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Number - Ratio and proportion

Grade 7IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Definition of Ratio: A way to compare two or more quantities of the same kind, expressed as a:ba:b.

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Simplifying Ratios: Ratios are simplified by dividing all terms by their Highest Common Factor (HCF). Ratios must have the same units before simplifying.

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Dividing a Quantity: To share a total amount into a given ratio, find the total number of parts, calculate the value of one part, and multiply by the required shares.

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Direct Proportion: Two quantities are in direct proportion if one increases at the same rate as the other (y=kxy = kx).

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Inverse Proportion: Two quantities are in inverse proportion if one increases while the other decreases at the same rate (y=kxy = \frac{k}{x}).

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Map Scales: Expressed as a ratio 1:n1:n, where 1 unit on the map represents nn units in real life.

📐Formulae

Total Parts=a+b+c\text{Total Parts} = a + b + c

Value of One Part=Total QuantityTotal Parts\text{Value of One Part} = \frac{\text{Total Quantity}}{\text{Total Parts}}

Direct Proportion (Unitary Method):Price per unit=Total CostQuantity\text{Direct Proportion (Unitary Method)}: \text{Price per unit} = \frac{\text{Total Cost}}{\text{Quantity}}

Scale Ratio=Map DistanceActual Distance\text{Scale Ratio} = \frac{\text{Map Distance}}{\text{Actual Distance}}

💡Examples

Problem 1:

Simplify the ratio 450g:2kg450\text{g} : 2\text{kg}.

Solution:

9:409:40

Explanation:

First, convert both to the same units: 450g:2000g450\text{g} : 2000\text{g}. Divide both sides by the HCF, which is 50. 450÷50=9450 \div 50 = 9 and 2000÷50=402000 \div 50 = 40.

Problem 2:

Divide 120intotheratio120 into the ratio 3:5$.

Solution:

45and45 and 75

Explanation:

Total parts = 3+5=83 + 5 = 8. Value of one part = 120÷8=15120 \div 8 = 15. First share = 3×15=453 \times 15 = 45. Second share = 5×15=755 \times 15 = 75.

Problem 3:

If 8 pens cost $12.40, how much do 5 pens cost?

Solution:

$7.75

Explanation:

Find the cost of one pen (unitary method): 12.40÷8=1.5512.40 \div 8 = 1.55. Then multiply by 5: 1.55×5=7.751.55 \times 5 = 7.75.

Problem 4:

On a map with a scale of 1:50,0001:50,000, the distance between two towns is 6cm6\text{cm}. What is the actual distance in kilometers?

Solution:

3km3\text{km}

Explanation:

Actual distance = 6cm×50,000=300,000cm6\text{cm} \times 50,000 = 300,000\text{cm}. To convert cm to km: 300,000÷100=3,000m300,000 \div 100 = 3,000\text{m}, then 3,000÷1,000=3km3,000 \div 1,000 = 3\text{km}.