Mathematics • Year 8 • Unit 1 • Lesson 1
Fractions, Decimals, Percentages
Build fluency with the three ways of writing the same proportion. One worked example, one guided example with blanks, then eight independent problems from quick recall to mixed conversions.
1. I do — fully worked example
Read every line. Each step has a short reason so you can see why, not just what.
Problem. Write 3/4 as a decimal and as a percentage.
Step 1 — Spot what a fraction means.
3/4 means "3 of 4 equal parts of one whole".
Reason: the top (numerator) counts the parts you have, the bottom (denominator) tells you how many parts make a whole.
Step 2 — Convert to a decimal by dividing top by bottom.
3 ÷ 4 = 0.75
Reason: the fraction bar IS a division sign. 3 ÷ 4 gives the same value as 3/4.
Step 3 — Convert the decimal to a percentage by × 100.
0.75 × 100 = 75, so 0.75 = 75%
Reason: "%" means "out of 100". Multiplying by 100 moves the decimal point two places right.
Step 4 — Check they're all the same value.
3/4 = 0.75 = 75%
Reason: three different ways of writing the SAME amount — three-quarters of a whole.
Answer: 3/4 = 0.75 = 75%.
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. Write 2/5 as a decimal and as a percentage.
Step 1 — What does 2/5 mean? ____ of ____ equal parts of one whole.
Step 2 — Divide top by bottom:
2 ÷ 5 = ______
Step 3 — Multiply by 100 to get a percentage:
______ × 100 = ______%
Step 4 — Put it together:
2/5 = ______ = ______%
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation (single conversion). The middle two are standard (two-step conversion). The last two are extension (compare or order across forms).
Foundation — single conversion
3.1 Write 1/2 as a decimal AND as a percentage. 1 mark
3.2 Write 30% as a fraction over 100 and as a decimal. 1 mark
3.3 Write the decimal 0.6 as a percentage. 1 mark
3.4 Write 1/10 as a decimal AND as a percentage. 1 mark
Standard — two-step conversion
3.5 Convert 4/5 to a percentage. Show the decimal step in your working. 2 marks
3.6 Convert 65% to a simplified fraction. (Hint: start with 65/100, then divide top and bottom by their HCF.) 2 marks
Extension — compare or order
3.7 Which is bigger: 7/10 or 68%? Convert both to decimals to compare, and write a one-sentence conclusion. 2 marks
3.8 Order these three values from smallest to largest: 3/5, 0.55, 58%. Show the form you converted them to before ordering. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded 2/5)
Step 1: 2 of 5 equal parts of one whole.
Step 2: 2 ÷ 5 = 0.4.
Step 3: 0.4 × 100 = 40%.
Step 4: 2/5 = 0.4 = 40%.
3.1 — 1/2
1 ÷ 2 = 0.5, then 0.5 × 100 = 50%. So 1/2 = 0.5 = 50%.
3.2 — 30%
30% = 30/100 = 0.30 (or just 0.3). As a fraction it's 30/100, which simplifies to 3/10.
3.3 — 0.6 as a percentage
0.6 × 100 = 60%. (Move the decimal point two places to the right.)
3.4 — 1/10
1 ÷ 10 = 0.1, then 0.1 × 100 = 10%. So 1/10 = 0.1 = 10%.
3.5 — 4/5 as a percentage
Decimal step: 4 ÷ 5 = 0.8. Then 0.8 × 100 = 80%.
3.6 — 65% as a simplified fraction
65% = 65/100. HCF of 65 and 100 is 5, so divide top and bottom by 5: 65 ÷ 5 = 13, 100 ÷ 5 = 20. Answer: 13/20.
3.7 — Which is bigger, 7/10 or 68%?
7/10 = 0.7. 68% = 0.68. Since 0.70 > 0.68, 7/10 is bigger (by 2 percentage points / 0.02).
3.8 — Order 3/5, 0.55, 58%
Convert all to decimals: 3/5 = 0.60; 0.55 stays as 0.55; 58% = 0.58. Ordered smallest to largest: 0.55 < 58% < 3/5.