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Learn: Fractions, Decimals, and Percentages
OCR GCSE Mathematics J560
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Welcome!I've reviewed your growth areas, and this lesson is designed to strengthen your understanding of fractions, decimals, and percentages. We'll explore key concepts, examples, and practice questions to help you master them.
What are Fractions, Decimals, and Percentages?Fractions, decimals, and percentages are three ways of expressing parts of a whole. A fraction is written as a numerator over a denominator (e.g., 1/2). A decimal represents the same value in base-10 form (e.g., 0.5). A percentage expresses it as a proportion out of 100 (e.g., 50%). These are used in everyday life, like calculating discounts, comparing quantities, and estimating values.
Converting Between Fractions, Decimals, and PercentagesTo convert a fraction to a decimal, divide the numerator by the denominator (e.g., 1 ÷ 2 = 0.5). To convert a decimal to a percentage, multiply by 100 and add the percentage sign (e.g., 0.5 × 100 = 50%). Converting percentages back to fractions involves writing the percentage as a fraction over 100 and simplifying (e.g., 50% = 50/100 = 1/2).
Quick check: What is 3/4 as a decimal?
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Calculating PercentagesA percentage represents a part out of 100. To find a percentage of a number, multiply the number by the percentage (as a decimal). For example, to find 20% of £50, calculate £50 × 0.2 = £10. This is useful for things like finding discounts or tax amounts.
Match the items on the left with their correct pairs on the right
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Percentage ChangeTo calculate percentage change, use the formula: ((new value - original value) ÷ original value) × 100. This tells you how much a quantity has increased or decreased as a percentage. For example, if a price rises from £40 to £50, the percentage increase is ((£50 - £40) ÷ £40) × 100 = 25%.
The percentage change formula is (({{blank0}} - original value) ÷ {{blank1}} value) × 100.
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Reverse PercentagesA reverse percentage helps you find the original value of something after a percentage change. To reverse a percentage increase, divide the final value by (1 + percentage increase as a decimal). For example, if £120 is 20% more than the original price, divide £120 by 1.2 to find the original price (£120 ÷ 1.2 = £100).
Quick check: If £72 is after a 10% discount, what was the original price?
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Review Time!Great work! You've learned about fractions, decimals, percentages, and percentage change. Let’s test your understanding with a few final questions.
Select all that apply: Which of the following are equivalent to 1/4?
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Match the items on the left with their correct pairs on the right
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Match the items on the left with their correct pairs on the right
Start the lesson to answer this matching question
Well done!You’ve completed the lesson on fractions, decimals, and percentages. Keep practising to strengthen your understanding further!
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