📚 Year 7 Topic Series - 700: Fractions, Decimals and Percentages | 7年级主题系列-700：分数、小数和百分数
In Year 7 IGCSE Maths, fractions, decimals and percentages are not separate topics: they are three ways of describing the same proportion. Mastering the conversions and comparisons between them gives you a reliable toolkit for algebra, probability, ratio and real-life problems such as discounts, interest and data interpretation.
在 IGCSE 数学 7 年级课程中，分数、小数和百分数并不是三个孤立的主题，而是描述同一比例的三种形式。掌握它们之间的互化与大小比较，可以为你学习代数、概率、比和比例以及折扣、利息、数据解释等实际问题提供可靠的工具。
1. What Are Fractions, Decimals and Percentages? | 什么是分数、小数和百分数？
A fraction shows a part of a whole using a numerator and a denominator. For example, 3/4 means 3 parts out of 4 equal parts. A decimal uses place value after a decimal point, so 0.75 means 7 tenths and 5 hundredths. A percentage is a number out of 100, so 75% means 75 out of 100.
分数用分子和分母表示整体的一部分，例如 3/4 表示 4 等份中的 3 份。小数利用小数点后的数位表示数值，因此 0.75 表示 7 个十分之一和 5 个百分之一。百分数表示每一百份中的多少份，因此 75% 表示 100 份中的 75 份。
All three represent the same shaded part if a shape is divided into 4 equal parts and 3 are shaded. This is the key idea behind every conversion in this topic.
如果一个图形被分成 4 等份并涂色 3 份，这三种写法表示同一个涂色部分。这是本主题所有互化的核心思想。
3/4 = 0.75 = 75%
2. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions have the same value but different numerators and denominators. You can make an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number. Simplifying means dividing both parts by their highest common factor (HCF).
等值分数数值相同，但分子和分母不同。你可以将分子和分母同时乘以或除以同一个非零数，得到等值分数。化简就是用分子和分母的最大公因数 (HCF) 同时去除它们。
2 = 3 and 8 ÷ 2 = 4. Likewise, 12/16 simplifies to 3/4 because the HCF of 12 and 16 is 4.
例如，6/8 = 3/4，因为 6 ÷ 2 = 3，8 ÷ 2 = 4。同样，12/16 化简为 3/4，因为 12 和 16 的最大公因数是 4。
- Multiply: 3/4 = 6/8 = 9/12. 乘法：3/4 = 6/8 = 9/12。
- Divide by HCF: 12/16 = 3/4. 除以 HCF：12/16 = 3/4。
- Always check whether the fraction can be simplified before rounding. 四舍五入前始终检查分数是否还能化简。
3. Converting Between Fractions and Decimals | 分数与小数互化
To convert a fraction to a decimal, divide the numerator by the denominator. If the denominator is 10, 100 or 1000, you can use place value directly. To convert a terminating decimal to a fraction, write the decimal over its place value and simplify.
将分数化为小数时，用分子除以分母。如果分母是 10、100 或 1000，可以直接使用数位。将有限小数化为分数时，把小数写成分母为对应数位的分数，再化简。
8 = 0.375. The decimal 0.25 means 25 hundredths, so 0.25 = 25/100 = 1/4 after simplifying.
例如，3/8 = 3 ÷ 8 = 0.375。小数 0.25 表示 25 个百分之一，因此 0.25 = 25/100，化简后得到 1/4。
3/8 = 0.375; 0.25 = 25/100 = 1/4
s written with a dot or bar notation. In Year 7, you are usually expected to recognise simple recurring decimals rather than convert them into exact fractions.
有些分数会产生循环小数，例如 1/3 = 0.333...，通常用点或横线记号表示。在 7 年级，你只需识别简单的循环小数，一般不需要将其化为精确分数。
4. Converting Decimals to Percentages and Back | 小数与百分数互化
To convert a decimal to a percentage, multiply by 100. To convert a percentage to a decimal, divide by 100. This works because percent means 'per 100'.
将小数化为百分数时乘以 100；将百分数化为小数时除以 100。这是因为 percent 表示“每 100”。
o the right. Dividing by 100 moves it two places to the left. For example, 0.47 × 100 = 47%, and 12% ÷ 100 = 0.12.
乘以 100 相当于把小数点向右移动两位；除以 100 相当于把小数点向左移动两位。例如，0.47 × 100 = 47%，12% ÷ 100 = 0.12。
0.05 = 5%; 1.2 = 120%; 0.6 = 60%
Watch the position of the decimal point. 0.5% is not the same as 5%, and 0.05 is not the same as 0.5.
注意小数点的位置。0.5% 与 5% 不同，0.05 与 0.5 也不同。
5. Converting Fractions to Percentages | 分数与百分数互化
To convert a fraction to a percentage, first convert the fraction to a decimal, then multiply by 100. If the denominator is a factor of 100, you can make an equivalent fraction with denominator 100.
将分数化为百分数时，先把分数化为小数，再乘以 100。如果分母是 100 的因数，可以先将分数化为分母为 100 的等值分数。
For example, 7/20 = 35/100 = 35%. Since 3/8 = 0.375, we have 3/8 = 0.375 × 100 = 37.5%.
例如，7/20 = 35/100 = 35%。因为 3/8 = 0.375，所以 3/8 = 0.375 × 100 = 37.5%。
3/8 = 0.375 = 37.5%
| Fraction 分数 | Decimal 小数 | Percentage 百分数 |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
6. Ordering and Comparing Numbers | 数的大小比较与排序
To compare fractions, decimals and percentages, convert them all to the same form. Usually decimals or percentages are easiest because they have a common scale. Remember to compare digits in the same place value.
比较分数、小数和百分数时，应先把它们化为同一种形式。通常化为小数或百分数最简单，因为两者都有统一的数位。比较时要逐位比较相同数位上的数字。
Order from smallest to largest: 2/5, 0.45, 38%, 0.4. First convert: 2/5 = 0.4, 38% = 0.38, so 38% < 2/5 = 0.4 < 0.45.
从小到大排列：2/5、0.45、38%、0.4。先化为小数：2/5 = 0.4，38% = 0.38，因此 38% < 2/5 = 0.4 < 0.45。
38% < 2/5 = 0.4 < 0.45
A common trap is to think 0.4 is smaller than 0.38 because 4 is smaller than 38. In decimals, compare tenths first: 0.4 has 4 tenths, while 0.38 has 3 tenths, so 0.4 is larger.
一个常见陷阱是认为 0.4 比 0.38 小，因为 4 小于 38。在小数中，先比较十分位：0.4 有 4 个十分之一，而 0.38 有 3 个十分之一，因此 0.4 更大。
7. Finding a Percentage of a Quantity | 求一个数量的百分之几
To find a percentage of a quantity, write the percentage as a decimal or fraction, then multiply
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