📚 Mastering Fractions, Decimals and Percentages for IGCSE Maths | IGCSE 数学：分数、小数与百分数完全掌握
Fractions, decimals and percentages are three equivalent ways of describing parts of a whole. In IGCSE Mathematics, you must be able to convert between these forms fluently, simplify results correctly, and apply percentage multipliers in real-life problems such as discounts, tax, profit and reverse percentage questions.
分数、小数和百分数是描述整体中某一部分的三种等价方式。在 IGCSE 数学中，你必须能够熟练地在这三种形式之间转换、正确化简结果，并在折扣、税收、利润和逆向百分数等实际问题中应用百分数乘数。
1. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions have the same value even though they are written differently. You can create an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same non-zero number.
等值分数虽然写法不同但数值相同。将分子和分母同时乘以或除以同一个非零数，可以得到等值分数。
To simplify a fraction, divide the numerator and denominator by their highest common factor, or HCF. A final answer should normally be written in its lowest terms.
化简分数时，用分子和分母的最大公因数（HCF）同时相除。最终答案通常应写成最简形式。
lent fractions such as 1/2 = 2/4 = 3/6 and 2/5 = 4/10 = 6/15 without detailed calculation.
你应当能够不经过详细计算就识别出常见等值分数，例如 1/2 = 2/4 = 3/6 以及 2/5 = 4/10 = 6/15。
If both the numerator and denominator are even, you can divide by 2 repeatedly; however, dividing by the HCF in one step is more efficient and less prone to error.
如果分子和分母都是偶数，可以反复除以 2；但一步除以最大公因数更高效，也更不容易出错。
- Example / 示例：18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4, because HCF(18, 24) = 6.
2. Mixed Numbers and Improper Fractions | 带分数与假分数
A mixed number contains a whole number and a proper fraction, such as 2 3/5. An improper fraction has a numerator that is greater than or equal to its denominator, such as 13/5.
带分数包含一个整数和一个真分数，例如 2 3/5。假分数的分子大于或等于分母，例如 13/5。
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place this total over the original denominator.
将带分数化为假分数时，用整数乘以分母，加上分子，再把结果写在原分母上方。
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole-number part, the remainder is the new numerator, and the denominator stays the same.
将假分数化为带分数时，用分子除以分母。商为整数部分，余数为新的分子，分母保持不变。
- Example / 示例：2 3/5 = (2 × 5 + 3)/5 = 13/5.
- Example / 示例：17/4 = 4 1/4 because 17 ÷ 4 = 4 remainder 1.
3. Adding and Subtracting Fractions | 分数加减
Before adding or subtracting fractions, rewrite them with a common denominator. The most efficient common denominator is usually the lowest common multiple, or LCM, of the denominators.
在加减分数之前，先把它们写成同分母分数。最方便的公分母通常是各分母的最小公倍数（LCM）。
Once the denominators are the same, add or subtract the numerators and keep the common denominator unchanged. Always simplify your final answer if possible.
分母相同后，分子相加或相减，分母保持不变。最后如果可能，一定要化简答案。
For mixed numbers, you can deal with the whole-number parts and fraction parts separately, but converting to improper fractions first is usually more reliable, especially when borrowing is involved.
对于带分数，可以分别处理整数部分和分数部分，但先化为假分数通常更可靠，尤其是在需要借位时。
- Example / 示例：1/4 + 2/3 = 3/12 + 8/12 = 11/12.
- Example / 示例：1 1/2 + 2 2/3 = 3/2 + 8/3 = 9/6 + 16/6 = 25/6 = 4 1/6.
4. Multiplying and Dividing Fractions | 分数乘除
To multiply fractions, multiply the numerators together and multiply the denominators together. Cancel any common factors before multiplying to make the working smaller and quicker.
分数相乘时，分子乘分子，分母乘分母。在相乘之前先约去公因数，可以使计算更简洁、更快速。
To divide by a fraction, multiply by its reciprocal. This means you invert the second fraction and change the division sign into a multiplication sign.
除以一个分数等于乘以它的倒数。也就是说，把第二个分数上下颠倒，并将除号改为乘号。
whole number can be written as a fraction with denominator 1, so 4 ÷ 2/3 = 4/1 × 3/2 = 6.
请记住，整数可以写成分母为 1 的分数，因此 4 ÷ 2/3 = 4/1 × 3/2 = 6。
Check whether the question expects a mixed number or an improper fraction. If the question does not specify, either form is usually acceptable, but you should simplify the fraction fully.
检查题目要求的是带分数还是假分数。如果题目没有说明，两种形式通常都可以，但分数必须完全化简。
- Example / 示例：3/5 ÷ 2/7 = 3/5 × 7/2 = 21/10 = 2 1/10.
5. Fractions to Decimals and Decimals to Fractions | 分数与小数互化
To convert a fraction to a decimal, divide the numerator by the denominator. Some fractions produce terminating decimals, while others produce recurring decimals.
将分数化为小数时，用分子除以分母。有些分数会得到有限
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图