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Ratio and Proportion - Direct proportion in real-life contexts

Grade 6IGCSE

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

🔑Concepts

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Definition of Direct Proportion: Two quantities are in direct proportion if they increase or decrease at the same rate. As one amount doubles, the other also doubles.

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The Constant of Proportionality: In a direct proportion, the ratio between the two quantities (y/x) always remains constant.

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The Unitary Method: A technique where you first find the value of a single unit (one item) and then multiply to find the required amount.

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Scaling: Multiplying or dividing both parts of a ratio by the same number to maintain the proportion.

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Graphing: The graph of two quantities in direct proportion is always a straight line passing through the origin (0,0).

📐Formulae

y1x1=y2x2\frac{y_1}{x_1} = \frac{y_2}{x_2} (Equality of Ratios)

y=kxy = kx (where kk is the constant of proportionality)

Unit Value=Total ValueNumber of Units\text{Unit Value} = \frac{\text{Total Value}}{\text{Number of Units}}

x1×y2=x2×y1x_1 \times y_2 = x_2 \times y_1 (Cross-multiplication for solving proportions)

💡Examples

Problem 1:

If 5 kg of apples cost $12.50, how much will 8 kg of apples cost?

Solution:

$20.00

Explanation:

Using the unitary method: First, find the cost of 1 kg. 12.50÷5=12.50 \div 5 = 2.50 per kg. Then, multiply the unit price by the desired quantity: 2.50×8=2.50 \times 8 = 20.00.

Problem 2:

A recipe for 6 people requires 300g of flour. How much flour is needed for 15 people?

Solution:

750g

Explanation:

Using the ratio method: 3006=x15\frac{300}{6} = \frac{x}{15}. Simplify the first ratio: 300÷6=50300 \div 6 = 50 (this is the flour per person). Multiply the flour per person by 15 people: 50×15=75050 \times 15 = 750g.

Problem 3:

A car travels 150 km in 3 hours at a constant speed. How far will it travel in 7 hours?

Solution:

350 km

Explanation:

Find the constant speed (distance per hour): 150÷3=50150 \div 3 = 50 km/h. Since distance is directly proportional to time at a constant speed, multiply speed by the new time: 50×7=35050 \times 7 = 350 km.