Practice Maths

Topic Review — Rates & Ratios

Mixed Practice — L17 – L19

This review covers all lessons in the Rates & Ratios topic. Try each question before checking your answers.

Review Questions

  1. Unit rates — calculate and compare: Fluency

    1. Calculate the unit rate: $36 for 9 L of juice.
    2. Calculate the unit rate: 280 km in 4 hours.
    3. A car travels 480 km on 60 L of fuel. Express this as a unit rate in km/L and also in L/100 km.
    4. Convert 3 L/min to L/hour.
    5. Convert 90 km/h to m/s.
    6. Store A sells 6 apples for $2.40. Store B sells 8 apples for $3.60. Which store has the cheaper unit price?

  2. Simplifying and using ratios: Fluency

    1. Simplify 36:24.
    2. Simplify 75:100.
    3. Find the missing value: 4:7 = ?:35.
    4. Find the missing value: 5:3 = 25:?.
    5. Write ratio 3:5 as a fraction of the total for each part.
    6. Write ratio 2:3 as a percentage for each part.

  3. Graphing proportional relationships: Understanding

    1. A tap fills a tank at 20 L per minute. Write the ratio of time (min) to volume (L) and list four coordinate pairs you would plot on a graph.
    2. State the equation of the proportional relationship from the table: x = 1, 2, 3, 4 and y = 5, 10, 15, 20.
    3. A graph passes through (0, 0) and (8, 40). Find the gradient (rate) and write the equation.
    4. Does the equation y = 3x + 2 represent a proportional relationship? Explain why or why not.

  4. Dividing quantities in a given ratio: Fluency

    1. Divide $180 in ratio 2:3.
    2. Divide 420 mL in ratio 3:4.
    3. Divide $1200 in ratio 1:3:2.
    4. In ratio 5:3, the smaller share is $60. Find the total amount.
    5. Three friends divide a $540 winnings in ratio 4:3:2. How much does each friend receive?

  5. Mixed problem solving: Problem Solving

    1. A car uses petrol at 8.5 L/100 km. Petrol costs $1.75/L. What is the fuel cost for a 400 km trip?
    2. Paint is mixed in ratio 3:1 (red to white). How much white paint is needed to mix with 750 mL of red to make the correct colour?
    3. Two workers are paid in ratio 5:4 from a total wage bill of $1620. How much does each worker earn?
    4. A distance–time graph shows a straight line from (0, 0) to (2.5, 175). What is the speed represented by the gradient? How far would the object travel in 4 hours at this rate?
    5. A 2 L bottle of shampoo costs $8.40, and a 500 mL bottle costs $2.30. Calculate the unit price per 100 mL for each and determine which is better value.
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