Year 7 Maths: Fractions Decimals and Percentages

Q: What is 4/5 written as a percentage?

Correct Answer: B) 80%. Explanation: 4/5 = 8/10 = 80/100 = 80%. Mark Scheme: 1 mark for 80%.

Q: Calculate 15% of £160.

Correct Answer: A) £24. Explanation: 10% of £160 = £16. 5% of £160 = £8. 15% = £16 + £8 = £24. Mark Scheme: 1 mark for £24.

Q: Which value is the LARGEST: 0.72, 3/4, 73%, or 7/10?

Correct Answer: B) 3/4. Explanation: 0.72 = 72%, 3/4 = 75%, 73% = 73%, 7/10 = 70%. Therefore, 3/4 (75%) is the largest. Mark Scheme: 1 mark for 3/4.

Key Learning Objectives

By the end of this lesson and revision module, Year 7 students will be able to:

Convert seamlessly between Fractions, Decimals, and Percentages (FDP equivalents).
Calculate fractions and percentages of amounts in real-life problem solving.
Order and compare fractional values by finding a common denominator.

Topic Summary & Essential Notes

Fractions, Decimals, and Percentages are three different ways of representing the exact same proportion or part of a whole. Percent literally means 'per hundred' or out of 100 (e.g. 45% = 45/100 = 0.45). To convert a fraction to a percentage, multiply by 100 or convert to an equivalent fraction over 100. To convert a percentage to a decimal, divide by 100 (move the decimal point 2 places left). Mastering benchmark equivalents (such as ½ = 0.5 = 50%, ¼ = 0.25 = 25%, ¾ = 0.75 = 75%, ⅕ = 0.2 = 20%, ⅛ = 0.125 = 12.5%, and ⅓ = 0.333... = 33.3%) allows rapid mental arithmetic.

Key Rules, Formulas & Definitions

Fraction of an Amount

(Amount ÷ Denominator) × Numerator (Divide by bottom, multiply by top)

Percentage to Decimal

Percentage ÷ 100 (e.g. 35% ÷ 100 = 0.35)

Benchmark Equivalents

½ = 0.5 = 50% | ¼ = 0.25 = 25% | ⅕ = 0.2 = 20% | ⅛ = 0.125 = 12.5% | 1/10 = 0.1 = 10%

2 Step-by-Step Worked Examples

Study these model solutions to understand how examiners award method and accuracy marks:

Worked Example 1

Worked Example 1: Finding a Fraction and Percentage of an Amount

Question: Calculate: (a) 3/8 of £240, and (b) 35% of £240.

Step-by-Step Solution:

Step 1: Part (a) Fraction calculation. Divide by denominator: £240 ÷ 8 = £30. Multiply by numerator: £30 × 3 = £90.
Step 2: Part (b) Percentage calculation. Method 1 (Non-calculator): 10% = £24, so 30% = £72; 5% = £12; Total 35% = £72 + £12 = £84.
Method 2 (Decimal multiplier): 0.35 × £240 = £84.

Final Answer: (a) £90, (b) £84

Senior Examiner Insight: Building percentages from 10%, 5%, and 1% is the safest non-calculator method.

Worked Example 2

Worked Example 2: Ordering Fractions, Decimals & Percentages

Question: Write the following numbers in ascending order (smallest to largest): 0.65, 3/5, 70%, 5/8.

Step-by-Step Solution:

Step 1: Convert all to decimals or percentages.
• 0.65 = 65% = 0.650
• 3/5 = 6/10 = 60% = 0.600
• 70% = 0.700
• 5/8 = 5 ÷ 8 = 0.625 = 62.5%
Step 2: Compare decimals. 0.600 < 0.625 < 0.650 < 0.700.
Step 3: Write in original format. 3/5, 5/8, 0.65, 70%.

Final Answer: 3/5, 5/8, 0.65, 70%

Senior Examiner Insight: Always convert to decimals with 3 decimal places to easily compare values like 0.625 and 0.650.

Common Pitfalls & Examiner Warnings

Avoid these common mistakes frequently identified by examiners in Key Stage 3 assessments:

Common Mistake: Treating 5% as 0.5 instead of 0.05

0.5 is 50%. 5% is 0.05. Misplacing the decimal loses the entire calculation mark.

Common Mistake: Thinking 0.6 is smaller than 0.58 because 6 < 58

0.6 is 0.60, which is larger than 0.58.

Common Mistake: Leaving answers in decimal form when asked for original numbers

When ordering mixed FDP lists, write your final answer using the original fractions/percentages given.

Interactive Self-Check Quiz (3 Questions)

Test your understanding before checking the full worked answer and examiner mark scheme:

Question 1 of 3

What is 4/5 written as a percentage?

A) 45%

B) 80%

C) 40%

D) 85%

Click to Reveal Answer & Mark Scheme

Correct Answer: B) 80%

Detailed Explanation: 4/5 = 8/10 = 80/100 = 80%.

Mark Scheme & Scoring Points: 1 mark for 80%.

Question 2 of 3

Calculate 15% of £160.

A) £24

B) £16

C) £32

D) £20

Click to Reveal Answer & Mark Scheme

Correct Answer: A) £24

Detailed Explanation: 10% of £160 = £16. 5% of £160 = £8. 15% = £16 + £8 = £24.

Mark Scheme & Scoring Points: 1 mark for £24.

Question 3 of 3

Which value is the LARGEST: 0.72, 3/4, 73%, or 7/10?

A) 0.72

B) 3/4

C) 73%

D) 7/10

Click to Reveal Answer & Mark Scheme

Correct Answer: B) 3/4

Detailed Explanation: 0.72 = 72%, 3/4 = 75%, 73% = 73%, 7/10 = 70%. Therefore, 3/4 (75%) is the largest.

Mark Scheme & Scoring Points: 1 mark for 3/4.

Created by Fiaraz Iqbal

Former Headteacher & Senior Science / Maths Examiner

With over 15 years of leadership and classroom experience, Fiaraz creates high-yield revision resources aligned with National Curriculum standards to help Key Stage 3 and GCSE students secure top grades.

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