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Cambridge KS3 Maths: Fractions, Decimals and Percentages - Page 41 Exercise 2 | 剑桥KS3数学：分数、小数与百分数 - 第41页练习2

2026-08-21 11:17 · 本文部分内容由AI辅助创作

📚 Cambridge KS3 Maths: Fractions, Decimals and Percentages - Page 41 Exercise 2 | 剑桥KS3数学：分数、小数与百分数 - 第41页练习2

This revision article covers the key skills from a typical Cambridge KS3 mathematics exercise on fractions, decimals and percentages. You will learn how to switch between these three forms, calculate with fractions, solve percentage problems, and avoid common errors. The examples are designed to match the style of questions you may meet in a Page 41, Exercise 2 worksheet.

本文复习剑桥KS3数学中关于分数、小数和百分数的核心知识，内容对应典型的第41页练习2。你将学习如何在这三种形式之间转换、进行分数计算、解决百分数问题，并避免常见错误。文中例题贴近你在第41页练习2中可能遇到的题型。

1. Equivalent Fractions and Simplifying | 等值分数与化简

A fraction represents a part of a whole. The top number is the numerator, and the bottom number is the denominator. Equivalent fractions have the same value but different numerators and denominators, such as 1/2, 2/4, and 3/6.

分数表示整体的一部分。上面的数是分子，下面的数是分母。等值分数数值相同但分子和分母不同，例如 1/2、2/4 和 3/6。

their highest common factor, or HCF. For 12/18, the HCF of 12 and 18 is 6, so 12/18 = 2/3.

化简分数时，用分子和分母的最大公因数，即 HCF，同时相除。例如 12/18，12 和 18 的最大公因数是 6，所以 12/18 = 2/3。

plying or dividing both parts by the same non-zero number. For example, 3/5 = 6/10 = 9/15.

等值分数可以通过将分子和分母同时乘以或除以同一个非零数得到。例如 3/5 = 6/10 = 9/15。

2. Fractions of an Amount | 求一个数量的几分之几

multiply by the numerator. For example, 3/5 of 40 is found by 40 ÷ 5 = 8, then 8 × 3 = 24.

求一个数量的几分之几时，先除以分母，再乘以分子。例如 40 的 3/5：先算 40 ÷ 5 = 8，再算 8 × 3 = 24。

This method works because the denominator tells you how many equal parts the whole is split into, and the numerator tells you how many of those parts are needed.

这种方法成立是因为分母表示整体被分成多少等份，分子表示需要取其中的几份。

3. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分数的转换

The three forms are connected. A fraction can be written as a decimal by dividing the numerator by the denominator. A decimal becomes a percentage by multiplying by 100.

这三种形式相互关联。分数可以通过分子除以分母化成小数；小数乘以 100 就变成百分数。

Fraction | 分数Decimal | 小数Percentage | 百分数
1/20.550%
1/40.2525%
3/40.7575%
1/100.110%
2/50.440%
3/80.37537.5%

e by 100. To write a decimal as a fraction, use place value, such as 0.35 = 35/100 = 7/20.

将百分数转回小数时，除以 100。将小数写成分数时，利用数位值，例如 0.35 = 35/100 = 7/20。

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4. Ordering Fractions, Decimals and Percentages | 分数、小数和百分数的比较排序

To compare mixed forms, first convert them all to the same form. The easiest form is usually a decimal or a percentage.

比较混合形式的数时，先把它们都转换成同一种形式。通常最简单的是小数或百分数。

Example: Arrange 3/5, 0.55, and 52% in ascending order. Convert: 3/5 = 0.6, 0.55 = 0.55, 52% = 0.52. The order is 52%, 0.55, 3/5.

例：将 3/5、0.55 和 52% 按从小到大排列。转换后：3/5 = 0.6，0.55 = 0.55，52% = 0.52。顺序为 52%、0.55、3/5。

5. Adding and Subtracting Fractions | 分数的加减

To add or subtract fractions, they must have the same denominator. If they do not, find the lowest common multiple, or LCM, of the denominators and write equivalent fractions.

分数加减时，它们必须有相同的分母。如果分母不同，求分母的最小公倍数，即 LCM，并写成等值分数。

ample: 1/4 + 1/6. The LCM of 4 and 6 is 12. So 1/4 = 3/12 and 1/6 = 2/12. The sum is 5/12.

例：1/4 + 1/6。4 和 6 的最小公倍数是 12。因此 1/4 = 3/12，1/6 = 2/12。两者之和为 5/12。

For mixed numbers, convert them to improper fractions first, then add or subtract, and simplify if possible.

对于带分数，先化成假分数，再进行加减，最后尽可能化简。

6. Multiplying and Dividing Fractions | 分数的乘除

To multiply fractions, multiply the numerators together and the denominators together. Simplify the result if possible.

分数相乘时，分子相乘，分母相乘，最后能化简就化简。

Example: 2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15.

例：2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15。

To divide by a fraction, multiply by its reciprocal. The reciprocal of a/b is b/a.

除以一个分数等于乘以它的倒数。a/b 的倒数是 b/a。

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1⅞.

例：3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1⅞。

7. Percentages of Quantities and Percentage Change | 百分数量与百分比变化

antity, write the percentage as a fraction over 100 or as a decimal, then multiply. For 25% of 60, use 0.25 × 60 = 15.

求一个数量的百分数时，把百分数写成分数，即分母为 100，或写成小数，然后相乘。例如 60 的 25%，用 0.25 × 60 = 15。

Percentage increase and decrease are common in real-life problems. Increase £80 by 15%: find 15% of 80 = 12, then add: 80 + 12 = £92.

百分比增加和减少在现实问题中很常见。将 80 英镑增加 15%：先求 80 的 15% = 12，再加起来：80 + 12 = 92 英镑。