Fractions, Decimals and Percentages | 分数、小数和百分数

📚 Fractions, Decimals and Percentages | 分数、小数和百分数

Understanding fractions, decimals and percentages is essential for success in Cambridge KS3 mathematics. These three forms describe the same idea: a part of a whole. You will need to convert between them, compare them and use them in real-life problems such as finding sale prices, working out test scores and sharing quantities.

理解分数、小数和百分数是剑桥 KS3 数学成功的关键。这三种形式描述的是同一个概念：整体的一部分。你需要学会在它们之间进行转换、比较大小，并在实际生活中运用，例如计算折扣价、考试成绩和分配数量。

1. What Are Fractions? | 什么是分数？

A fraction shows a part of a whole. It is written as a numerator over a denominator, for example ¾ means 3 parts out of 4 equal parts. The denominator tells you how many equal parts the whole is split into, and the numerator tells you how many of those parts you have.

分数表示整体的一部分。它写作分子在上、分母在下的形式，例如 ¾ 表示 4 等份中的 3 份。分母表示整体被平均分成多少份，分子表示你取了多少份。

Another way to think about a fraction is as division: ¾ is exactly the same as 3 ÷ 4. Fractions can be proper (numerator smaller than denominator), improper (numerator larger than denominator) or mixed numbers such as 1½.

另一种理解分数的方式是除法：¾ 完全等同于 3 ÷ 4。分数可以是真分数（分子小于分母）、假分数（分子大于分母）或带分数，如 1½。

2. Equivalent Fractions and Simplifying | 等值分数与约分

Equivalent fractions have the same value even though they look different. You can multiply or divide the numerator and denominator by the same non-zero number to find an equivalent fraction.

等值分数虽然形式不同但数值相同。你可以把分子和分母同时乘以或除以同一个非零数，得到等值分数。

For example, ½ = 2/4 = 3/6 = 50/100. To simplify a fraction, divide both the numerator and denominator by their highest common factor (HCF).

例如，½ = 2/4 = 3/6 = 50/100。约分时，用分子和分母的最大公因数（HCF）同时除上下两个数。

• Simplify 12/16: HCF of 12 and 16 is 4, so 12 ÷ 4 = 3 and 16 ÷ 4 = 4, giving ¾.
• 约分 12/16：12 和 16 的最大公因数是 4，所以 12 ÷ 4 = 3，16 ÷ 4 = 4，得到 ¾。
• Simplify 25/100: HCF of 25 and 100 is 25, giving ¼.
• 约分 25/100：25 和 100 的最大公因数是 25，得到 ¼。

3. Converting Fractions to Decimals | 分数化小数

To convert a fraction to a decimal, divide the numerator by the denominator. For simple fractions, you can also make an equivalent fraction with a denominator of 10, 100 or 1000 and then write the decimal directly.

把分数化为小数，可以用分子除以分母。对于简单分数，也可以先化成分母为 10、100 或 1000 的等值分数，然后直接写成小数。

For example, ¾ = 3 ÷ 4 = 0.75. Similarly, 1/8 = 1 ÷ 8 = 0.125. Some fractions give recurring decimals, such as 1/3 = 0.333…, which can be written as 0.3̇ in short form.

例如，¾ = 3 ÷ 4 = 0.75。同样，1/8 = 1 ÷ 8 = 0.125。有些分数会得到循环小数，例如 1/3 = 0.333…，可以简写为 0.3̇。

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