📚 Year 7 Topic Series 200: Fractions, Decimals and Percentages | 7年级主题系列200：分数、小数与百分数
Fractions, decimals and percentages are three connected ways of describing parts of a whole. In IGCSE Mathematics Year 7, students learn to convert between these forms, compare values, and apply them in calculations and real-life contexts. This topic builds number fluency and prepares you for ratio, proportion, and algebra later in the course.
分数、小数和百分数是描述整体的一部分的三种相互关联的方式。在 IGCSE 数学 7 年级中，学生要学会在这些形式之间转换、比较数值，并将它们用于计算和实际情境。本主题培养数字运算的流畅性，并为后续的比、比例和代数打下基础。
1. What Are Fractions? | 什么是分数？
A fraction is written as a/b, where a is the numerator and b is the denominator. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts are taken. For example, 3/4 means 3 out of 4 equal parts.
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。例如，3/4 表示 4 等份中的 3 份。
A unit fraction has numerator 1, such as 1/5. 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.
分子为 1 的分数是单位分数，例如 1/5。分子小于分母的是真分数，例如 2/3。分子大于或等于分母的是假分数，例如 7/4。带分数由一个整数和一个真分数组成，例如 1 3/4。
2. Equivalent Fractions and Simplifying | 等值分数与化简
rator and the denominator by the same non-zero whole number. For example, 1/2 = 2/4 = 4/8.
等值分数看起来不同但数值相同。你可以将分子和分母同时乘或除以同一个非零整数，得到等值分数。例如，1/2 = 2/4 = 4/8。
a/b = (a × k)/(b × k), k ≠ 0
To simplify a fraction, divide the numerator and denominator by their highest common factor. For instance, 8/12 simplifies to 2/3 because both 8 and 12 can be divided by 4.
化简分数时，用分子和分母的最大公因数分别去除。例如，8/12 化简为 2/3，因为 8 和 12 都可以除以 4。
3. Fractions of an Amount | 求一个数量的几分之几
To find a fraction of an amount, divide the amount by the denominator and then multiply the result by the numerator. This method works because the denominator shows the number of equal parts in the whole.
求一个数量的几分之几时，先用这个数量除以分母，再将结果乘以分子。这个方法之所以有效，是因为分母表示整体被分成的等份数。
For example, to find 3/5 of 60, first divide 60 by 5 to get 12, then multiply 12 by 3 to get 36. So 3/5 of 60 is 36.
例如，求 60 的 3/5，先算 60 ÷ 5 得 12，再算 12 × 3 得 36。所以 60 的 3/5 是 36。
This method is useful in word problems involving discounts, test scores, or sharing quantities. Always check whether the answer is smaller than the original amount, because a proper fraction of a quantity must be less than the quantity itself.
这种方法在涉及折扣、考试分数或分配数量的应用题中很有用。务必检查答案是否小于原数量，因为一个数量乘以真分数后一定比原数量小。
4. Adding and Subtracting Fractions | 分数的加法与减法
the denominator the same and add or subtract the numerators. For example, 2/7 + 3/7 = 5/7.
同分母分数相加或相减时，分母不变，只将分子相加或相减。例如，2/7 + 3/7 = 5/7。
a/c + b/c = (a + b)/c
minator, then add or subtract the numerators. For example, 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
如果分母不同，先找一个公分母，通常是各分母的最小公倍数。把每个分数转换成以这个公分母为分母的等值分数，然后再加或减分子。例如，1/4 + 1/6 = 3/12 + 2/12 = 5/12。
5. Multiplying and Dividing Fractions | 分数的乘法与除法
2/3 × 4/5 = 8/15. If mixed numbers are involved, change them to improper fractions first.
分数相乘时，分子乘分子，分母乘分母。例如，2/3 × 4/5 = 8/15。如果含有带分数，先把带分数化为假分数。
a/b × c/d = (a × c)/(b × d)
iply the first fraction by the reciprocal of the second fraction. For example, 3/4 ÷ 2/5 =
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