📚 Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions, decimals and percentages are three equivalent ways of describing parts of a whole. In IGCSE Mathematics, you must be able to convert between them, calculate with them and apply percentage changes in real-world contexts such as discounts, interest and taxation.
分数、小数和百分数是描述整体中一部分的三种等价方式。在 IGCSE 数学中，你必须能够在它们之间进行转换，进行计算，并在折扣、利息和税收等实际情境中应用百分数变化。
1. Understanding Fractions | 理解分数
A fraction is written as a/b, where a is called the numerator and b is called the denominator. The denominator tells how many equal parts the whole is divided into, and the numerator tells how many of those parts are taken. The denominator can never be zero because division by zero is undefined.
分数写作 a/b，其中 a 叫做分子，b 叫做分母。分母表示整体被分成多少等份，分子表示取了多少份。分母不能为零，因为除以零没有定义。
A proper fraction has a numerator smaller than its denominator, for example 3/7. An improper fraction has a numerator that is larger than or equal to its denominator, for example 9/4. A mixed number combines a whole number and a proper fraction, for example 2 1/3.
真分数的分子小于分母，例如 3/7。假分数的分子大于或等于分母，例如 9/4。带分数由一个整数和一个真分数组成，例如 2 1/3。
Proper: 3/7 | Improper: 9/4 | Mixed: 2 1/3
2. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions represent the same value even though they look different. You can create an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same non-zero number.
等值分数表示相同的值，尽管形式不同。你可以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。
To simplify a fraction to its lowest terms, divide both the numerator and the denominator by their highest common factor (HCF). For example, 18/24 simplifies to 3/4 because the HCF of 18 and 24 is 6.
要把分数化简到最简形式，用分子和分母的最大公因数（HCF）同时除它们。例如，18/24 化简为 3/4，因为 18 和 24 的最大公因数是 6。
18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4
3. Fractions of an Amount | 求一个数量的几分之几
To find a fraction of an amount, first divide the amount by the denominator, then multiply the result by the numerator. This method helps in word problems involving lengths, masses, money and time.
要求一个数量的几分之几，先用分母去除这个数量，再把结果乘以分子。这个方法适用于涉及长度、质量、金钱和时间的文字题。
For example, to find 3/5 of 60 kg, divide 60 by 5 to get 12, then multiply 12 by 3 to get 36 kg. Always write the units in your final answer.
例如，求 60 kg 的 3/5，先用 5 除 60 得到 12，再把 12 乘以 3 得到 36 kg。最终答案中一定要写出单位。
(60 ÷ 5) × 3 = 12 × 3 = 36 kg
4. Adding and Subtracting Fractions | 分数的加减
To add or subtract fractions, they must have the same denominator. Find the lowest common multiple (LCM) of the denominators and convert each fraction to an equivalent fraction with that common denominator.
分数相加或相减时，它们必须有相同的分母。先求分母的最小公倍数（LCM），再把每个分数转化为以这个公分母为分母的等值分数。
Once the denominators are the same, add or subtract the numerators only. Keep the denominator unchanged. For mixed numbers, convert them to improper fractions first, then work as usual.
一旦分母相同，只对分子进行加减，分母保持不变。对于带分数，先把它们转化为假分数，然后按常规方法计算。
1/4 + 1/3 = 3/12 + 4/12 = 7/12
5. Multiplying and Dividing Fractions | 分数的乘除
To multiply fractions, multiply the numerators together and multiply the denominators together. You can simplify before or after multiplying to make the calculation easier, but your final answer must be in its lowest terms.
分数相乘时，分子乘分子，分母乘分母。你可以在乘法前或后进行约分，使计算更简单，但最终答案必须是最简形式。
To divide by a fraction, multiply by its reciprocal. The reciprocal is found by swapping the numerator and the denominator. For mixed numbers, change them to improper fractions before multiplying or dividing.
除以一个分数时，乘以它的倒数。倒数就是把分子和分母交换位置。对于带分数，在
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