Ratio and Rate - Grade 7 Mathematics Revision Notes

• Ratio and rate
  • Exercise 9
• SHARING A “WHOLE” IN A GIVEN RATIO
  • Exercise 10
• CALCULATING PERCENTAGE INCREASE AND DECREASE
  • Exercise 11

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.

Exercise 9

1. Simplify the ratio 32:16.
2. Write the fraction 32 /48 in its simplest form.
3. Now write the ratio 32:48 in its simplest form.
4. The ratio of women engineers to men engineers in a construction company is 2:7.
   1. There are six women engineers. How many men engineers are there in the company?
   2. How many engineers are there in the company altogether?
   3. What fraction of the total number of engineers are women?
   4. 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

Exercise 10

1. Divide R 200,00 between you and your best friend in the ratio 3:2
2. Divide R 240,00 in the ratio 3:4:5
3. Share 28 sweets between Joe and Amy in the ratio 3:1
4. 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

Exercise 11

1. 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?
   1. R11 800
   2. R27 540
   3. R4 400
2. 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.
   1. Sugar: 500g – R5.65;1kg – R11.90; 2kg – R18.99
   2. Coffee: 50g – R54.90;100g – R75.80;200g – R99.00
   3. Eggs: 6 – R11.40; 12 – R18.80; 30 – R31.99
   4. Cereal: 350g – R24.99; 500g – R28.00; 400g – R26.50
3. Give the rate for each of these statements below:
   1. A bus travels 480km in 8 hours. (km/h)
   2. 12 apples for R 7,20 (R/apple)
   3. A tap dripped 300ml of water in half an hour (ml/minute)
   4. 19,95 Gigabytes transferred in 19 minutes (Gb/minute)