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Fractions Decimals and Percentages
Fractions, Decimals & Percentages
Year 7 — Clear conversions, examples, and practice..
1. Key ideas (quick)
Fractions, decimals and percentages are different ways to show the same part of a whole.
Fraction
A fraction like 3/5 shows parts of a whole (3 parts out of 5).
Decimal
A decimal like 0.6 is a fraction written in base 10.
Percentage
A percentage like 60% means per hundred — 60 out of 100.
Quick links
Fraction ↔ Decimal ↔ Percentage conversions are essential for comparison and real-life problems.
2. Converting between forms
Fraction → Decimal
Divide numerator by denominator.
Example:
3/4 = 3 ÷ 4 = 0.75Fraction → Percentage
Convert to decimal first, then ×100, or multiply fraction by 100/1.
Example:
3/4 = 0.75 = 75%Decimal → Fraction
Write the decimal over the place value, then simplify.
Example:
0.6 = 6/10 = 3/5Decimal → Percentage
Multiply by 100. 0.25 × 100 = 25%
Percentage → Decimal
Divide by 100. 45% = 45 ÷ 100 = 0.45
Percentage → Fraction
Write over 100 and simplify. 30% = 30/100 = 3/10
3. Worked examples
a) Convert 7/8 to a decimal and percentage.
7 ÷ 8 = 0.875 → 0.875 × 100 = 87.5%
b) Convert 0.375 to a fraction and percentage.
0.375 = 375/1000 = 3/8 → 0.375 × 100 = 37.5%
c) Convert 55% to fraction and decimal.
55% = 55/100 = 11/20 → 55 ÷ 100 = 0.55
4. Comparing amounts
To compare fractions, decimals or percentages, convert them to the same form — usually decimal or percentage is quickest.
Which is larger: 3/5 or 0.58?
3/5 = 0.6, so 0.6 > 0.58, therefore 3/5 is larger.
5. Real-life uses & tips
- Percentages are used for discounts, interest rates and statistics.
- Use calculators for tricky divisions, but teach exact fraction answers when possible.
- When a decimal terminates or repeats — show both (e.g. 1/3 = 0.333… = 33.3%).
6. Practice
- Convert to a decimal:
5/8. - Convert to a percentage:
7/20. - Convert to a fraction:
0.125. - Which is larger:
0.72or3/4? - Convert
12.5%to a fraction and a decimal. - Express
2/3as a decimal (to 3 decimal places) and a percentage (to 1 decimal place). - Write
0.08as a percentage and fraction. - Convert
125%to a decimal and fraction. - Simplify and convert
45/60to a percentage. - Explain why
1/4 = 25% = 0.25.
Answers (teacher)
5/8 = 0.6257/20 = 0.35 = 35%0.125 = 125/1000 = 1/83/4 = 0.75, 0.75 > 0.7212.5% = 12.5 ÷ 100 = 0.125 = 1/82/3 = 0.666… ≈ 0.667 (3 d.p.), 2/3 = 66.7% (1 d.p.)0.08 = 8% = 8/100 = 2/25125% = 125 ÷ 100 = 1.25 = 5/445/60 = 3/4 = 0.75 = 75%1/4 = 1 ÷ 4 = 0.25 and 0.25 × 100 = 25%