Fractions, Decimals and Percentages | KS3 数学：分数、小数与百分数

📚 Fractions, Decimals and Percentages | KS3 数学：分数、小数与百分数

Fractions, decimals and percentages are three different ways of describing the same value. They appear constantly in everyday life, from measuring ingredients in a recipe to calculating discounts in a shop.

分数、小数和百分数是描述同一数值的三种不同方式。它们在日常生活中随处可见，从按食谱称量食材到在商店里计算折扣都离不开它们。

In this KS3 revision guide, you will learn how to convert between the three forms, compare them and use them to solve problems confidently.

在这份 KS3 复习指南中，你将学习如何在这三种形式之间进行转换、比较它们，并自信地运用它们解决问题。

---

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 tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts are taken.

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，分子表示取了多少份。

For example, 3/5 means the whole is split into 5 equal parts and 3 of them are selected. A unit fraction has a numerator of 1, such as 1/2 or 1/8.

例如，3/5 表示整体被分成 5 等份，并选取其中的 3 份。单位分数的分子为 1，如 1/2 或 1/8。

Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator greater than or equal to the denominator, and mixed numbers combine an integer with a proper fraction.

真分数的分子小于分母，假分数的分子大于或等于分母，带分数由一个整数和一个真分数组成。

Fractions are useful when a value is not a whole number, but decimals and percentages are often easier to compare in practical situations.

当数值不是整数时，分数非常有用，但在实际情境中，小数和百分数通常更容易比较。

---

2. Equivalent Fractions and Simplifying | 等值分数与化简

Equivalent fractions have different numerators and denominators but represent the same value. You can create an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same non-zero number.

等值分数的分子和分母不同，但表示相同的值。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得到等值分数。

For example, 2/3 = 4/6 = 8/12 because each form is obtained by multiplying the top and bottom by the same factor.

例如，2/3 = 4/6 = 8/12，因为每种形式都是将分子和分母同时乘以相同的因数得到的。

To simplify a fraction, divide both terms by their highest common factor (HCF). The fraction 18/24 simplifies to 3/4 because the HCF of 18 and 24 is 6.

化简分数时，将分子和分母同时除以它们的最大公因数 (HCF)。分数 18/24 化简为 3/4，因为 18 和 24 的最大公因数是 6。

You can check if two fractions are equivalent by cross-multiplying. For example, 2/3 and 4/6 are equivalent because 2 × 6 = 3 × 4.

你可以通过交叉相乘来检验两个分数是否等值。例如，2/3 和 4/6 等值，因为 2 × 6 = 3 × 4。

Always simplify your final answer unless the question specifically asks for an unsimplified fraction.

除非题目明确要求保留未化简的分数，否则最终答案一定要化简。

---

3. Fractions to Decimals | 分数转小数

To convert a fraction to a decimal, divide the numerator by the denominator. A fraction is simply a division statement.

将分数转换为小数，用分子除以分母即可。分数本质上就是除法。

For example, 3/8 means 3 ÷ 8 = 0.375, so 3/8 = 0.375. You can use short division or a calculator if allowed.

例如，3/8 表示 3 ÷ 8 = 0.375，因此 3/8 = 0.375。你可以使用短除法，或者如果允许的话使用计算器。

Some fractions produce terminating decimals, such as 1/4 = 0.25, while others produce recurring decimals, such as 1/3 = 0.333… which can be written as 0.3 with a dot over the 3.

有些分数产生有限小数，如 1/4 = 0.25；另一些则产生循环小数，如 1/3 = 0.333…，可写作 0.3，在 3 上方加点。

If the denominator is 10, 100 or 1000, conversion is immediate: 7/10 = 0.7, 23/100 = 0.23, and 9/1000 = 0.009.

如果分母是 10、100 或 1000，转换非常直接：7/10 = 0.7，23/100 = 0.23，9/1000 = 0.009。

Remember that the decimal point separates the whole number part from the fractional part, so 2/5 = 0.4 means 4 tenths, not 4 hundredths.

记住小数点把整数部分和小数部分分开，所以 2/5 = 0.4 表示 4 个十分之一，而不是 4 个百分之一。

---

4. Decimals to Fractions | 小数转分数

To convert a terminating decimal to a fraction, write the decimal as the numerator over a power of 10, then simplify if possible.

将有限小数转换为分数时，把小数作为分子，分母为 10 的幂，然后尽可能化简。

For example, 0.65 = 65/100. Dividing the numerator and denominator by 5 gives 13/20.

例如，0.65 = 65/100。将分子和分母同时除以 5，得到 13/20。

The number of decimal places determines the denominator: one decimal place gives 10, two decimal places gives 100, three decimal places gives 1000, and so on.

小数位数决定分母：一位小数对应 10，两位对应 100，三位对应 1000，依此类推。

For mixed decimals such as 2.4, write the integer part separately: 2.4 = 2 + 4/10 = 2 2/5.

对于像 2.4 这样的带小数，先写出整数部分：2.4 = 2 + 4/10 = 2 2/5。

Always check if the fraction can be simplified. For example, 0.25 = 25/100 = 1/4, so 0.25, 25/100 and 1/4 all describe the same value.

一定要检查分数是否可以化简。例如，0.25 = 25/100 = 1/4，所以 0.25、25/100 和 1/4 都表示相同的值。

---

5. Percentages as Fractions and Decimals | 百分数作为分数与小数

A percentage is a fraction with a denominator of 100. The symbol ‘%’ means ‘out of 100’, so 45% = 45/100 = 0.45.

百分数是分母为 100 的分数。符号 ‘%’ 表示“每 100”，因此 45% = 45/100 = 0.45。

To convert a percentage to a fraction, write it over 100 and simplify. For example, 25% = 25/100 = 1/4.

将百分数转换为分数时，把它写在 100 之上并化简。例如，25% = 25/100 = 1/4。

To convert a percentage to a decimal, divide by 100. This is the same as moving the decimal point two places to the left: 7% = 0.07 and 130%

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）