Week 10 - Ratios, Rates and proportion

Question 1

Ratio definition

Answer 1

The relationship between 2 or more variables

A ratio is the comparison of two values of the same kind, which may be written as a to b, a:b or as a fraction a/b.

Question 2

Part-part ratio definition

Answer 2

A part-part ratio compares a number of parts of a whole to other parts in the whole.

Question 3

Part-whole ratio definition

Answer 3

A part-whole ratio compares a number of parts of a whole to the total of all parts in the whole.

Question 4

Ratio examples

Answer 4

Concrete mix is made up using a cement to builder’s mix in a ratio of 1:5

A Jamaican Zombie (drink) is light and dark rum mixed in a ratio of 5:2

Question 5

Ratio

Concrete is comprised of:

Answer 5

1 part cement
2 parts sand
3 parts aggregate

1:2:3

Question 6

Ratio example

Approximately 16 20kg bags of cement are required per cubic metre of finished concrete

How much sand and aggregate is needed?

Answer 6

Cement:
1 part cement
therefore 16x20kg bags

Sand
2 parts sand
therefore 2 x (16x20kg bags)

Aggregate
3 parts sand
therefore 3 x (16x20kg bags)

Question 7

Ratios as fractions

Concrete examples

Answer 7

Cement as a fraction of the entire mixture
= 1/6
Sand and aggregate to the entire mixture
= 5/6
Cement to sand
= 1/2
Sand to aggregate
= 2/3

Question 8

When a ratio becomes a rate

Answer 8

When the units in a ratio comprising of 2 variables are different, the ratio is known as a rate.

Examples of rates include:
Speed
Fuel economy

E.g. 150km per hour
2.5 per minute (150km divided by 60)
41.66 metres per second (2.5km divided by 60)

Question 9

Ratio to rate example

It costs $18 dollars to buy 12 cans of soft drink. How many cans can you get for…

36 dollars (double)

How much would 6 cans cost?

How many cans could you buy with $6

Answer 9

24 cans

$9

4 cans

Question 10

Ratio proportion

Answer 10

When two ratios are equal, then they are in direct proportion