Ratio

A ratio is a relationship between two quantities of the same type.

For example, 2:1 may represent the ratio of girls to boys in a class. This means that there are 2 times as many girls as there are boys in the class.

Ratios are commonly used in:

Maths Fun - Waist to Hip Ratio

The Waist-Hip Ratio is used by doctors to determine a person's "fatness", a risk factor in cardio-vascular (heart) disease. For adult women, a WHR less than 8.5 is healthy. For adult men, a WHR less than 9 is healthy.

Use a tape measure to measure around your waist and your hips. Divide your waist measurement by your hip measurement. How did you do?

Example One - Simplifying Ratios

Simplify these ratios by dividing both numbers by the greatest common factor.

10 : 2 = 5 : 1

3 : 6 = 1 : 2

25 : 30 = 5 : 6

$4 : 60 cents = 400 cents : 60 cents = 400 : 60 = 20 : 3

5 kilometres : 200 metres = 5000 metres : 200 metres = 25 : 1

Questions

Simplify these ratios:
Q1. 30 : 9
Q2. 45 : 18
Q3. $4.20 : 14 cents

Answers
A1. 10 : 3
A2. 5 : 2
A3. 30 : 1

Example Two - Solar System to Scale

Planets


PLANETAVERAGE DISTANCE FROM SUN (KM)
Mercury57 million
Venus108 million
Earth150 million
Mars228 million
Jupiter779 million
Saturn1 430 million
Uranus2 880 million
Neptune4 500 million

My homework assignment is to draw a line marking the Sun and then all 8 planets' positions. The distances must be to scale. I only have A4 photocopy paper which is 30 cm long. What scale should I use? What will be the scaled planetary distances?

Answer:
Estimated scale = 4 500 000 000 ÷ 30 = 150 000 000
If I use this scale, I won't be able to fit the names of the Sun and Neptune on my paper so I need a larger scale. I'll use a scale of 1: 200 000 000.

Now, I'll divide all the real distances by 200 000 000 e.g.
Scaled distance of Neptune = 4 500 000 000 ÷ 200 000 000 = 22.5 cm

PLANETSCALED AVERAGE DISTANCE FROM SUN
Mercury0.285 cm or 2.85 mm
Venus0.54 cm or 5.4 mm
Earth0.75 cm or 7.5 mm
Mars1.14 cm
Jupiter3.895 cm
Saturn7.15 cm
Uranus14.4 cm
Neptune22.5 cm

Questions - Scale Drawings

A house plan has a scale of 200:1 which means that the real house is 200 times larger than the measurement shown on the plan. Because carpenters must work accurately, house plan dimensions are marked in millimetres. Change these room dimensions to show the lengths that would be drawn on a house plan.

Q1. Bedroom - 3000 mm by 4000 mm
Q2. Real Bathroom - 2500 mm by 2400 mm

Answers
A1. Bedroom - 15 mm by 20 mm
A2. Bathroom - 12.5 mm by 12 mm

Did You Know That...?

A remote sensing system called Geographic Information System (GIS) is used to map locations for:

Example Three - Drag Car Fuel

Drag Car

Drag car fuel is a mixture in the ratio of 9:1 (9 parts Nitromethane and 1 part Methanol). A drag car can consume up to 120 litres of fuel for one quarter-mile sprint including the warm-up. How much of this is Nitromethane and how much is Methanol?

Answer:
Total number of parts = 9 + 1 = 10 parts

Quantity of Nitromethane = 910 × 120 = 108 litres

Quantity of Methanol = 110 × 120 = 12 litres

Question - Concrete

Concrete is made in the ratio of 1:2:3. This means 1 part of cement, 2 parts of sand and 3 parts of gravel. How much of each would I need to make a concrete house slab with a volume of 90 cubic metres?

Answer
15 m3 cement : 30 m3 sand : 45 m3 gravel