# Year 8 Maths Chapter 5 - Ratios and Rates

## Ratios

For example, a dead rabbit could have a ratio of fur to flesh, of 1:3. The colon (“:”) is used to represent ratios. A written ratio `(a : b)` is read as a to be or a is to b.

The order of the numbers in a ratio is important. 1:3 is not the same as 3:1.

Equivalent ratios can be formed, for example, by multiplying the ratio by the same amount. What you do to one side you must do to the other. 1:3, 2:6 and 10:30 are equivalent ratios.

Simplifying ratios can be done by dividing the ratio by the same amount, or multiplying if the ratio is not a whole number such as a fraction. You should attempt to express ratios in simplest forms.

Ratios must ALWAYS BE in the same unit.

The unitary method allows ratios to be shared into parts. For example, a ratio of 2:3 can be considered as 2 parts and 3 parts, and to divide a cost, for example, \$20, can be divided into all five parts. Therefore, where 1 part is \$4, 2 parts is \$8 and 3 parts is \$12. Hence, the ratio of 2:3 is \$8:\$12.

A scale drawing is a drawing which is identical to another except for its size. A scale drawing usually has a scale ratio. The scale ratio is written as `Drawing (Scale) Length : Actual Length`.

For example, a scale ratio of 1:100 is that the actual lengths are 100 times greater than the presented length.

A scale should begin with 1. Hence, the second number can be referred to as the scale factor.

To convert a SCALED distance to an ACTUAL distance you multiply by the scale factor, and vice versa.

Remember!

• 1 km = 1000 m (kilo means 1000, however, not necessarily true when it is raised to a power)
• 1 m = 100 cm
• 1 cm = 10 mm

Rates compare quantities of different units. All rates must include quantities.

The forward slash (“/”) is used to represent rates. Rates should be written in their simplest form; where the second quantity is only 1 unit (1 km, 1 minute).

The average rate is calculated by:

1. Dividing the total amount of CHANGE in one quantity by the total amount of change in the second quantity.
2. What you do to one side you must do to the other.
3. For example, killing 400 rabbits in 4 days = 100 rabbits in 1 day.

The unitary method is:

1. Finding the value of 1 unit
2. Going back up to the required number of units

For example:

``````The ratio of dead rabbits to mutated pigs is 3:5. If there are 18 dead rabbits, how many mutated pigs are there?
``````

To solve it, you would identify that `3 parts = 18 dead rabbits`

Then, divide 18 by 3 to find 1 part

Therefore, `5 parts = 30 mutated pigs`. Therefore, there are 30 mutated pigs.

### Distance, Speed and Time

Distance, speed and time are important concepts for real life application of mathematics.

Terms you should know:

• Speed is a measure of how fast an object is travelling.
• Distance is a measure of how far an object has travelled (in this case).
• Time is a measure of how much indefinite continued progress of existence and events in the past, present, and future regarded as a whole has surpassed. Woah.

You can use two of the measures to find the third one. For example,

Where S is average speed, D is distance travelled and T is time lapsed…

``````S = D/T
``````

The best way to remember the equations required is to use a DST triangle. Where D is the numerator of a fraction in regards to S and T, and D is the product of the equation S x T.

So…

``````D = S x T
S = D/T
T = D/S
``````

If the speed of an object does not change over time, then the object is travelling at a constant speed. For example, when a dead rabbit driving a Prius is using cruise control at 80 km/h, then the car has a constant speed of 80 km/h.

Units should also be the same when solving DST equations.

Distance and time graphs are used to show the distance on a vertical axis and the time taken on the horizontal axis, also known as the y and x axis respectively.

Each segment shows whether the object is moving or is stopped. The steepness of any one line segment shows the speed.

Steeper lines = faster speed

Look at this crappy D/T graph (note that D/T stands for distance/time, not design and technology) Copyright © 2017-2020 aidswidjaja and other contributors. CC BY-SA 4.0 Australia unless otherwise stated.