Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分数

📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分数

Fractions, decimals and percentages are three ways of representing parts of a whole. In KS3 Cambridge Mathematics, you need to convert between them fluently and use them in calculations, comparisons and real-life problems.

分数、小数和百分数是表示整体部分的三种方式。在 KS3 剑桥数学中，你需要熟练地在它们之间进行转换，并在计算、比较和实际问题中加以运用。

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, 3/4 means 3 parts out of 4 equal parts. A proper fraction has a numerator smaller than the denominator; an improper fraction has a numerator larger than or equal to the denominator; a mixed number combines a whole number and a proper fraction.

例如，3/4 表示 4 等份中的 3 份。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。

A unit fraction has a numerator of 1, such as 1/2, 1/3 or 1/10. Non-unit fractions have a numerator greater than 1.

单位分数的分子为 1，如 1/2、1/3 或 1/10。非单位分数的分子大于 1。

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

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

等值分数表示相同的值，但使用不同的分子和分母。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, 1/2 = 2/4 = 3/6 = 5/10. To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF).

例如，1/2 = 2/4 = 3/6 = 5/10。化简分数时，用分子和分母的最大公因数（HCF）去除它们。

To simplify 12/18, divide both the numerator and denominator by 6 to get 2/3. Always check whether the fraction can be simplified further.

化简 12/18 时，将分子和分母同时除以 6，得到 2/3。一定要检查分数是否还能继续化简。

3. Converting Between Fractions and Decimals | 分数与小数的互化

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.

将分数转换为小数，用分子除以分母。例如，3/8 = 3 ÷ 8 = 0.375。

To convert a terminating decimal to a fraction, write the decimal as a fraction over 10, 100 or 1000 and then simplify. For example, 0.45 = 45/100 = 9/20.

将有限小数转换为分数时，先把小数写成分母为 10、100 或 1000 的分数，再化简。例如，0.45 = 45/100 = 9/20。

Some fractions give recurring decimals,

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