📚 Year 8 Core Homework Page i 139: Fractions, Decimals and Percentages | Year 8 核心作业第 i 139 页：分数、小数与百分数
This page focuses on core number skills that appear frequently in Year 8 homework and assessments. You will convert between fractions, decimals and percentages, compare values, calculate percentage changes and apply fraction arithmetic to word problems. Mastering these skills now builds a strong foundation for IGCSE and beyond.
本页聚焦 Year 8 作业和考试中频繁出现的核心数技能。你将练习分数、小数和百分数的互化，比较数值大小，计算百分比增减，并将分数运算应用于应用题。现在掌握这些技能可为 IGCSE 及后续学习打下坚实基础。
1. Reading the Core Task | 解读核心任务
Page i 139 usually presents a mixed set of core questions. Read each instruction carefully because a small change in wording, such as 'of' versus 'out of', changes the method entirely.
第 i 139 页通常呈现一组混合核心题。请仔细阅读每道题的指令，因为 'of' 和 'out of' 这类措辞的细微变化会完全改变解题方法。
Identify whether the question asks for a conversion, a comparison, a percentage change or a fraction operation before you start writing. Underline key words like 'increase', 'decrease', 'of' and 'simplify' to avoid misreading.
在动笔前，先判断题目要求的是互化、比较大小、百分比变化还是分数运算。划出 'increase'、'decrease'、'of' 和 'simplify' 等关键词，避免误读。
2. Conversion Between Fractions, Decimals and Percentages | 分数、小数和百分数的互化
n to a decimal, divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.
这三种形式表示相同的值。要将分数化为小数，用分子除以分母。例如，3/8 = 3 ÷ 8 = 0.375。
To convert a decimal to a percentage, multiply by 100. Thus 0.375 × 100 = 37.5% ercentage to a fraction, write the percentage over 100 and simplify fully. For example, 65% = 65/100 = 13/20.
要将小数化为百分数，乘以 100。因此 0.375 × 100 = 37.5%。要将百分数化为分数，将百分数写在 100 上方并完全化简。例如，65% = 65/100 = 13/20。
Fraction → Decimal: a/b = a ÷ b Decimal → Percent: d × 100 = p%
3. Ordering Rational Numbers | 有理数的大小排序
When comparing fractions, decimals and percentages, convert all values to the same form. Converting to decimals is often the fastest method because decimal place value is easy to scan.
比较分数、小数和百分数时，将所有数值化为同一种形式。化为小数通常是最快的方法，因为小数位值便于快速比较。
For example, to order 2/5, 0.45 and 38% from smallest to largest, write 2/5 = 0.4 and 38% = 0.38. Then the order is 0.38, 0.4, 0.45.
例如，要将 2/5、0.45 和 38% 从小到大排序，先写出 2/5 = 0.4，38% = 0.38。然后顺序为 0.38、0.4、0.45。
| Original | Decimal |
|---|---|
| 2/5 | 0.4 |
| 38% | 0.38 |
| 0.45 | 0.45 |
4. Finding a Percentage of a Quantity | 求一个数量的百分之几
ercentage of a quantity, convert the percentage to a decimal and multiply. For example, 15% of 80 = 0.15 × 80 = 12.
要求一个数量的百分之几，先将百分数化为小数再相乘。例如，80 的 15% = 0.15 × 80 = 12。
A common mental method is to find 10% first, then adjust. 10% of 80 is 8, so 5% is 4, and 15% is 8 + 4 = 12. This is useful when no calculator is allowed.
常见的心算方法是先求 10%，再调整。80 的 10% 是 8，所以 5% 是 4，15% 就是 8 + 4 = 12。这在不允许使用计算器时非常有用。
Percentage of quantity: P% of n = (P ÷ 100) × n
5. Percentage Increase and Decrease | 百分比增加与减少
ntage increase adds a percentage of the original amount. For example, increasing 200 by 12% gives 200 + 0.12 × 200 = 224.
百分比增加是在原量上增加一个百分比。例如，200 增加 12% 得到 200 + 0.12 × 200 = 224。
A percentage decrease subtracts the percentage. Decreasing 200 by 12% tiplier method is to use 1 + r for an increase and 1 - r for a decrease, where r is the decimal form of the percentage.
百分比减少则是减去该百分比。200 减少 12% 得到 200 - 0.12 × 200 = 176。快速乘数法是：增加时使用 1 + r，减少时使用 1 - r，其中 r 是百分数的小数形式。
Increase: new = original × (1 + r) Decrease: new = original × (1 - r)
6. Adding and Subtracting Fractions | 分数的加法与减法
To add or subtract fractions, they must have a common denominator. Rewrite each fraction as an equivalent fraction with the lowest common denominator before combining the numerators.
分数的加减需要公分母。在合并分子前，将每个分数化为以最小公分母为分母的等值分数。
owest common denominator of 3 and 4 is 12. So 2/3 = 8/12 and 1/4 = 3/12. Add to get 11/12.
例如：2/3 + 1/4。3 和 4 的最小公分母是 12。因此 2/3 = 8/12，1/4 = 3/12。相加得 11/12。
For mixed numbers, convert to improper fractions first, then follow the same rule. Always simplify your final answer if possible.
对于带分数，先化为假分数，再按同样规则运算。最终答案如能化简，务必化简。
a/b + c/d = (ad + bc) / bd a/b - c/d = (ad - bc) / bd
7. Multiplying and Dividing Fractions | 分数的乘法与除法
tors and multiply the denominators. Simplify if possible. Example: 2/3 × 3/5 = 6/15 = 2/5.
分数相乘时，分子乘分子，分母乘分母。能化简则化简。例如：2/3 × 3/5 = 6/15 = 2/5。
by a fraction, multiply by its reciprocal. Example: 2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9 = 1 1/9.
除以一个分数，等于乘以它的倒数。例如：2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9 = 1 1/9。
a/b × c/d = (a × c) / (b × d) a/b ÷ c/d = (a/b) × (d/c)
8. Real-Life Word Problems | 实际应用题
Word problems often ask you to find a fraction or percentage of a real amount, such as discounts, test scores or recipe adjustments. Translate the words into a calculation step by step.
应用题常要求你求实际数量的分数或百分数，例如折扣、测验成绩或食谱调整。请逐步将文字转化为计算式。
Example: A jacket costs £48 and is reduced by 25%. The discount is 0.25 × 48 = £12, so the sale price is 48 - 12 = £36.
例如：一件夹克售价 48 英镑，降价 25%。折扣为 0.25 × 48 = 12 英镑，因此售价为 48 - 12 = 36 英镑。
Underline the key numbers and the operation words before setting up your calculation. Check that your answer makes sense in the context of the question.
在列式计算前，划出关键数字和表示运算的词语。检查答案在题目情境中是否合理。
9. Common Mistakes to Avoid | 常见错误及避免方法
A very common error is confusing 0.5% with 5%. 0.5% is 0.005 as a decimal, while 5% is 0.05. This can lead to answers that are ten times too large or too small.
一个常见错误是混淆 0.5% 和 5%。0.5% 的小数形式是 0.005，而 5% 是 0.05。这可能导致答案大十倍或小十倍。
Another error is adding denominators when adding fractions. You must never add denominators: 1/2 + 1/3 is not 2/5. The correct sum is 5/6.
另一个错误是分数相加时把分母也相加。分母绝不能相加：1/2 + 1/3 不等于 2/5。正确和是 5/6。
When converting a percentage to a fraction, remember to simplify fully. 40% = 40/100 = 2/5, not 4/10. Leaving an unsimplified fraction can lose marks in a test.
将百分数化为分数时，记得完全化简。40% = 40/100 = 2/5，而不是 4/10。留下未化简的分数
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