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Ratios and rates
Ratios and rates
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Simplify ratios, divide quantities in a ratio, and solve rate problems.
Number · MA4-RAT-C-01
Sub-topics
Ratios
Simplify ratios and divide quantities in a given ratio.
Rates
Find unit rates and apply rates to solve problems involving speed, cost and other contexts.
Open Math
Ratios and rates
Number · MA4-RAT-C-01
Name:
Date:
Ratios
Q1
Straightforward
Simplify the ratio
6
:
9
6:9
6
:
9
.
A.
2
:
3
2:3
2
:
3
B.
3
:
2
3:2
3
:
2
C.
3
:
6
3:6
3
:
6
D.
1
:
2
1:2
1
:
2
Q2
Straightforward
Simplify the ratio
15
:
20
15:20
15
:
20
.
A.
3
:
4
3:4
3
:
4
B.
4
:
3
4:3
4
:
3
C.
5
:
4
5:4
5
:
4
D.
3
:
5
3:5
3
:
5
Q3
Straightforward
Simplify the ratio
12
:
8
12:8
12
:
8
.
A.
3
:
2
3:2
3
:
2
B.
2
:
3
2:3
2
:
3
C.
4
:
3
4:3
4
:
3
D.
6
:
4
6:4
6
:
4
Q4
Straightforward
Simplify the ratio
10
:
25
10:25
10
:
25
.
A.
2
:
5
2:5
2
:
5
B.
5
:
2
5:2
5
:
2
C.
1
:
3
1:3
1
:
3
D.
2
:
3
2:3
2
:
3
Q5
Moderate
Divide
$
60
\$60
$60
in the ratio
1
:
2
1:2
1
:
2
. How much is the smaller share, in dollars?
Q6
Moderate
40 lollies are shared in the ratio
3
:
5
3:5
3
:
5
. How many lollies does the first person receive?
Q7
Moderate
A 56 cm length of ribbon is divided in the ratio
3
:
4
3:4
3
:
4
. What is the length of the shorter piece, in centimetres?
Q8
Moderate
90 minutes is divided in the ratio
2
:
1
2:1
2
:
1
. How long is the longer time, in minutes?
Q9
Challenging
Find
x
x
x
if the ratio
3
:
x
3:x
3
:
x
is equivalent to
9
:
15
9:15
9
:
15
.
Q10
Challenging
Find
n
n
n
if the ratio
n
:
8
n:8
n
:
8
is equivalent to
6
:
24
6:24
6
:
24
.
Q11
Challenging
A map uses a scale of
1
:
50
000
1:50\,000
1
:
50
000
. Two towns are
4
4
4
cm apart on the map. What is the actual distance between them, in kilometres?
Q12
Challenging
Amira and Ben share some money in the ratio
3
:
7
3:7
3
:
7
. Amira receives
$
120
\$120
$120
. How many dollars does Ben receive?
Rates
Q13
Straightforward
5 pens cost
$
3.50
\$3.50
$3.50
. What is the cost per pen, in dollars?
Q14
Straightforward
A car travels 240 km in 3 hours. What is the speed in km/h?
Q15
Straightforward
A printer prints 60 pages in 4 minutes. How many pages per minute does it print?
Q16
Straightforward
A tap fills 45 litres in 9 minutes. What is the flow rate in litres per minute?
Q17
Moderate
A car travels at 90 km/h for 3 hours. How many kilometres does it travel?
Q18
Moderate
A plumber charges
$
45
\$45
$45
per hour. How much does she charge for 4 hours of work, in dollars?
Q19
Moderate
Water flows into a tank at 15 litres per minute. How many minutes does it take to fill a 210-litre tank?
Q20
Moderate
A recipe uses 300 mL of cream per serve. How many millilitres of cream are needed for 6 serves?
Q21
Challenging
Store A sells 3 bottles of water for
$
2.70
\$2.70
$2.70
. Store B sells 5 bottles for
$
4.25
\$4.25
$4.25
. Which store has the cheaper unit price?
A.
Store A at
$
0.90
\$0.90
$0.90
per bottle
B.
Store B at
$
0.85
\$0.85
$0.85
per bottle
C.
Both stores charge the same price
D.
Store A at
$
0.54
\$0.54
$0.54
per bottle
Q22
Challenging
A cyclist rides at 12 km/h for 30 minutes, then at 18 km/h for 20 minutes. What is the total distance in kilometres?
Q23
Challenging
A factory produces 180 items in 6 hours. How many items can it produce in 10 hours?
Q24
Challenging
A bus travels 280 km at 70 km/h. A train covers the same distance at 140 km/h. How many hours less does the train take than the bus?
Worked solutions and answers at openmath.au/year-7/ratios-and-rates