📚 Fractions, Decimals and Percentages: Core Skills | 分数、小数和百分数：核心技能
In the Cambridge Lower Secondary Mathematics course, a strong grasp of fractions, decimals and percentages is essential for solving problems across number, algebra, ratio and everyday contexts. This article reviews key methods, common misconceptions and useful revision tables.
在剑桥初中数学课程中，牢固掌握分数、小数和百分数是解决数字、代数、比值以及日常生活问题的基础。本文梳理核心方法、常见易错点，并提供复习表格。
1. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions have the same value even though their numerators and denominators look different. To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same non-zero whole number.
等值分数看似分子和分母不同，但数值相同。要找出等值分数，可以把分子和分母同时乘以或除以同一个不为零的整数。
Example: 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3, so 12/18 simplifies to 2/3.
例如：12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3，因此 12/18 化简为 2/3。
- Always divide the numerator and denominator by their highest common factor when simplifying.
- 化简时始终用分子和分母的最大公因数去除。
- Simplifying before multiplying or adding can make calculations easier.
- 在乘法或加法之前先化简，往往能使计算更简便。
2. Mixed Numbers and Improper Fractions | 带分数与假分数
A mixed number contains a whole part and a fractional part, such as 2 ¾. An improper fraction has a numerator larger than or equal to its denominator, such as 11/4.
带分数包含整数部分和分数部分，例如 2 ¾。假分数的分子大于或等于分母，例如 11/4。
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
将带分数化为假分数时，用整数部分乘分母，加上分子，再把结果写在原分母上。
Example: 2 ¾ = (2 × 4 + 3)/4 = 11/4.
例如：2 ¾ = (2 × 4 + 3)/4 = 11/4。
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
将假分数化为带分数时，用分子除以分母。商为整数部分，余数为新的分子，分母保持不变。
Example: 17/5 = 3 2/5 because 17 ÷ 5 = 3 remainder 2.
例如：17/5 = 3 2/5，因为 17 ÷ 5 = 3 余 2。
3. Comparing and Ordering Fractions | 分数的大小比较与排序
To compare fractions, rewrite them with a common denominator. The least common multiple of the denominators is usually the best choice.
比较分数时，先把它们改写为同分母分数。分母的最小公倍数通常是最佳选择。
/8 and 2/3. The LCM of 8 and 3 is 24, so 5/8 = 15/24 and 2/3 = 16/24. Therefore 5/8 < 2/3.
例如：比较 5/8 和 2/3。8 和 3 的最小公倍数是 24，因此 5/8 = 15/24，2/3 = 16/24，所以 5/8 < 2/3。
On a number line, fractions increase from left to right once they share the same denominator.
在同分母的情况下，数轴上分数从左到右依次增大。
When ordering mixed numbers, first compare the whole number parts. If the whole parts are equal, then compare the fractional parts.
排序带分数时，先比较整数部分。如果整数部分相同，再比较分数部分。
4. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分数的互化
Fractions, decimals and percentages are three ways of expressing the same proportion. The key conversions are shown below.
分数、小数和百分数是表示同一比例的三种形式。关键互化方法如下表所示。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100. To convert a percentage to a fraction, write it over 100 and simplify.
将分数化为小数时，用分子除以分母；将小数化为百分数时，乘以 100；将百分数化为分数时，先写成分母为 100 的分数，再化简。
Example: 3/8 = 0.375 = 37.5%.
例如：3/8 = 0.375 = 37.5%。
For recurring decimals, use a dot or a bar above the repeating digit, such as writing 0.333... as 0.3 with a dot above the 3.
对于循环小数，在循环数字上方加点或横线，例如 0.333... 可写作 0.3 并在 3 的上面加一点。
5. Adding and Subtracting Fractions | 分数的加减法
To add or subtract fractions, first give them a common denominator. Then add or subtract the numerators and keep the denominator unchanged. Simplify if possible.
分数加减时，先把分数化为同分母，然后分子相加或相减，分母不变，最后尽可能化简。
Example: 2/3 + 1/4. The LCM of 3 and 4 is 12, so 8/12 + 3/12 = 11/12.
例如：2/3 + 1/4。3 和 4 的最小公倍数是 12，因此 8/12 + 3/12 = 11/12。
For mixed numbers, add the whole parts and fractional parts separately, or convert to improper fractions first.
对于带分数，可以分别相加整数部分和分数部分，也可以先化为假分数再计算。
Example: 1 ½ + 2 ⅓ = 1 3/6 + 2 2/6 = 3 5/6.
例如：1 ½ + 2 ⅓ = 1 3/6 + 2 2/6 = 3 5/6。
When subtracting, you may need to borrow from the whole part if the fraction being subtracted is larger.
做减法时，如果被减数的分数部分不够减，需要从整数部分借 1。
Example: 3 1/4 − 1 3/4 = 2 5/4 − 1 3/4 = 1 2/4 = 1 1/2.
例如：3 1/4 − 1 3/4 = 2 5/4 − 1 3/4 = 1 2/4 = 1 1/2。
6. 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 whenever possible.
分数相乘时，分子乘分子，分母乘分母。尽量在乘之前或之后进行约分。
a/b × c/d = ac/bd
Example: 2/5 × 3/4 = 6/20 = 3/10.
例如：2/5 × 3/4 = 6/20 = 3/10。
To divide by a fraction, multiply by its reciprocal: invert the second fraction and change the division sign to multiplication.
除以一个分数等于乘以它的倒数：把第二个分数的分子分母调换，并将除号改为乘号。
a/b ÷ c/d = a/b × d/c
Example: 3/7 ÷ 2/5 = 3/7 × 5/2 = 15/14 = 1 1/14.
例如：3/7 ÷ 2/5 = 3/7 × 5/2 = 15/14 = 1 1/14。
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图