📚 KS3 Cambridge Maths: Fractions, Decimals and Percentages | 剑桥KS3数学：分数、小数与百分数
eet: converting between fractions, decimals and percentages, comparing quantities, and using percentages in real-life problems. These skills form the foundation for ratio, proportion and probability work in later stages.
在本篇剑桥 KS3 数学复习文章中，我们重点讲解 p36_2.pdf 练习中覆盖的核心技能：分数、小数和百分数之间的转换、数量比较，以及在现实问题中应用百分数。这些技能为后续阶段的比、比例和概率学习打下基础。
1. Understanding Equivalent Fractions | 理解等值分数
= 5/10. This idea is essential when simplifying fractions or finding common denominators.
等值分数虽然形式不同，但表示相同的数值。我们可以将分子和分母同时乘或除以同一个非零数来得到等值分数。例如，1/2 = 2/4 = 5/10。这个概念在化简分数或寻找公分母时非常关键。
a/b = (a × n) / (b × n)
2. Converting Fractions to Decimals | 分数化小数
. Knowing common equivalents like 1/4 = 0.25 and 3/4 = 0.75 speeds up mental calculation.
将分数化为小数，可以用分子除以分母。有些分数得到有限小数，例如 3/8 = 0.375。有些分数得到循环小数，例如 1/3 = 0.333...。熟记常见等值关系，如 1/4 = 0.25 和 3/4 = 0.75，可以加快心算速度。
3/8 = 3 ÷ 8 = 0.375
3. Converting Decimals to Fractions | 小数化分数
method works for terminating decimals only; recurring decimals need a separate technique.
把小数写成分母为 10、100、1000 等的分数，然后化简。例如 0.45 = 45/100 = 9/20。对于像 1.6 这样的带小数，可以写成 1 + 6/10 = 1 3/5。这个方法只适用于有限小数；循环小数需要单独的方法。
0.45 = 45/100 = 9/20
4. Converting Fractions and Decimals to Percentages | 分数和小数化百分数
Percent means 'per hundred'. To change a decimal to a percentage, multiply by 100%. For example, 0.62 = 62% To change a fraction to a percentage, first convert it to a decimal, then multiply by 100%. For example, 3/5 = 0.6 = 60%. You can also write an equivalent fraction with denominator 100.
百分数表示 '每一百'。将小数化为百分数，乘以 100%。例如 0.62 = 62%。将分数化为百分数，可以先化为小数，再乘以 100%。例如 3/5 = 0.6 = 60%。也可以先写出分母为 100 的等值分数。
3/5 = 60/100 = 60%
5. Converting Percentages to Fractions and Decimals | 百分数化分数和小数
To change a percentage to a decimal, divide by 100. For example, 45% .45. To change a percentage to a fraction, write it over 100 and simplify. For example, 65% = 65/100 = 13/20. When the percentage includes a decimal, such as 12.5%, write 12.5/100 = 125/1000 = 1/8.
将百分数化为小数，除以 100。例如 45% = 0.45。将百分数化为分数，写成 100 作分母的分数并化简。例如 65% = 65/100 = 13/20。当百分数含有小数时，如 12.5%，写作 12.5/100 = 125/1000 = 1/8。
12.5% = 12.5/100 = 1/8
| Fraction 分数 | Decimal 小数 | Percentage 百分数 |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
6. Finding a Percentage of a Quantity | 求一个量的百分比
a quantity, convert the percentage to a decimal or fraction and multiply. For example, 15% ed in discounts, test scores and data interpretation. A useful mental method is to find 10% first and scale: 10% of 240 is 24, so 5% is 12, and 15% is 24 + 12 = 36.
求一个量的百分之几，先将百分数化为小数或分数，再相乘。例如 240 的 15% = 0.15 × 240 = 36。这个方法常用于折扣、考试成绩和数据分析。一个有用的心算方法是先找 10% 再倍增：240 的 10% 是 24，所以 5% 是 12，15% 就是 24 + 12 = 36。
15% of 240 = 0.15 × 240 = 36
7. Percentage Increase and Decrease | 百分数增减
An increase of 20% means the new value is 120% of the original, so multiply by 1.2. A decrease of 15% means the new value is 85% of the original, so multiply by 0.85. Do not add or subtract the percentage directly to the original if the change is calculated on a different base. For example, a 20% increase followed by a 20% decrease does not return to the starting value.
增加 20% 意味着新值是原值的 120%，所以乘以 1.2。减少 15% 意味着新值是原值的 85%，所以乘以 0.85。如果变化基于不同的基数，不能直接把百分数加到原值上或从原值中减去。例如，先增加 20% 再减少 20%，不会回到原来的数值。
Increase by 20%: new = old × 1.2
Decrease by 15%: new = old × 0.85
8. Comparing Fractions, Decimals and Percentages | 比较分数、小数和百分数
l to the same form, usually decimals or percentages. For example, compare 3/5, 0.58 and 55%. Start by converting: 3/5 = 0.6 = 60%, 0.58 = 58%, 55% = 55%. Now it is clear that 3/5 > 0.58 > 55%. This method reduces mistakes in ordering questions.
比较混合形式时，先把它们都转为同一种形式，通常是小数或百分数。例如，比较 3/5、0.58 和 55%。先转换：3/5 = 0.6 = 60%，0.58 = 58%，55% = 55%。现在很清楚 3/5 > 0.58 > 55%。这个方法可以减少排序题中的错误。
