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Ratio and Proportion - Dividing quantities into ratios

Grade 6IGCSE

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

🔑Concepts

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A ratio compares the sizes of two or more quantities.

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The 'Total Parts' is the sum of all the numbers in the ratio (e.g., in a:b, total parts = a + b).

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Dividing a quantity involves finding the value of 'one part' first.

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The sum of the divided shares must always equal the original total quantity.

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Always ensure all quantities are in the same units before dividing into a ratio.

📐Formulae

Total Number of Parts=a+b+c+…\text{Total Number of Parts} = a + b + c + \dots

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

Share=Ratio Number×Value of One Part\text{Share} = \text{Ratio Number} \times \text{Value of One Part}

💡Examples

Problem 1:

Divide $240 between Alice and Bob in the ratio 5:3.

Solution:

Alice gets 150andBobgets150 and Bob gets 90.

Explanation:

Step 1: Find total parts (5+3=85 + 3 = 8). Step 2: Find value of one part (240÷8=30240 \div 8 = 30). Step 3: Multiply by ratio values (Alice: 5×30=1505 \times 30 = 150; Bob: 3×30=903 \times 30 = 90).

Problem 2:

A recipe uses flour, sugar, and butter in the ratio 5:2:1. If the total weight of the mixture is 400g, find the weight of the sugar.

Solution:

100g

Explanation:

Step 1: Total parts = 5+2+1=85 + 2 + 1 = 8. Step 2: One part = 400g÷8=50g400g \div 8 = 50g. Step 3: Sugar is the middle part of the ratio (2), so 2×50g=100g2 \times 50g = 100g.

Problem 3:

A piece of wood is 1.2 meters long. It is cut into two pieces in the ratio 1:3. Calculate the length of the shorter piece in centimeters.

Solution:

30 cm

Explanation:

First, convert 1.2m to 120cm. Total parts = 1+3=41 + 3 = 4. One part = 120cm÷4=30cm120cm \div 4 = 30cm. The shorter piece represents 1 part, so 1×30cm=30cm1 \times 30cm = 30cm.