Lesson 1: What is Percentage?

§Text Passage

1Summary 重點摘要

Percentage tells us how many parts out of 100. The symbol is %. For example, 50% means 50100, which is half.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: What is Percentage?A percentage shows how many parts out of a hundred one number takes. Example: out of 100 sweets, 25 are green, so the green sweets are 25100 of the total, written as 25%. A percentage is a fraction whose denominator is fixed at 100, which makes comparison easy because everyone uses the same standard. Another example: in a class of 40, 10 students wear glasses; the denominator is not 100, so write nothing yet — first 10 ÷ 40 = 0.25, and only then do you know 25% wear glasses.
2. Part 2: How to read it?To read a percentage, read the number before the % sign, then say 'percent'. Example: 50% reads as 'fifty percent', 75% as 'seventy-five percent', 100% as 'one hundred percent'. The symbol % itself means 'out of 100', so whenever you see it, you know the number is divided by 100. Another example: 6% reads 'six percent' and 120% reads 'one hundred and twenty percent'; a decimal percentage such as 12.5% reads 'twelve point five percent', following the decimal reading.
3. Part 3: Percentage and FractionsA percentage is really a fraction with denominator 100. Example: 30% = 30100, and simplifying (dividing top and bottom by 10) gives 310. To turn a fraction into a percentage, first write it with denominator 100, then use the % sign. Another example: 75% = 75100, simplifying to 34; conversely, 34 can be pictured as 75100 and written 75%. In every conversion, aim for denominator 100 before the % sign.
4. Part 4: Percentage and DecimalsPercentages and decimals convert easily. To change a percentage into a decimal, divide the number before the % sign by 100. Example: 45% = 45 ÷ 100 = 0.45. To change a decimal into a percentage, multiply by 100 and add the % sign: 0.45 × 100 = 45%. Another example: 8% = 8 ÷ 100 = 0.08; the single digit 8 needs a padded zero after moving two places left, and the check 0.08 × 100 = 8% agrees.
5. Part 5: Everyday ExamplesPercentages appear everywhere in daily life. Example: a test is out of 100 and you scored 85, so your result is 85%. If the test is out of 50 and you scored 40, first rewrite it with denominator 100: 4050 = 80100 = 80%, which makes comparing results easy. Another example: a juice bottle labelled '30% juice' means every 100 mL contains 30 mL of juice; labels use percentages precisely to state proportions clearly.
6. Part 6: What is 100%?100% means the whole amount, because 100100 = 1. Example: '100% win' means everyone wins; '100% satisfied' means every person asked is satisfied. Remember that 100% is exactly the whole thing, no more and no less. Another example: spending 100% of $100 leaves not a dollar; spending 50% means half. Picture 100% as 'the whole', and the sizes of all percentages become easy to grasp.
7. Part 7: Can it exceed 100%?A percentage can be more than 100% to show more than the whole. Example: if this year's sales are 200% of last year's, this year is double last year; 150% means one and a half times. Because a percentage only counts how many hundreds, there is no limit: 200% and 300% are both fine. Another example: savings growing from $2000 to $2600 in a year rise by $600, which is 600 ÷ 2000 = 30% of the original, so the new amount is 130% of the old.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Percentage is a fraction with denominator 100, symbol is %
• 50% = 50100 = 0.5
• Percentage, fraction and decimal can be converted
• 100% means the whole thing, i.e. 1
• Percentage can exceed 100%