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Ratio and Proportion - Understanding and simplifying ratios

Grade 6IGCSE

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

🔑Concepts

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A ratio is a way of comparing two or more quantities of the same kind, showing how much of one thing there is compared to another.

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Ratios can be written in three ways: using a colon (a:b), as a fraction (a/b), or using the word 'to' (a to b).

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The order of numbers in a ratio is very important; 2:3 is not the same as 3:2.

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To simplify a ratio, divide all numbers in the ratio by their Highest Common Factor (HCF) until they cannot be divided further.

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Before simplifying a ratio involving measurements, all quantities must be converted to the same units.

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Ratios do not have units themselves (e.g., the ratio of 5cm to 10cm is 1:2, not 1cm:2cm).

📐Formulae

Simplified Ratio=an:bn (where n=HCF of a and b)\text{Simplified Ratio} = \frac{a}{n} : \frac{b}{n} \text{ (where } n = \text{HCF of } a \text{ and } b)

Total number of parts=a+b\text{Total number of parts} = a + b

Fractional part of a=aa+b\text{Fractional part of } a = \frac{a}{a+b}

💡Examples

Problem 1:

Simplify the ratio 15:3515:35.

Solution:

3:73:7

Explanation:

Find the Highest Common Factor (HCF) of 15 and 35, which is 5. Divide both sides of the ratio by 5: 15á5=315 \div 5 = 3 and 35á5=735 \div 5 = 7.

Problem 2:

Simplify the ratio 400m:2km400\text{m} : 2\text{km}.

Solution:

1:51:5

Explanation:

First, convert both quantities to the same units. Since 1km=1000m1\text{km} = 1000\text{m}, then 2km=2000m2\text{km} = 2000\text{m}. The ratio becomes 400:2000400:2000. Divide both by the HCF (400) to get 1:51:5.

Problem 3:

Simplify the three-part ratio 12:18:2412:18:24.

Solution:

2:3:42:3:4

Explanation:

Find the HCF of 12, 18, and 24, which is 6. Divide each part by 6: 12á6=212 \div 6 = 2, 18á6=318 \div 6 = 3, and 24á6=424 \div 6 = 4.