Practice Maths

Topic Review — Fractions, Decimals & Percentages #2

Mixed Practice — L35 – L37

This review covers all three lessons: converting between representations (L35), expressing quantities as fractions and percentages (L36), and multiplying decimals in context (L37). Try every question before checking your answers.

Review Questions

  1. Converting Between Fractions, Decimals and Percentages Fluency

    Convert each value into the other two forms:

    1. 3/5 → decimal and percentage
    2. 0.45 → fraction (simplified) and percentage
    3. 70% → decimal and fraction (simplified)
    4. 7/8 → decimal and percentage
    5. 0.06 → fraction (simplified) and percentage
    6. 37.5% → decimal and fraction (simplified)

  2. Expressing Quantities as Fractions and Percentages Fluency

    Convert to the same units where needed, then express as a simplified fraction and a percentage:

    1. 18 out of 24
    2. 35 out of 50
    3. 9 out of 36
    4. 150 cm out of 2 m
    5. 800 mL out of 2 L
    6. 30 minutes out of 2 hours
    7. 6 months out of 3 years
    8. 750 m out of 3 km

  3. Multiplying and Dividing Decimals Fluency

    Calculate each answer. Show your working for multiplication questions.

    1. 4.6 × 3
    2. 2.5 × 1.4
    3. 0.8 × 0.7
    4. 3.6 × 0.05
    5. 0.12 × 0.4
    6. 9.6 ÷ 4
    7. 7.2 ÷ 0.9
    8. 0.54 ÷ 0.06
    9. 5.85 × 10
    10. 0.034 × 1000

  4. Order and Missing Values Understanding

    1. Order from smallest to largest: 0.72, 68%, 3/4, 0.7, 71%
    2. Order from smallest to largest: 1/3, 0.34, 33%, 0.3, 2/6
    3. Find the missing number: 30% of n = 21
    4. Find the missing number: 2/5 of n = 16
    5. Find the missing number: 0.4 × __ = 2.8
    6. True or False: 0.7 × 0.7 = 0.49. Explain.

  5. Real-World Applications Problem Solving

    1. A student scored 42 out of 56 on a test. Express this as a percentage. If a pass requires 75%, did the student pass?
    2. In a class of 30 students, 18 walk to school. What fraction and percentage walk to school?
    3. Strawberries cost $5.80 per kg. How much do 2.5 kg cost?
    4. A hoodie costs $75. It is on sale with a 20% discount. What is the sale price? (Multiply by 0.8.)
    5. A recipe for 6 people calls for 1.2 kg of mince. How much mince is needed for 10 people?
    6. A car uses 7.2 litres per 100 km. Petrol costs $2.05 per litre. What is the total fuel cost for a 350 km trip?
    7. Emily saves $45 from her weekly earnings of $180. James saves $30 from $100. Express each saving as a percentage. Who saves the higher proportion?
    8. A tank holds 2500 litres. After some use it contains 1750 litres. Express the amount used as a fraction and percentage of the total capacity.

  6. Find the original amount: Understanding

    1. After a 20% discount, a shirt costs $48. What was the original price?
    2. 15% of a number is 12. What is the number?
    3. After an 8% increase, a value is 54. What was the original value (round to the nearest whole number)?

  7. Express each as a percentage: Fluency

    1. 45 out of 180
    2. 7 out of 28
    3. 12 out of 80
    4. 55 cm out of 2.2 m

  8. Currency and unit conversions using decimals: Understanding

    1. Convert AUD $45.60 to USD if the exchange rate is 0.65 (multiply by 0.65).
    2. A petrol station charges $1.89 per litre. A car has a 52 L tank. How much does a full tank cost?

  9. Compare and interpret: Problem Solving

    Team A won 14 out of 20 games. Team B won 21 out of 30 games.

    1. Express each team’s win rate as a percentage.
    2. Which team performed better?
    3. If Team A plays 10 more games at the same win rate, how many total games will they have won?

  10. True or False — explain each answer: Understanding

    1. 0.09 × 10 = 0.9
    2. 3/8 as a decimal is 0.375
    3. 50% of 80 equals 80% of 50
    4. 0.1 × 0.1 = 0.1
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