the units
of goals/game
96/12
= 8 goals per game



2.

a)
We want to find out how long it will take to travel 200 kms
if we are travelling at a rate of 60 km/h. We know the units
of our answer will be in hours.
200
km divided by 60 km/h = 3.30 h
It
will take 3.33 hours to travel 200 kilometres at this rate.


b)
A specialist has 14 appointments a day. If she works 6 hours
in a day then she has 14 appointments per 6 hours.
To
find out how much time is scheduled for each patient we need
to divide the time available by the number of appointments.
6
hours = 6 x 60 minutes = 360 minutes
360
minutes/14 appointments = 25.7
There
is about 25 minutes scheduled for each patient.


c)
The shower runs at a rate of 5 litres/minute and Rory showers
for 7 minutes per day. We want to find out the number of litres
of water used per week. first we will find out the rate of litres
per day.
5
litres/minute x 7 minutes/day = 35 litres/day
As
there are 7 days per week then the rate of litres used per week
is,
35
litres/day x 7 days/week
=
245 litres/week
(This
problem shows us that being aware of the units we require in
our answer helps us to work out our answer)


d)
John is paid 8 $/h and he works 17 h/week.
We
want to find out how much he is paid per week, so our answer
will be in dollars per week.
8
$/h x 17 h/week = 136 $/week
If
his pay is increased by $1.70 per hour then his new rate of
pay will be $9.70 per hour.



3.

a)
To compare the speeds of the cars we need to convert them all
into a rate of km/h.
Car
X travels 330 km in 3 hours = 110 km/h
Car Y travels 500 km in 4.5 hours = 111 km/h
Car Z travels 120 km in 1 hour = 120 km/h
Therefore
car Z is the fastest at 120 km/h


b)
To compare the rate of claims for each age group we need to
convert them all to the same rate.
2130:
16 claims per year
3150: 56 claims per 2 years
51+: 17 claims per quarter
we
are asked to work out the claim rate per quarter so we will
convert all rates into claims per quarter.
2130:
16 claims per year = 16 ÷ 4 = 4 claims per quarter
3150: 56 claims per 2 years = 56 ÷ 8 = 7 claims per
quarter
51+: 17 claims per quarter
So
the 51+ age group has the most claims per quarter.


c)
If the factory makes chocolate bars at 300 bars per minute then
the number of bars made in 12 minutes is 300 x 12 = 3600 bars.
If
the rate of production is 300 bars per minute then we can also
say that it is 300 bars per 60 seconds.
300
bars/60 seconds = 50 bars/second, or 0.02 seconds to make each
bar.



