Rates Revision Notes

A rate is a way to compare two different quantities by division, showing how much of one quantity corresponds to a unit of another. For example, hourly wages express money earned per hour worked, and fuel efficiency shows distance travelled per unit of fuel. Understanding rates helps in interpreting everyday information and solving practical problems.

Rates are often expressed with units that combine the two quantities, such as kilometres per hour (km/h) for speed or dollars per hour ($/h) for wages. Correct use of units is essential to avoid confusion and ensure meaningful answers.

• Rates compare two different quantities.
• Units combine the quantities, e.g., km/h, $/h, litres/min.

Standard rates include hourly wages, currency exchange rates, rates of flow, and fuel efficiency. Calculations involve dividing one quantity by another to find the rate per unit.

For example, to calculate hourly wages, divide total earnings by total hours worked. If a worker earns $240 for 8 hours, hourly wage = $240 ÷ 8 = $30 per hour.

Currency exchange rates show how much one currency is worth in terms of another. If 1 US dollar equals 0.85 euros, the exchange rate is 0.85 euros per US dollar. To convert 100 US dollars to euros, multiply 100 × 0.85 = 85 euros.

• Hourly wage = total earnings ÷ hours worked.
• Currency exchange rate = amount of one currency per unit of another.
• Rates of flow measure volume or quantity per unit time, e.g., litres per minute.
• Fuel efficiency = distance travelled ÷ fuel used.

Some rates involve physical properties and require specific formulas, which will be provided in questions. Understanding these helps in science and geography contexts.

Pressure is defined as force per unit area, calculated as pressure = force ÷ area. For example, if a force of 200 newtons acts on an area of 0.5 m², pressure = 200 ÷ 0.5 = 400 pascals (Pa).

Density measures mass per unit volume, density = mass ÷ volume. For instance, if a block has mass 300 g and volume 100 cm³, density = 300 ÷ 100 = 3 g/cm³. This indicates how compact the material is within the given space, with units like g/cm³ or kg/m³ depending on context. Population density is the number of people per unit area, calculated as population density = population ÷ area. If a city has 1,000,000 people living in 250 km², population density = 1,000,000 ÷ 250 = 4,000 people per km².

• Pressure = force ÷ area (units: newtons per square metre or pascals).
• Density = mass ÷ volume (units: g/cm³ or kg/m³).
• Population density = population ÷ area (units: people per km²).

Average speed is a common rate that measures how fast something moves over a period of time. The fundamental formula is: speed = distance ÷ time.

To use this formula, ensure distance and time are in compatible units. For example, if a cyclist travels 45 km in 3 hours and 45 minutes, first convert 3 hours 45 minutes to hours: 3 + 45/60 = 3.75 hours.

Then calculate average speed: speed = 45 km ÷ 3.75 h = 12 km/h. This means the cyclist covers 12 kilometres every hour on average during the trip.

• Convert all units to compatible forms before calculating.
• Average speed = total distance ÷ total time.
• Example: 45 km in 3 h 45 min → 45 ÷ 3.75 = 12 km/h.

Correct units and notation are crucial for clarity and accuracy. For speed, common units include metres per second (m/s) or kilometres per hour (km/h). For density, units like grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³) are used.

When writing rates, use a slash or the word 'per' to indicate division, e.g., m/s means metres divided by seconds. Always include units in your final answer to communicate what the number represents.

Pay attention to unit conversions, such as converting minutes to hours or centimetres to metres, to maintain consistency in calculations.

• Use appropriate units for each rate type.
• Write units clearly, e.g., m/s, g/cm³, $/h.
• Convert units as needed before calculations.
• Include units in final answers.