Year 9 Maths Unit 5: Fractions, Decimals and Percentages | 九年级数学第5单元：分数、小数与百分数

📚 Year 9 Maths Unit 5: Fractions, Decimals and Percentages | 九年级数学第5单元：分数、小数与百分数

This revision guide brings together the essential skills in Unit 5: simplifying fractions, operations with mixed numbers, converting between fractions, decimals and percentages, understanding recurring decimals, and applying percentage increase, decrease and reverse percentage calculations. Use the paired explanations and worked examples to check your understanding before attempting timed practice questions.

本复习指南汇总第5单元的核心技能：分数化简、带分数运算、分数与小数及百分数的互化、理解循环小数，以及百分数增减和逆运算的应用。请使用中英对照讲解和例题检验理解，再进行限时练习。

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

A fraction is written in the form a/b, where a is the numerator and b is the denominator. The denominator cannot be zero. Equivalent fractions have the same value but different numerators and denominators. You can create an equivalent fraction by multiplying or dividing both numerator and denominator by the same non-zero number.

分数写作 a/b，其中 a 是分子，b 是分母。分母不能为 0。等值分数数值相同，但分子和分母不同。将分子和分母同时乘以或除以同一个非零数，可以得到等值分数。

To simplify a fraction, find the highest common factor, or HCF, of the numerator and denominator. For example, to simplify 24/36, the HCF of 24 and 36 is 12, so divide both terms by 12: 24/36 = 2/3. Unless the question says otherwise, final answers should be given in the simplest form.

化简分数时，先找出分子与分母的最大公因数，即 HCF。例如化简 24/36，24 和 36 的 HCF 是 12，因此分子分母同时除以 12：24/36 = 2/3。除非题目另有说明，最终答案应为最简形式。

• 1/2 = 2/4 = 3/6 = 4/8
• 3/5 = 6/10 = 9/15 = 12/20
• 10/15 = 2/3

2. Adding and Subtracting Fractions | 分数加减法

To add or subtract fractions, they must have the same denominator. Find the lowest common denominator, or LCD, which is the lowest common multiple, or LCM, of the denominators. For 1/3 + 1/4, the LCM of 3 and 4 is 12, so convert: 1/3 = 4/12 and 1/4 = 3/12. Then add the numerators: 4/12 + 3/12 = 7/12.

分数加减时，必须先使分母相同。找出最小公分母，即 LCD，也就是各分母的最小公倍数 LCM。以 1/3 + 1/4 为例，3 和 4 的 LCM 是 12，所以转化为：1/3 = 4/12，1/4 = 3/12。然后分子相加：4/12 + 3/12 = 7/12。

For mixed numbers, you can add the whole number parts first and then the fraction parts, or convert both mixed numbers to improper fractions first. Example: 2 1/3 + 1 1/6 = 2 + 1 + 2/6 + 1/6 = 3 3/6 = 3 1/2.

带分数运算时，可以先加整数部分再加分数部分，也可以先把带分数化为假分数。例如：2 1/3 + 1 1/6 = 2 + 1 + 2/6 + 1/6 = 3 3/6 = 3 1/2。

a/b + c/d = (ad + cb) / bd

a/b − c/d = (ad − cb) / bd

3. Multiplying and Dividing Fractions | 分数乘除法

Multiplication of fractions does not require a common denominator. Multiply the numerators together and the denominators together directly. Cross-cancelling can make the work easier: 3/8 × 4/9 = (3 × 4)/(8 × 9) = 12/72 = 1/6. With cross-canc

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