📚 IGCSE Mathematics: Number Skills - Fractions, Decimals and Percentages | IGCSE 数学：数与运算——分数、小数和百分数
In this T-K-1001 topic, fractions, decimals and percentages appear in every IGCSE Mathematics paper, from simple calculations to multi-step problems involving ratio, probability and compound interest. A strong grasp of how these three number forms connect is essential for accuracy, speed and confidence.
在本 T-K-1001 专题中，分数、小数和百分数出现在每一份 IGCSE 数学试卷中，从简单的计算到涉及比、概率和复利的多步问题。牢固掌握这三种数字形式之间的联系对于准确、快速和自信地解题至关重要。
1. Number Forms and Place Value | 数字形式与位值
Whole numbers are written using the digits 0 to 9, and each digit has a place value, such as units, tens, hundreds, tenths and hundredths. A fraction is a number written as a/b, where a is the numerator and b is the denominator. Decimals also use place value, with digits after the decimal point representing tenths, hundredths and thousandths.
整数使用数字 0 到 9 书写，每个数字都有位值，例如个位、十位、百位、十分位和百分位。分数是写成 a/b 的数，其中 a 是分子，b 是分母。小数也使用位值，小数点后的数字表示十分位、百分位和千分位。
- Proper fractions: numerator is smaller than denominator, e.g. 3/8.
- 真分数：分子小于分母，例如 3/8。
- Improper fractions: numerator is larger than denominator, e.g. 11/5.
- 假分数：分子大于分母，例如 11/5。
- Mixed numbers: a whole number with a proper fraction, e.g. 2 1/4.
- 带分数：整数与真分数结合，例如 2 1/4。
2. Equivalent Fractions and Simplest Form | 等值分数与最简形式
Equivalent fractions represent the same value even though they look different. You can create equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number. This is sometimes called cancelling when the fraction is simplified.
等值分数表示相同的值，尽管它们看起来不同。你可以通过将分子和分母同时乘以或除以同一个非零数来构造等值分数。当分数被化简时，这种方法有时被称为约分。
a/b = (a × k)/(b × k), k ≠ 0
a/b = (a × k)/(b × k)，其中 k ≠ 0。
r highest common factor (HCF). For example, 18/24 = 3/4 because the HCF of 18 and 24 is 6.
要化简分数，将分子和分母同时除以它们的最大公因数（HCF）。例如，18/24 = 3/4，因为 18 和 24 的最大公因数是 6。
3. Converting Fractions to Decimals | 分数转换为小数
ch as 1/2 = 0.5, 1/4 = 0.25 and 1/10 = 0.1, as these frequently appear in IGCSE questions.
分数可以通过用分子除以分母转换为小数。你应该熟记关键数值，例如 1/2 = 0.5、1/4 = 0.25 和 1/10 = 0.1，因为这些数值经常出现在 IGCSE 题目中。
| Fraction | 分数 | Decimal | 小数 |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/3 | 0.333... |
Recurring decimals repeat a digit or block of digits forever, such as 0.666..., while terminating decimals stop after a finite number of decimal places, such as 0.25. Both types are rational numbers because they can be written as fractions.
循环小数会无限重复一个数字或一组数字，例如 0.666...，而终止小数在小数点后有限位数停止，例如 0.25。这两种小数都是有理数，因为它们都可以写成分数。
4. Fractions, Decimals and Percentages | 分数、小数与百分数
A percentage is a number out of 100. To convert a fraction to a percentage, first convert it to a decimal, then multiply by 100. To convert a decimal to a percentage, multiply by 100 and add the percentage sign.
百分数是以 100 为基准的数。要将分数转换为百分数，先将其转换为小数，再乘以 100。要将小数转换为百分数，乘以 100 并加上百分号。
0.85 = 0.85 × 100 = 85%
0.85 = 0.85 × 100 = 85%
To convert a percentage to a fraction, write it over 100 and simplify. For example, 65% on between all three forms is a core skill tested in non-calculator and calculator papers.
要将百分数转换为分数，将其写在 100 之上并化简。例如，65% = 65/100 = 13/20。三种形式之间的转换是无计算器和有计算器试卷中都会考查的核心技能。
5. Ordering Rational Numbers | 有理数的大小比较
To compare fractions, decimals and percentages, write them all in the same form. Converting to decimals is often the quickest method for ordering rational numbers, because decimal place values are easy to compare digit by digit.
要比较分数、小数和百分数，需要将它们写成同一种形式。转换为小数通常是最快的排序有理数的方法，因为小数的位值可以逐位比较。
Example: Order 3/5, 0.57 and 58% from smallest to largest. Convert: 3/5 = 0.6 and 58% = 0.58. Therefore the correct order is 0.57 < 58% < 3/5.
示例：将 3/5、0.57 和 58% 从小到大排列。转换：3/5 = 0.6，58% = 0.58。因此正确顺序是 0.57 < 58% < 3/5。
On a number line, numbers increase from left to right, so the smallest value is placed on the left. This visual method helps avoid errors when ordering negative values as well.
在数轴上，数字从左到右递增，因此最小值放在左边。这种直观方法也有助于避免在排列负值时出错。
6. 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 (LCD), rewrite each fraction using equivalent fractions, then add or subtract the numerators while keeping the denominator unchanged.
要加减分数，它们必须有相同的分母。找到最小公分母（LCD），用等值分数重写每个分数，然后加减分子，分母保持不变。
1/4 + 2/3 = 3/12 + 8/12 = 11/12
1/4 + 2/3 = 3/12 + 8/12 = 11/12
For mixed numbers, add or subtract the whole number parts separately, or convert to improper fractions first. Always give your final answer in its simplest form, and where appropriate as a mixed number.
对于带分数，可以先将整数部分分开加减，或者先转换为假分数。最终答案必须化为最简形式，并在合适的情况下以带分数表示。
7. Multiplying and Dividing Fractions | 分数乘除法
To multiply fractions, multiply the numerators together and the denominators together. Simplify before or after multiplying to keep the numbers small. Cross-cancelling can save time in exam questions.
要乘分数，将分子相乘作为新的分子，分母相乘作为新的分母。可以在乘法之前或之后约分，以保持数字较小。交叉约分可以节省考试中的解题时间。
3/4 × 2/5 = 6/20 = 3/10
3/4 × 2/5 = 6/20 = 3/10
und by swapping the numerator and denominator. For example, 5/8 ÷ 2/3 = 5/8 × 3/2 = 15/16.
要除以一个分数，乘以它的倒数。倒数是将分子和分母交换得到的。例如，5/8 ÷ 2/3 = 5/8 × 3/2 = 15/16。
8. Finding a Percentage of a Quantity | 求一个量的百分数
To find a percentage of a quantity, write the percentage as a fraction over 100 and multiply, or convert the percentage to a decimal and multiply. The decimal method is usually faster in calculator questions.
要求一个量的百分数，将百分数写成 100 分之几后相乘，或将百分数转换为小数后相乘。在有计算器的题目中，小数方法通常更快。
15% of 240 = 0.15 × 240 = 36Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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