📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数和百分数
Fractions, decimals and percentages are three connected ways of describing parts of a whole. In the Cambridge KS3 Mathematics curriculum, fluency in converting between these forms is essential for algebra, probability and real-world problem solving. This article explains the key ideas step by step, with exam-style tips for Cambridge learners.
分数、小数和百分数是描述整体部分量的三种相互关联的方式。在剑桥 KS3 数学课程中，熟练进行这三种形式之间的换算是学习代数、概率和解决实际问题的基础。本文将逐步讲解核心概念，并为剑桥学习者提供考试风格的建议。
1. Understanding Fractions | 理解分数
A fraction is written as a/b, where a is the numerator and b is the denominator. The denominator shows how many equal parts a whole is divided into, and the numerator shows how many of those parts are being considered.
分数写作 a/b，其中 a 是分子，b 是分母。分母表示整体被分成多少等份，分子表示我们考虑其中的几份。
For example, 3/4 means 3 parts out of 4 equal parts. A proper fraction has a numerator smaller than the denominator; an improper fraction has a numerator that is equal to or larger than the denominator; a mixed number combines a whole number and a proper fraction.
例如，3/4 表示 4 等份中的 3 份。真分数的分子小于分母；假分数的分子大于或等于分母；带分数由整数和真分数组成。
2. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions have the same value even though they look different. You can create an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same non-zero number.
等值分数的值相同，但形式不同。你可以将分子和分母同时乘或除以同一个不为零的数来得到等值分数。
2/3 = (2×4)/(3×4) = 8/12
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For example, 12/16 simplifies to 3/4 because the HCF of 12 and 16 is 4.
化简分数时，将分子和分母除以它们的最大公因数 (HCF)。例如，12/16 化简为 3/4，因为 12 和 16 的最大公因数是 4。
3. Converting Fractions to Decimals | 分数换算为小数
To convert a fraction to a decimal, divide the numerator by the denominator. Key fractions are worth memorising: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/3 = 0.333…, and 1/5 = 0.2.
要将分数换算为小数，用分子除以分母。一些关键分数值得记住：1/2 = 0.5，1/4 = 0.25，3/4 = 0.75，1/3 = 0.333…，1/5 = 0.2。
If the denominator is a power of 10, conversion is quick. For example, 7/10 = 0.7 and 23/100 = 0.23. For harder fractions, use short division or a calculator.
如果分母是 10 的幂，换算很快。例如，7/10 = 0.7，23/100 = 0.23。对于较难的分数，可以使用短除法或计算器。
4. Converting Decimals to Percentages and Back | 小数与百分数的互换
A percentage means ‘out of 100’. To change a decimal to a percentage, multiply by 100 and add the % symbol. To change a percentage to a decimal, divide by 100.
百分数表示 ‘每一百份中的多少’。要将小数换算为百分数，乘以 100 并加上 % 符号。要将百分数换算为小数，除以 100。
0.47 × 100 = 47% and 85% ÷ 100 = 0.85
Remember that multiplying by 100 moves the decimal point two places to the right, while dividing by 100 moves it two places to the left.
请记住，乘以 100 会将小数点向右移动两位，而除以 100 会将小数点向左移动两位。
5. Ordering Fractions, Decimals and Percentages | 排序分数、小数和百分数
To compare and order different forms, change them all to the same form, usually decimals or percentages. Convert each value, then write them in ascending or descending order.
要比较和排序不同形式的数，应先将它们全部化为同一种形式，通常化为小数或百分数。换算每个值后，再按升序或降序排列。
| Original | As decimal |
|---|---|
| 3/5 | 0.6 |
| 58% | 0.58 |
| 0.62 | 0.62 |
Now it is easy to see that 0.58 < 0.6 < 0.62, so 58% < 3/5 < 0.62.
现在很容易看出 0.58 < 0.6 < 0.62，因此 58% < 3/5 < 0.62。
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 (LCD), rewrite each fraction, then add or subtract the numerators only.
分数的加减法要求它们具有相同的
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导