Fractions, Decimals and Percentages: KS3 Cambridge Mathematics Revision | 分数、小数与百分数：剑桥 KS3 数学复习

📚 Fractions, Decimals and Percentages: KS3 Cambridge Mathematics Revision | 分数、小数与百分数：剑桥 KS3 数学复习

This revision guide covers the key skills in Fractions, Decimals and Percentages that appear throughout Cambridge KS3 Mathematics. It is written for learners who are revising mixed questions, including those similar to the exercise on page 145 of the Cambridge learner book.

本复习指南涵盖剑桥 KS3 数学中分数、小数与百分数的核心技能。文章适用于正在复习综合练习的学习者，包括与剑桥教材第 145 页练习类似的题目。

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1. Equivalent Forms of Numbers | 数的等价形式

Fractions, decimals and percentages are three different ways of describing the same part of a whole. Being able to convert between them quickly is an essential KS3 skill.

分数、小数和百分数是描述整体中同一部分的三种不同方式。能够在它们之间快速转换是一项关键的 KS3 技能。

The table below gives common equivalents that should be memorised.

下表列出了应当熟记的常见等价关系。

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/10	0.1	10%
1/3	0.333…	33⅓%

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2. Converting Between Fractions, Decimals and Percentages | 分数、小数与百分数之间的转换

To convert a fraction into a decimal, divide the numerator by the denominator. For example, 7/8 = 7 ÷ 8 = 0.875.

要把分数转换为小数，用分子除以分母。例如 7/8 = 7 ÷ 8 = 0.875。

To convert a decimal into a percentage, multiply by 100. To convert a percentage into a decimal, divide by 100.

要把小数转换为百分数，乘以 100。要把百分数转换为小数，除以 100。

To convert a decimal into a fraction, use place value. For example, 0.36 = 36/100 = 9/25 after simplifying.

要把小数转换为分数，先根据数位写成分母。例如 0.36 = 36/100，化简后为 9/25。

To convert a percentage into a fraction, write it over 100 and simplify. For example, 65% = 65/100 = 13/20.

要把百分数转换为分数，先写成除以 100 的形式并化简。例如 65% = 65/100 = 13/20。

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3. Ordering Fractions, Decimals and Percentages | 排序分数、小数与百分数

When comparing mixed forms, the easiest strategy is to change every value into a decimal. This avoids common mistakes with denominators.

比较混合形式的数时，最简单的策略是把每个值都转换为小数。这样可以避免分母不同造成的常见错误。

Example: Arrange 3/5, 0.58, 61% and 13/20 in ascending order.

例题：将 3/5、0.58、61% 和 13/20 按从小到大的顺序排列。

First convert: 3/5 = 0.6, 61% = 0.61, 13/20 = 0.65. The order is 0.58, 3/5, 61%, 13/20.

先转换：3/5 = 0.6，61% = 0.61，13/20 = 0.65。所以顺序为 0.58、3/5、61%、13/20。

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4. Adding and Subtracting Fractions | 分数的加法与减法

To add or subtract fractions, the denominators must be the same. Find the lowest common denominator and rewrite each fraction before combining.

进行分数加减时，分母必须相同。先找最小公分母并改写每个分数，再进行合并。

Example: Work out 2/3 + 1/4.

例题：计算 2/3 + 1/4。

The lowest common denominator of 3 and 4 is 12. So 2/3 + 1/4 = 8/12 + 3/12 = 11/12.

3 和 4 的最小公分母是 12。因此 2/3 + 1/4 = 8/12 + 3/12 = 11/12。

For mixed numbers, change them into improper fractions first, then add or subtract the whole-number parts or use the common-denominator method.

对于带分数，可以先转换为假分数，再进行同分母加减；也可以分别处理整数部分与分数部分。

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5. 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 before or after multiplying.

分数相乘时，分子相乘作分子，分母相乘作分母。可在相乘前或相乘后化简。

Example: 3/5 × 5/8 = 15/40 = 3/8.

例题：3/5 × 5/8 = 15/40 = 3/8。

To divide by a fraction, multiply by its reciprocal. Flip the second fraction, then multiply as usual.

除以一个分数等于乘以它的倒数。把第二个分数倒过来，然后按乘法计算。

Example: 3/5 ÷ 6/7 = 3/5 × 7/6 = 21/30 = 7/10.

例题：3/5 ÷ 6/7 = 3/5 × 7/6 = 21/30 = 7/10。

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6. Finding a Percentage of an Amount | 求一个数的百分之几

There are two common methods: use a simple fraction for known percentages, or use a decimal multiplier.Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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