📚 IGCSE Mathematics: Fractions, Decimals and Percentages | IGCSE 数学：分数、小数和百分数
Understanding fractions, decimals and percentages is a core IGCSE Mathematics skill. These three forms all describe parts of a whole, and you must be able to convert between them, calculate with them, and apply them to real problems.
理解分数、小数和百分数是 IGCSE 数学的核心技能。这三种形式都描述整体的一部分，你必须能够在它们之间转换、进行计算并应用于实际问题。
1. Equivalent Fractions and Simplifying | 等值分数与化简
An equivalent fraction is obtained by multiplying or dividing both the numerator and denominator by the same non-zero whole number. Simplifying a fraction means reducing it to its lowest terms by dividing both parts by their highest common factor (HCF).
等值分数是指将分子和分母同时乘以或除以同一个非零整数所得到的分数。化简分数是指将分子和分母同时除以它们的最大公因数 (HCF)，把分数化为最简形式。
both 12 and 16 are divisible by 4. Dividing top and bottom by 4 gives 3/4, so 12/16 = 3/4.
例如，12/16 可以化简，因为 12 和 16 都能被 4 整除。分子和分母同时除以 4 得到 3/4，因此 12/16 = 3/4。
12/16 = 3/4
2. Mixed Numbers and Improper Fractions | 带分数与假分数
An improper fraction has a numerator larger than its denominator, such as 7/3. A mixed number combines a whole number and a proper fraction, such as 2 1/3. IGCSE questions often require you to switch between the two forms before adding, subtracting, multiplying or dividing.
假分数的分子大于分母，例如 7/3。带分数由一个整数和一个真分数组成，例如 2 1/3。IGCSE 题目常常要求你在进行加、减、乘、除之前先在两种形式之间转换。
hole number by the denominator and add the numerator: 2 × 3 + 1 = 7, so the result is 7/3.
要将 2 1/3 转换为假分数，把整数乘以分母再加上分子：2 × 3 + 1 = 7，因此结果是 7/3。
2 1/3 = (2 × 3 + 1)/3 = 7/3
a mixed number, divide 11 by 4. The quotient is 2 and the remainder is 3, so 11/4 = 2 3/4.
要将 11/4 转换回带分数，用 11 除以 4。商为 2，余数为 3，因此 11/4 = 2 3/4。
3. Adding and Subtracting Fractions | 分数加减
Before adding or subtracting fractions, you must write them with a common denominator. The best common denominator is the lowest common multiple (LCM) of the original denominators.
在加减分数之前，必须先把它们写成同分母分数。最合适的公分母是原分母的最小公倍数 (LCM)。
For example, to calculate 1/4 + 2/5, the LCM of 4 and 5 is 20. Rewrite the fractions as 5/20 and 8/20, then add the numerators.
例如，计算 1/4 + 2/5 时，4 和 5 的最小公倍数是 20。将两个分数改写为 5/20 和 8/20，然后分子相加。
1/4 + 2/5 = 5/20 + 8/20 = 13/20
For subtraction, use the same method but subtract the numerators. Always check whether the final fraction can be simplified.
减法使用相同的方法，但分子相减。最后一定要检查所得分数是否还能化简。
4. Multiplying and Dividing Fractions | 分数乘除
Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. You can simplify first by cancelling any common factor between a numerator and a denominator.
分数乘法很简单：分子相乘，分母相乘。你可以先约分，即约去任一分子与任一分母之间的公因数。
3/8 × 4/9. Cancel 3 with 9 to get 1/8 × 4/3, then cancel 4 with 8 to get 1/2 × 1/3 = 1/6.
示例：3/8 × 4/9。先将 3 和 9 约分，得到 1/8 × 4/3；再将 4 和 8 约分，得到 1/2 × 1/3 = 1/6。
3/8 × 4/9 = 1/6
ultiply by its reciprocal. For instance, 5/6 ÷ 2/3 is the same as 5/6 × 3/2 = 15/12 = 5/4.
除以一个分数等于乘以它的倒数。例如，5/6 ÷ 2/3 等于 5/6 × 3/2 = 15/12 = 5/4。
5. Fractions to Decimals and Terminating Decimals | 分数转小数与有限小数
Some fractions give a terminating decimal, such as 3/8 = 0.375, because the division ends.
要将分数转换为小数，用分子除以分母。有些分数会得到有限小数，例如 3/8 = 0.375，因为除法可以除尽。
nd 5. For example, 1/20 terminates because 20 = 2² × 5, but 1/6 repeats because 6 = 2 × 3.
一个最简分数只有在分母的质因数只有 2 和 5 时才会变成有限小数。例如，1/20 是有限小数，因为 20 = 2² × 5；而 1/6 是循环小数，因为 6 = 2 × 3。
n, write the decimal over its place value and simplify. For instance, 0.75 = 75/100 = 3/4.
要将小数转换为分数，把小数写成对应位值的分数再化简。例如，0.75 = 75/100 = 3/4。
6. Recurring Decimals | 循环小数
A recurring decimal repeats a digit or block of digits forever, such as 0.333... or 0.272727.... To convert a recurring decimal to a fraction, use an algebraic method.Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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