Ratio, Rate and Speed

Ratio, Rate and Speed1. Ratio

- What’s ratio- Writing ratios as fractions- Simplifying ratios (Equivalent ratios)- Ratios in measurement- Ratios involving rational numbers

2. Rate- Dividing a quantity in a given ratio- Rate and average rate

3. Speed- Speed, average speed and uniform speed- Conversion of units for speed

RatioWe otten need to compare two or more numbers or quantities. Look atthe pictures below.

The ratio of the number of cats to the number of birds.....

where the symbol “:” means “is to”.The ratio 3 : 1 —> there are three cats for every one bird.

Ratio and Proportion

A ratio can also be used to compare more than two numbers or quantities.As shown in the pictures below,

The ratio of ...... the number of bicycles to the number of cars to the number of motorcycles can be expressed as 3:3:1.

We can tell from the ratio that there are three bicycles for every one motorcycle and two cars for every one motorcycle.

Ratio and Proportion

A ratio is a comparison of two quantities, say a and b, given in a particular order. The ratio of a to b can be written as a : b, where the symbol : stands for “is to”.

A ratio can also be extended to compare more than two quantities. For example, when there are more than two quantities, say a, b and c, the ratio can be written as a : b : c.

Example I(a) The picturc below shows some cups and mugs. Write down the ratio of the number of mugs to the number of cub.

(b) A bowl contains 2 pears some cups and mugs. Write down the ratio of the number of pears to the number of orunges to the number of apples.

Exercise 5A1. Express each of the following as a ratio in the order given.

(a) The pumter of knives to the numiber of forks.

(b) The number of mice to the number of cheese.

(c) The number of shirts to the number of pegs.

(d) The numiber of birds to the number of tree.

(e) The numher of drums to the number of whistles

(f) The number of car to the number of trucks.

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Exercise 5A2. In a recent term test, Alvin obrained 31 marks for Science, 24 marks for Mathematics and 35 marks for English. Write down the ralio of his Science marks to his Mathematics marks to his English mark.

3. The Cabinet of a government has a prime minister, 2 deputy prime ministers and 12 ministers. Write down the ratio of the number of prime ministers to the number of deputy prime ministens to the number of ministers.

4. In a molecule of an organic acid, there are 3 carbon atoms, 6 hydrogen atoms and 2 oxygen atoms. Write down the ratio of the number of oxygen atoms to the number of hydrogen atoms to the number of carbon atoms.

Exercise 5A5. To make a pound cake, 7 cups of flour, 3 cups of butter and 2 cups of sugur are needed. Wite down the ratio of

(a) the amount of flour to the amount of sugar. the amount of sugar,

(b) the amount of sugar to the amount of butter to the ammount of four.

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Writing ratios as fraction

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3.Expressing Percentages as Fractions and Decimals

3.1.1 Percentages less than 100%

9 out of 100 plants is when expressed as a percentage.

9% can be written as in fraction from.

9% can also be written as in decimal form

A percentage is indicated by symbol % (percent), which mean “out of one hundred”. Thus, a percentage is a fraction whose denominator is 100.

Example : 11% =

5% =



Exercise 3A1. Express the following percentages as fractions in the simplest from.

a) 20% b) 50% c) 25%

d) 75% e) 2.5% f) 12.5%

g) 87 % h) 33 % i) 66 %



Exercise 3A1. Express the following percentages as decimals.

a) 50% b) 40% c) 24%

d) 42% e) 37.5% f) 42.5%

g) 2 % h) 16 % i) 21 %


3.1.1 Percentages greater than 100%Example : 110% =

250% =

130% =

235% =



Exercise 3A4. Express the following percentages as fractions and decimals.

a) 120% b) 180% c) 150%

d) 160% e) 125% f) 175%

g) 275% h) 225% i) 304%

Percent Calculation

• What is 5 % of 200?• What percent is 9 of 45?• 25% of what number is 4?

We can use the equation to solve percentage problems:

Example: What is 5 % of 200?

Percent Calculation



Example: What percent is 9 of 45?

Percent Calculation



Example: 25% of what number is 4?

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Exercise 3.1A

• What is 25 % of 375?

• What is 150% of 90?

• What percent is 134 of 670?

• What percent is 40 of 160?

• What percent is 1.2 of 6.0?

• 40% of what number is 18?



Ratio, Rate and Speed

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