📚 Cambridge KS3 Maths: Fractions, Decimals and Percentages | 剑桥 KS3 数学：分数、小数和百分数
Understanding how fractions, decimals and percentages are connected is a core skill in Cambridge KS3 Mathematics. This revision guide walks you through key conversions, operations and real-world applications, with plenty of examples.
理解分数、小数和百分数之间的联系是剑桥 KS3 数学的核心技能。本复习指南将带你掌握关键转换、运算和实际应用，并提供大量例题。
1. Place Value and Decimal Basics | 位值与小数基础
Decimals are based on place value. The first digit after the decimal point is tenths, the second is hundredths, and the third is thousandths.
小数基于位值。小数点后第一位是十分位，第二位是百分位，第三位是千分位。
For example, 0.35 means 3 tenths and 5 hundredths, which is the same as 35/100.
例如，0.35 表示 3 个十分之一和 5 个百分之一，也就是 35/100。
You should be able to read and write decimals in words. 0.07 is seven hundredths, and 2.405 is two and four hundred five thousandths.
你应该能够读写小数。0.07 是百分之七，2.405 是二又千分之四百零五。
2. Converting Fractions to Decimals | 分数转换为小数
To convert a fraction to a decimal, divide the numerator by the denominator. For simple fractions, you can use equivalent fractions with denominators of 10, 100 or 1000.
要将分数转换为小数，用分子除以分母。对于简单分数，可以利用分母为 10、100 或 1000 的等值分数。
: 3/4 = 75/100 = 0.75. You can also divide 3 by 4 on a calculator or using short division.
例如：3/4 = 75/100 = 0.75。你也可以用计算器或短除法计算 3 除以 4。
recurring decimals, such as 1/3 = 0.333... which is written as 0.3 with a dot above the 3.
有些分数会得到循环小数，例如 1/3 = 0.333... 写作 0.3，并在 3 上方加一个点。
3. Converting Decimals to Percentages | 小数转换为百分数
To convert a decimal to a percentage, multiply the decimal by 100 and add the percent symbol. This is the same as moving the decimal point two places to the right.
要将小数转换为百分数，将小数乘以 100 并加上百分号。这相当于将小数点向右移动两位。
Example: 0.65 × 100 = 65%, so 0.65 = 65%. Another example: 0.08 = 8%.
例如：0.65 × 100 = 65%，所以 0.65 = 65%。另一个例子：0.08 = 8%。
If the decimal is greater than 1, the percentage will be greater than 100%. For instance, 1.25 = 125%.
如果小数大于 1，百分数将大于 100%。例如，1.25 = 125%。
4. Converting Fractions to Percentages | 分数转换为百分数
To convert a fraction to a percentage, first convert the fraction to a decimal, then multiply by 100. Alternatively, find an equivalent fraction with denominator 100.
要将分数转换为百分数，先将分数转换为小数，再乘以 100。或者，找到一个分母为 100 的等值分数。
Example: 2/5 = 40/100 = 40%. Another example: 7/20 = 35/100 = 35%.
例如：2/5 = 40/100 = 40%。另一个例子：7/20 = 35/100 = 35%。
vide the numerator by the denominator and multiply by 100. For example, 5/8 = 0.625 = 62.5%.
对于不容易转换成分母为 100 的分数，用分子除以分母再乘以 100。例如 5/8 = 0.625 = 62.5%。
5. Ordering Fractions, Decimals and Percentages | 排序分数、小数和百分数
To compare and order fractions, decimals and percentages, convert all of them into the same form. Decimals are often the easiest to compare.
要比较和排序分数、小数和百分数，需要将它们转换成相同的形式。小数通常最容易比较。
Example: Order 3/5, 0.55 and 58% from smallest to largest. Convert: 3/5 = 0.6, 58% = 0.58. The order is 0.55, 0.58, 0.6.
例如：将 3/5、0.55 和 58% 从小到大排列。转换后：3/5 = 0.6，58% = 0.58。顺序是 0.55、0.58、0.6。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/2 | 0.5 | 50% |
| 3/4 | 0.75 | 75% |
Use a number line or place value chart to help you see which value is largest or smallest.
可以使用数轴或位值表来帮助判断哪个值最大或最小。
6. Adding and Subtracting Fractions | 分数的加法与减法
To add or subtract fractions, they must have the same denominator. If they do not, find the lowest common denominator first.
要对分数进行加法或减法，它们必须有相同的分母。如果分母不同，首先找到最小公分母。
denominator is 12, so 1/3 = 4/12 and 1/4 = 3/12. Therefore 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
例如：1/3 + 1/4。最小公分母是 12，因此 1/3 = 4/12，1/4 = 3/12。所以 1/3 + 1/4 = 4/12 + 3/12 = 7/12。
For mixed numbers, add or subtract the whole number parts and the fraction parts separately, borrowing if necessary.
对于带分数，分别加减整数部分和分数部分，必要时进行借位。
7. Multiplying and Dividing Fractions | 分数的乘法与除法
To multiply fractions, multiply the numerators together and multiply the denominators together. Simplify the result if possible.
要相乘分数，将分子相乘，分母相乘。如果可能，化简结果。
Example: 2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15.
例如：2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15。
To divide by a fraction, multiply by its reciprocal. The reciprocal of a fraction is obtained by swapping the numerator and denominator.
要除以一个分数，乘以它的倒数。分数的倒数是将分子和分母互换后得到的。
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
例如：3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8。
8. Percentage of an Amount | 求一个数的百分数
To find a percentage of an amount, convert the percentage to a decimal and multiply by the amount. You can also find 1% first and then scale up.
要求一个数的百分数，将百分数转换为小数，再乘以这个数。你也可以先求 1%，然后再扩大。
Example: Find 15% of 240. 15% = 0.15, so 0.15 × 240 = 36.
例如：求 240 的 15%。15% = 0.15，所以 0.15 × 240 = 36。
Alternative method: 10% of 240 = 24, 5% of 240 = 12, so 15% = 24 + 12 = 36.
另一种方法：240 的 10% 是 24，240 的 5% 是 12，因此 15% = 24 + 12 = 36。
9. Percentage Increase and Decrease | 百分数增减
To increase an amount by a percentage, find the percentage of the amount and add it to the original. To decrease, subtract it.
要将一个数增加某个百分数，先求出这个百分数对应的值，再加到原数上。减少则减去该值。
Example: Increase 80 by 25%. 25% of 80 = 20, so the new amount is 80 + 20 = 100.
例如：将 80 增加 25%。80 的 25% 是 20，所以新的数是 80 + 20 = 100。
You can also use a multiplier. For a 25% increase, the multiplier is 1.25. For a 15% decrease, the multiplier is 0.85.
也可以使用乘数。增加 25% 时，乘数是 1.25。减少 15% 时，乘数是 0.85。
New value = Original value × Multiplier
新值 = 原值 × 乘数
10. Real-World Problems and Word Problems | 实际问题与文字题
Many KS3 exam questions ask you to apply fractions, decimals and percentages to real-life situations such as discounts, sales, interest and recipes.
许多 KS3 考试题目要求你将分数、小数和百分数应用到实际生活中，例如折扣、销售、利息和食谱等。
Example: A jacket costs £45. In a sale, the price is reduced by 20%. Find the sale price. 20% of 45 = £9, so the sale price is £45 - £9 = £36.
例如：一件夹克售价 45 英镑。促销期间价格降低 20%。求促销价。45 的 20% 是 9 英镑，因此促销价为 45 - 9 = 36 英镑。
uses 2/3 cup of sugar. You want to make 1 1/2 times the recipe. How much sugar do you need? 2/3 × 3/2 = 6/6 = 1 cup.
另一个例子：一份食谱需要 2/3 杯糖。你想做原食谱的 1 1/2 倍。需要多少糖？2/3 × 3/2 = 6/6 = 1 杯。
Always read the question carefully, identify the operation needed, and check that your answer makes sense in the context.
务必仔细审题，确定所需的运算，并检查答案在上下文中是否合理。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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