IGCSE Maths Topic 916: Fractions, Decimals and Percentages | IGCSE 数学主题 916：分数、小数与百分比

📚 IGCSE Maths Topic 916: Fractions, Decimals and Percentages | IGCSE 数学主题 916：分数、小数与百分比

Fractions, decimals and percentages are three different ways of representing parts of a whole. In the IGCSE Mathematics syllabus, this topic is essential because it underpins almost every other area, from algebra and ratio to probability and statistics. Being fluent when converting between these three forms is often the key to solving multi-step problems efficiently and accurately.

分数、小数和百分比是表示整体中某一部分的三种不同方式。在 IGCSE 数学课程中，这个主题非常重要，因为它是代数、比例、概率和统计等几乎所有其他内容的基础。能够熟练地在三种形式之间进行转换，往往是高效、准确地解决多步骤问题的关键。

1. Understanding Fractions: Numerator and Denominator | 理解分数：分子与分母

A fraction is written as a/b, where a is the numerator and b is the denominator. The denominator tells you how many equal parts the whole has been divided into, while the numerator tells you how many of those parts are being considered. For example, in 3/5, the whole is split into 5 equal parts and we are interested in 3 of them.

分数写作 a/b，其中 a 是分子，b 是分母。分母表示整体被平均分成了多少份，分子表示我们关注其中的几份。例如，在 3/5 中，整体被分成 5 等份，我们关注其中的 3 份。

A proper fraction has a numerator smaller than its denominator, such as 2/3. An improper fraction has a numerator greater than or equal to its denominator, such as 7/4. A mixed number combines a whole number and a proper fraction, such as 1 3/4. In IGCSE questions, you often need to switch between mixed numbers and improper fractions before multiplying or dividing.

真分数的分子小于分母，例如 2/3。假分数的分子大于或等于分母，例如 7/4。带分数由整数和真分数组成，例如 1 3/4。在 IGCSE 题目中，进行乘法或除法之前，通常需要先在带分数和假分数之间转换。

To simplify a fraction, divide both numerator and denominator by their greatest common factor. For example, 18/24 can be simplified by dividing both parts by 6 to give 3/4. Equivalent fractions are created by multiplying or dividing both numerator and denominator by the same non-zero number.

要化简分数，将分子和分母同时除以它们的最大公因数。例如，18/24 可以同时除以 6，得到 3/4。等值分数是通过将分子和分母同时乘以或除以同一个非零数得到的。

2. Decimals and Place Value | 小数与位值

Decimals use a decimal point to separate whole numbers from fractional parts. The first digit after the point is tenths, the second is hundredths, and the third is thousandths. For example, 0.37 means 3 tenths + 7 hundredths, which is equivalent to 37/100.

小数使用小数点将整数部分与小数部分分开。小数点后第一位是十分位，第二位是百分位，第三位是千分位。例如，0.37 表示 3 个十分之一加 7 个百分之一，等同于 37/100。

When comparing decimals, it is helpful to line up the decimal points and look at the place values from left to right. Thus 0.7 is larger than 0.699 because 7 tenths is more than 6 tenths, even though 0.699 has more digits.

比较小数时，最好将小数点对齐，然后从左到右比较各位数字。因此，0.7 大于 0.699，因为 7 个十分之一大于 6 个十分之一，尽管 0.699 的位数更多。

3. The Meaning of Percent | 百分比的含义

The word ‘percent’ means ‘out of 100’. Therefore, 40% means 40 out of 100, which can be written as the fraction 40/100 or the decimal 0.40. Percentages are useful for comparing quantities because they express values on a common scale of 100.

“百分比”一词的意思是”每一百份中的若干份”。因此，40% 表示 100 份中的 40 份，可以写作分数 40/100 或小数 0.40。百分比便于比较数量，因为它将数值统一到以 100 为基准的尺度上。

Common percentages such as 50%, 25%, 10% and 1% are particularly useful in mental calculations. Knowing that 50% = 1/2, 25% = 1/4 and 10% = 1/10 allows you to estimate and check answers quickly.

50%、25%、10% 和 1% 等常见百分比在口算中特别有用。知道 50% = 1/2、25% = 1/4、10% = 1/10，可以帮助你快速估算和检查答案。

4. Converting Fractions to Decimals | 分数转换为小数

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375. If the denominator is a power of 10, the fraction can be written as a decimal immediately: 7/10 = 0.7, 23/100 = 0.23 and 5/1000 = 0.005.

要将分数转换为小数，用分子除以分母。例如，3/8 = 3 ÷ 8 = 0.375。如果分母是 10 的幂，则可以直接将分数写作小数：7/10 = 0.7，23/100 = 0.23，5/1000 = 0.005。

Some fractions produce recurring decimals. For instance, 1/3 = 0.333… and 2/7 = 0.285714285714…, where a digit or group of digits repeats forever. In IGCSE, you should be able to recognise when a decimal is terminating and when it is recurring

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）