**RATIO AND RATE**

**RATIO**

- A ratio is used to compare the sizes of two or more quantities that use the same unit of measurement.
- A ratio of 5:6 means that for every 5 of the first quantity, there are 6 of the second quantity.
- Ratio can also be written as a fraction. In the ratio 5:6, the first quantity would be written as
^{5}/_{11}. The second quantity would be written as^{6}/_{11}. - Ratios can be simplified, e.g., 10:12 can be simplified to 5:6.
- Another example: The ratio of an original price of a coat to the sale price is R300:R210. We simplify this to 10:7

**RATE**

A rate is used to compare the sizes of two or more quantities that use different units of measurement, e.g., hours (h), minutes (m), Rands (R), millimeters (mm), centimeters (cm), etc.

- Simplify the ratio 32:16.
- Write the fraction 32 /48 in its simplest form.
- Now write the ratio 32:48 in its simplest form.
- The ratio of women engineers to men engineers in a construction company is 2:7.
- There are six women engineers. How many men engineers are there in the company?
- How many engineers are there in the company altogether?
- What fraction of the total number of engineers are women?
- The company decides to improve their gender equality. The company wants to change the ratio of women engineers to men engineers to 2:5. The company cannot afford to employ more than 28 engineers in total. When the company achieves this ratio, how many women engineers and men engineers would they have?

**SHARING A “WHOLE” IN A GIVEN RATIO**

Share R 2 250,00 in the ratio 3:2:1

- This means 3:2:1 that 3+2+1= 6 parts of the whole 2 250.
- In fraction form, this means
^{3}/_{6}of 2 250

= 3 x 2 250

= 6 750 ÷ 6

= R 1 125 ^{2}/_{6}of 2 250

= 2 x 2 250

= 4 500 ÷ 6

= R 750^{1}/_{6}of 2 250

= 2 250 ÷ 6

= R 375

- Divide R 200,00 between you and your best friend in the ratio 3:2
- Divide R 240,00 in the ratio 3:4:5
- Share 28 sweets between Joe and Amy in the ratio 3:1
- Share an inheritance of R 50 000,00 between five children in the following ratio 7:9:3:2:4

**CALCULATING PERCENTAGE INCREASE AND DECREASE**

When increasing or decreasing a number by a given percentage, write the percentage out of 100 and multiply it by the given number.

Example: Increase R 1 500 by 25%

= ^{25}/_{100} x 1500 *Simplify / Cancel if possible

= R 375

Now add this amount to the original value:

i.e. R1500+R375

= R 1 875

- If decreasing, you would subtract this amount from the original value.

Example: Decrease R 3 000 by 45%

= ^{45}/_{100} x 3000

= R 1 350

Decreased amount: R3000–R1350

= R1650

- Rod decides to give his staff a 12% increase on their salaries.

These are the salaries of some of the staff before their increase. What will their salary be after the increase?- R11 800
- R27 540
- R4 400

- Given below are the prices for three items with the same content but different weight and price. Determine which of the three would be the least expensive to purchase.
- Sugar: 500g – R5.65;1kg – R11.90; 2kg – R18.99
- Coffee: 50g – R54.90;100g – R75.80;200g – R99.00
- Eggs: 6 – R11.40; 12 – R18.80; 30 – R31.99
- Cereal: 350g – R24.99; 500g – R28.00; 400g – R26.50

- Give the rate for each of these statements below:
- A bus travels 480km in 8 hours. (km/h)
- 12 apples for R 7,20 (R/apple)
- A tap dripped 300ml of water in half an hour (ml/minute)
- 19,95 Gigabytes transferred in 19 minutes (Gb/minute)

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