📚 KS3 Cambridge Maths: Page 111 Q2 – Percentages to Fractions | KS3 剑桥数学：第111页第2题——百分数化分数
In this KS3 Cambridge Mathematics revision article, we focus on a typical Page 111 Question 2 task: converting percentages into fractions in their simplest form. This topic is at the heart of the Cambridge Key Stage 3 curriculum and builds essential number skills for ratio, proportion, probability and everyday problem solving.
在这篇 KS3 剑桥数学复习文章中，我们聚焦第 111 页第 2 题这一典型任务：把百分数化为最简分数。该主题是剑桥 Key Stage 3 课程的核心，为比、比例、概率和日常问题解决打下重要的数字技能基础。
1. Understanding the Page 111 Q2 Task | 理解第111页第2题任务
Question 2 usually presents a list of percentages such as 30%, 45%, 12.5% and 150%, and asks you to write each one as a fraction in its lowest terms.
第 2 题通常会列出一组百分数，如 30%、45%、12.5% 和 150%，要求你把每个百分数写成最简分数。
The instruction "in its simplest form" means you must reduce the fraction until the numerator and denominator have no common factor except 1.
“最简形式”意味着你必须约分，直到分子和分母除了 1 之外没有公因数。
You should show clear working, as Cambridge examiners award method marks for the conversion and simplification steps.
你应当展示清晰的步骤，因为剑桥考官会为转换和约分步骤给予方法分。
2. What Is a Percentage? | 什么是百分数？
The word "percentage" comes from the Latin "per centum", meaning "out of 100". Therefore, x% simply means x out of 100, or x/100.
“百分数（percentage）”一词来自拉丁语 “per centum”，意思是“每一百”。因此，x% 就是每一百中的 x，或者 x/100。
This definition gives us a direct rule: to change a percentage to a fraction, write the percentage number over 100 and then simplify.
这个定义给了我们一条直接规则：要把百分数化为分数，先把百分数的数值写在 100 的上方，然后进行约分。
For example, 25% = 25/100, which simplifies to 1/4.
例如，25% = 25/100，约分后得到 1/4。
3. Step-by-Step Conversion Method | 分步转换方法
Follow these three steps for every percentage in Question 2: first, write the percentage as a fraction with denominator 100; second, find the greatest common factor of the numerator and denominator; third, divide both by that factor.
对于第 2 题中的每个百分数，按以下三步操作：第一，把百分数写成分母为 100 的分数；第二，找出分子和分母的最大公因数；第三，用该公因数同时除分子和分母。
If the percentage has a decimal part, such as 12.5%, first eliminate the decimal by multiplying numerator and denominator by 10, 100 or 1000 as needed.
如果百分数含有小数部分，例如 12.5%，
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