Show model answer and explanation
0.75
3 ÷ 4 = 0.75.
Class 6 · English Version · Mathematics
Number, fractions, decimals and percentages
Move between fraction, decimal and percentage forms and check proportional change.
About this lesson and its coverage
Shared cross-level core and stretch unit. Start with the core questions, then use the stretch example for deeper work. The same unit is available in related class and board pathways; it is not a full grade-specific or examination-specification course. A teacher should select the appropriate depth and further topics.
Learn the idea
A fraction compares a part with a whole; a percentage expresses a ratio per hundred. Divide the numerator by the denominator for a decimal. A percentage change uses the original value as its base, so equal percentage increases and decreases need not cancel.
Worked example
3/8 = 0.375 = 37.5%. A Tk 800 price increased by 10% becomes 800 × 1.10 = Tk 880; reducing 880 by 10% gives Tk 792, not Tk 800.
- Name the whole or original amount.
- Convert using division or a scale factor.
- Check size and explain the base used.
Stretch example
A quantity grows by 5% each year from 400. After two years it is 400 × 1.05² = 441. For growth model V = 400(1.05)^t, t counts whole years in this calculation; extrapolation needs the constant-rate assumption.
Your written practice
Show your working on paper. Check your answer, then choose Next.
Show model answer and explanation
20
Multiply the decimal by 100.
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36
0.15 × 240 = 36.
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5/6
4/6 + 1/6 = 5/6.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
Dividing the same whole into four equal parts gives larger parts than dividing it into five.
Keep the whole fixed in the explanation.
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480
500 × 1.2 × 0.8 = 480.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
t = ln(2) / ln(1.05), approximately 14.21.
Take logarithms on both sides; distinguish the continuous solution from the first whole year exceeding double.
Progress and browser storage
Notebook challenge, sources and further study
Compare changes
Compare simple and compound increases on the same starting amount for three years.
Review with a guardian or teacher
- State the original base.
- Show each year’s calculation.
- Explain why the results differ.
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