📚 Year 7 Unit 7 Support Homework Answers | 七年级第7单元辅导作业答案
This revision guide provides clear worked answers for common Year 7 Unit 7 support homework questions. The unit focuses on fractions, decimals, percentages, ratio and proportion. Each section gives example questions, step-by-step methods and final answers so you can check your work and learn from any mistakes.
本复习指南为七年级第7单元常见辅导作业题提供清晰的计算答案。本单元重点包括分数、小数、百分数、比和比例。每个小节都给出例题、分步方法和最终答案，帮助你检查作业并从错误中学习。
1. Simplifying Fractions | 化简分数
implify 12/18. The HCF of 12 and 18 is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The answer is 2/3.
化简分数时，用分子和分母的最大公因数同时相除。例如：化简 12/18。12 和 18 的最大公因数是 6，因此 12 ÷ 6 = 2，18 ÷ 6 = 3。答案是 2/3。
12/18 = 2/3, 20/45 = 4/9, 36/60 = 3/5
Always check whether the numerator and denominator can still be divided by the same number. A fully simplified fraction has no common factor other than 1.
一定要检查分子和分母是否还能被同一个数整除。完全化简后的分数除了 1 以外没有其他公因数。
2. Equivalent Fractions | 等值分数
xample: 3/5 = 6/10 = 9/15 because 3 × 2 = 6 and 5 × 2 = 10, then 3 × 3 = 9 and 5 × 3 = 15.
等值分数虽然形式不同，但数值相同。将分子和分母同时乘以或除以同一个非零数即可得到等值分数。例如：3/5 = 6/10 = 9/15，因为 3 × 2 = 6 且 5 × 2 = 10，接着 3 × 3 = 9 且 5 × 3 = 15。
3/5 = 6/10 = 9/15 = 12/20
This method is useful when comparing fractions or finding common denominators for addition and subtraction.
在比较分数或寻找加减法的公分母时，这一方法非常有用。
3. Converting Fractions to Decimals | 分数化小数
convert to recurring decimals, such as 5/6 = 0.8333... because 5 ÷ 6 repeats the digit 3.
将分数化为小数时，用分子除以分母。例如：3/8 表示 3 ÷ 8，结果是 0.375。有些分数会化为循环小数，例如 5/6 = 0.8333...，因为 5 ÷ 6 会重复出现数字 3。
3/8 = 0.375, 7/20 = 0.35, 5/6 = 0.8333...
n equivalent fraction with denominator 10, 100 or 1000. For example, 7/20 = 35/100 = 0.35.
你也可以先将分数化为分母是 10、100 或 1000 的等值分数。例如 7/20 = 35/100 = 0.35。
4. Converting Decimals to Fractions | 小数化分数
Write the decimal as a fraction over a power of ten, then simplify if needed. Example: 0.75 means 75/100. Divide both numbers by 25 to get 3/4. For 0.2, write 2/10 and divide by 2 to get 1/5.
将小数写成分母是 10、100 或 1000 的分数，然后根据需要进行化简。例如：0.75 表示 75/100，分子分母同时除以 25 得到 3/4。对于 0.2，写成 2/10，再除以 2 得到 1/5。
0.75 = 3/4, 0.2 = 1/5, 0.125 = 1/8
Remember to count how many digits appear after the decimal point. One digit means denominator 10, two digits mean denominator 100, and three digits mean denominator 1000.
请记住小数点后有几位数字：一位表示分母是 10，两位表示分母是 100，三位表示分母是 1000。
5. Converting Fractions to Percentages | 分数化百分数
raction to a decimal, then multiply by 100. Example: 3/5 = 3 ÷ 5 = 0.6, and 0.6 × 100 = 60%. Another example: 5/8 = 5 ÷ 8 = 0.625, then 0.625 × 100 = 62.5%.
先将分数化为小数，再乘 100。例如：3/5 = 3 ÷ 5 = 0.6，0.6 × 100 = 60%。另一个例子：5/8 = 5 ÷ 8 = 0.625，然后 0.625 × 100 = 62.5%。
3/5 = 60%, 7/10 = 70%, 5/8 = 62.5%
factor of 100, you can find an equivalent fraction first. For example, 7/10 = 70/100 = 70%.
如果分数的分母本身是 100 的因数，也可以先化为等值分数。例如 7/10 = 70/100 = 70%。
6. Finding Percentages of Amounts | 求一个数的百分之几
percentage of an amount, write the percentage as a decimal and multiply. Example: Find 15% of 240. Since 15% = 0.15, calculate 0.15 × 240 = 36. Alternatively, find 10% first and then 5%: 10% of 240 = 24, 5% of 240 = 12, so 15% = 24 + 12 = 36.
求一个数的百分之几时，先把百分数写成小数再相乘。例如：求 240 的 15%。因为 15% = 0.15，计算 0.15 × 240 = 36。也可以先求 10% 再求 5%：240 的 10% 是 24，240 的 5% 是 12，所以 15% = 24 + 12 = 36。
15% of 240 = 36, 35% of 86 = 30.1
Common percentage shortcuts include 50% = 1/2, 25% = 1/4, 10% = 1/10 and 1% = 1/100.
常见的百分数速算方法包括：50% = 1/2，25% = 1/4，10% = 1/10，1% = 1/100。
7. Percentage Increase and Decrease | 百分比增减
age increase, add the percentage amount to the original value. Example: Increase 120 by 10%. First find 10% of 120: 120 × 0.10 = 12. Then add: 120 + 12 = 132.
进行百分比增加时，先算出增加量，再加到原数上。例如：把 120 增加 10%。先求 120 的 10%：120 × 0.10 = 12。然后相加：120 + 12 = 132。
For a percentage decrease, subtract the percentage amount. Example: Decrease 80 by 15%. First find 15% of 80: 80 × 0.15 = 12. Then subtract: 80 - 12 = 68.
进行百分比减少时，先算出减少量，再从原数中减去。例如：把 80 减少 15%。先求 80 的 15%：80 × 0.15 = 12。然后相减：80 - 12 = 68。
120 increased by 10% = 132, 80 decreased by 15% = 68
A common mistake is adding or subtracting the percentage number directly without first finding the percentage amount.
一个常见错误是没有先求出百分比对应的量，而是直接把百分数数字相加或相减。
8. Simplifying and Using Ratios | 化简与应用比
Ratios compare two or more quantities. To simplify a ratio, divide all parts by the highest common factor. Example: 8:12 divide both numbers by 4 to get 2:3. For 15:25, divide both by 5 to get 3:5.
比用于比较两个或多个数量。化简比时，用最大公因数除以比的各项。例如：8:12 两项同时除以 4 得到 2:3。对于 15:25，两项同时除以 5 得到 3:5。
8:12 = 2:3, 15:25 = 3:5
To share an amount in a given ratio, first add the parts. Example: Share £60 in the ratio 2:3. Total parts = 2 + 3 = 5. One part = £60 ÷ 5 = £12. So the first share is 2 × £12 = £24 and the second share is 3 × £12 = £36.
按给定比例分配金额时，先把比例的项相加。例如：按 2:3 分配 £60。总份数 = 2 + 3 = 5。一份 = £60 ÷ 5 = £12。因此第一份为 2 × £12 = £24，第二份为 3 × £12 = £36。
9. Ordering Fractions, Decimals and Percentages | 分数、小数和百分数的排序
pare values, convert them all into the same form, usually decimals. Example: Order 0.3, 25%, 1/4 and 2/5 from smallest to largest. Convert each: 25% = 0.25, 1/4 = 0.25, 2/5 = 0.4. Now compare: 0.25, 0.25, 0.3, 0.4. So the order is 25% = 1/4, then 0.3, then 2/5.
比较大小时，先把所有数值转化成同一种形式，通常是小数。例如：将 0.3、25%、1/4 和 2/5 从小到大排列。逐一转化：25% = 0.25，1/4 = 0.25，2/5 = 0.4。然后比较：0.25、0.25、0.3、0.4。因此顺序为 25% = 1/4，然后是 0.3，最后是 2/5。
25% = 1/4 < 0.3 < 2/5
Be careful when two values are equal, such as 25% and 1/4. They can be written in either order relative to each other.
当两个数值相等时要特别注意，例如 25% 和 1/4 就相等，它们之间的先后顺序可以互换。
10. Worded Problems | 应用题
ully, identify the operation and show your working. Example 1: A class has 30 students. 20% are absent. How many students are present? 20% of 30 = 0.20 × 30 = 6 absent. Present = 30 - 6 = 24.
应用题需要仔细读题，确定运算方法并写出计算过程。例1：一个班有 30 名学生，20% 缺席。有多少名学生出席？30 的 20% = 0.20 × 30 = 6 人缺席。出席人数 = 30 - 6 = 24。
Example 2: A jacket costs £40. In a sale there is a 15% discount. Find the sale price. Discount = 15% of £40 = 0.15 × 40 = £6. Sale price = £40 - £6 = £34.
例2：一件夹克原价 £40，打八五折。求折后价。折扣 = £40 的 15% = 0.15 × 40 = £6。折后价 = £40 - £6 = £34。
xample 3: A recipe for 4 people needs 200g of flour. How much flour is needed for 6 people? :6 simplifies to 2:3. One part = 200g ÷ 2 = 100g. For 6 people, 3 parts = 3 × 100g = 300g.
例3：一份 4 人食谱需要 200 克面粉。6 人需要多少克面粉？比例 4:6 化简为 2:3。一份 = 200 克 ÷ 2 = 100 克。6 人需要 3 份 = 3 × 100 克 = 300 克。
11. Common Mistakes and How to Avoid Them | 常见错误与避免方法
Mistake 1: Forgetting to simplify a fraction fully. For example, writing 8/12 instead of 2/3. Always divide by the highest common factor.
错误1：分数没有完全化简。例如把 8/12 写成答案，而不是 2/3。一定要除以最大公因数。
Mistake 2: Confusing percentage increase with percentage decrease. For increase, add the percentage amount; for decrease, subtract it.
错误2：混淆百分比增加和百分比减少。增加时要加上百分比对应的量，减少时要减去。
Mistake 3: Comparing fractions before finding a common denominator or converting to decimals. Always convert to the same form first.
错误3：在找公分母或化小数之前直接比较分数。一定要先把所有数值转化为相同形式。
Mistake 4: Dividing a quantity in a ratio without adding the ratio parts first. Remember to find one part by dividing by the total number of parts.
错误4：按比例分配时没有先把比例的项相加。要记住用总份数去除总量，得到一份的大小。
12. Quick Answers Summary | 答案速查表
Use this table to check your final answers for the example questions in this revision guide.
使用下表检查本复习指南中例题的最终答案。
| Question | Answer |
|---|---|
| Simplify 12/18 | 2/3 |
| Simplify 20/45 | 4/9 |
| Convert 3/8 to a decimal | 0.375 |
| Convert 0.75 to a fraction | 3/4 |
| Convert 5/8 to a percentage | 62.5% |
| Find 15% of 240 | 36 |
| Increase 120 by 10% | 132 |
| Share £60 in the ratio 2:3 | £24 and £36 |
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