1.5

Ratio, proportion and rate

10 flashcards to master Ratio, proportion and rate

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Key Concept Flip

Simplify the ratio 24:36:18.

Answer Flip

Find the greatest common factor (GCF) of the numbers. The GCF of 24, 36, and 18 is 6. Divide each number by the GCF: 24/6 : 36/6 : 18/6 = 4:6:3. Therefore, the simplified ratio is 4:6:3.

Key Concept Flip

Divide £420 in the ratio 2:3:7.

Answer Flip

Add the ratio numbers: 2+3+7 = 12. Divide the total amount by the sum: £420 / 12 = £35. Multiply each ratio number by this value: 2*£35 : 3*£35 : 7*£35 = £70 : £105 : £245. The amounts are £70, £105, and £245.

Key Concept Flip

If y is directly proportional to x, and y=10 when x=2, find y when x=5.

Answer Flip

Direct proportion means y = kx, where k is a constant. First find k: 10 = k * 2, so k = 5. Now find y when x=5: y = 5 * 5 = 25. Therefore, y = 25.

Key Concept Flip

If y is inversely proportional to x, and y=6 when x=4, find y when x=3.

Answer Flip

Inverse proportion means y = k/x, where k is a constant. First find k: 6 = k / 4, so k = 24. Now find y when x=3: y = 24 / 3 = 8. Therefore, y = 8.

Definition Flip

Define 'rate' and give an example.

Answer Flip

A rate is a ratio that compares two quantities with different units.

Example: speed is a rate that compares distance (km) to time (hours), often written as km/h.
Key Concept Flip

A car travels 150 km in 2 hours. Calculate its average speed.

Answer Flip

Speed is calculated as distance divided by time. Speed = 150 km / 2 hours = 75 km/h. Therefore, the average speed of the car is 75 km/h.

Key Concept Flip

Explain how to determine the 'best buy' when comparing prices of different sized items.

Answer Flip

Calculate the unit price for each item (price per unit of measure,

Example: price per gram). Divide the total price by the total quantity/amount. The item with the lowest unit price is the 'best buy'.
Key Concept Flip

A map has a scale of 1:50000. What real-world distance, in kilometers, is represented by 4 cm on the map?

Answer Flip

1 cm on the map represents 50000 cm in reality. So 4 cm represents 4 * 50000 cm = 200000 cm. Convert cm to km: 200000 cm = 2000 m = 2 km. Therefore, 4 cm on the map represents 2 km in reality.

Definition Flip

Define 'proportion'.

Answer Flip

A proportion is a statement that two ratios are equal. It is often used to solve problems where one quantity changes in relation to another, maintaining a constant relationship.

Key Concept Flip

Convert 500 US dollars to British pounds (£) if the exchange rate is £1 = $1.25.

Answer Flip

To convert USD to GBP, divide the USD amount by the exchange rate. £ = $500 / $1.25 = £400. Therefore, $500 is equivalent to £400.

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1.4 Powers and roots 1.6 Approximation and estimation

Key Questions: Ratio, proportion and rate

Define 'rate' and give an example.

A rate is a ratio that compares two quantities with different units.

Example: speed is a rate that compares distance (km) to time (hours), often written as km/h.
Define 'proportion'.

A proportion is a statement that two ratios are equal. It is often used to solve problems where one quantity changes in relation to another, maintaining a constant relationship.

About Ratio, proportion and rate (1.5)

These 10 flashcards cover everything you need to know about Ratio, proportion and rate for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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