📚 Year 7 Higher Homework: Mixed Practice Set 7 | 七年级提高作业：综合练习第7套
This revision guide supports Year 7 Higher Homework Set 7. It brings together the key skills you need for mixed practice: number work, fractions, ratio, algebra, geometry and statistics. Each section gives a short explanation, worked examples and a reminder of common mistakes to avoid.
本复习指南配套七年级提高作业第7套。它汇集了综合练习所需的核心技能：数的运算、分数、比、代数、几何和统计。每一节都提供简要讲解、例题以及需要避免的常见错误提醒。
1. Number and Place Value | 数与位值
ng by 10 moves every digit one place to the right. For example, 34.6 × 100 = 3460 because the digits move two places to the left, while 34.6 ÷ 100 = 0.346.
在提高第7套中，位值问题通常涉及非常大或非常小的数。乘以10时数字向左移动一位，除以10时数字向右移动一位。例如，34.6 × 100 = 3460，因为数字向左移动了两位；而 34.6 ÷ 100 = 0.346。
Rounding to significant figures also appears regularly. To round 47,582 to two significant figures, identify the first two non-zero digits, which are 4 and 7. The next digit is 5, so the 7 rounds up to 8. The answer is 48,000, and the zeros must still be written to keep the size of the number.
按有效数字四舍五入也经常出现。将 47,582 四舍五入到两位有效数字，首先确定前两个非零数字，即 4 和 7。下一位是 5，所以 7 向上进一位变成 8。答案是 48,000，这些零必须写出来，才能保持数的大小不变。
the exact answer should be close to 1000. This helps you spot place value errors quickly.
一个有用的检查方法是在计算前先估算。对于 612 + 389，先四舍五入为 600 + 400 = 1000，因此精确答案应接近 1000。这能帮助你快速发现位值错误。
, and dropping place-holder zeros when rounding, for example writing 48 instead of 48,000.
这里的常见错误是：只数零的个数而不是移动数字；忘记 10⁰ = 1；四舍五入时丢掉占位的零，例如把 48,000 写成 48。
34.6 × 100 = 3460 34.6 ÷ 100 = 0.346 47,582 ≈ 48,000 (2 s.f.) 612 + 389 ≈ 600 + 400 = 1000
2. Negative Numbers | 负数
3. Subtracting a negative is the same as adding its positive value: 5 − (−8) = 5 + 8 = 13.
对于负数，要记住加上一个负数等于减去它的正数。例如，5 + (−8) = 5 − 8 = −3。减去一个负数等于加上它的正数：5 − (−8) = 5 + 8 = 13。
and (−12) ÷ (−3) = 4. If the signs are different, the result is negative: (−6) × 7 = −42.
乘法和除法遵循符号法则。如果两个数符号相同，结果为正：(−6) × (−7) = 42，( −12 ) ÷ (−3) = 4。如果符号不同，结果为负：(−6) × 7 = −42。
Use a number line if you are unsure. Moving right means becoming more positive, and moving left means becoming more negative. The difference between −8 and 4 is 12 because you move 12 steps from −8 to 4.
如果不确定，就使用数轴。向右移动表示数值变大，向左移动表示数值变小。−8 和 4 之间的差是 12，因为从 −8 到 4 需要移动 12 步。
bers, and confusing −3² = −9 with (−3)² = 9. A negative number squared is always positive.
常见错误包括把 5 + (−8) 写成 13；在三个或更多数相乘时忽略符号法则；把 −3² = −9 与 (−3)² = 9 混淆。负数的平方永远是正数。
5 + (−8) = −3 5 − (−8) = 13 (−6) × (−7) = 42 (−12) ÷ (−3) = 4 (−6) × 7 = −42
3. Fractions, Decimals and Percentages | 分数、小数和百分比
ividing the numerator and denominator by their highest common factor, for instance 18/24 = 3/4.
分数加减时，先找到公分母。例如，2/5 + 1/4 = 8/20 + 5/20 = 13/20。如果可能，最后要用分子和分母的最大公因数化简答案，例如 18/24 = 3/4。
tion, turn the second fraction upside down and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1½.
分数相乘时，分子乘分子、分母乘分母：2/3 × 3/5 = 6/15 = 2/5。除以一个分数时，把第二个分数颠倒后相乘：3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1½。
he denominator to get a decimal, then multiply by 100 for a percentage: 3/8 = 0.375 = 37.5%. Working the other way, 0.6 = 3/5 = 60%.
分数、小数和百分比的互相转换也是一项核心技能。用分子除以分母得到小数，再乘以 100 得到百分比：3/8 = 0.375 = 37.5%。反过来，0.6 = 3/5 = 60%。
To find a percentage of an amount, convert the percentage to a decimal and multiply: 15% of 240 = 0.15 × 240 = 36. A fraction of an amount works in the same way: 3/4 of 60 = 45.
求一个量的百分之几时，先把百分比化成小数再相乘：240 的 15% = 0.15 × 240 = 36。求一个量的几分之几同理：60 的 3/4 = 45。
Common mistakes: adding the denominators as well as the numerators, so 2/5 + 1/4 is wrongly written as 3/9, and forgetting to simplify the final answer.
常见错误：把分母也一起相加，于是把 2/5 + 1/4 错写成 3/9；以及忘记化简最后的答案。
2/5 + 1/4 = 8/20 + 5/20 = 13/20 3/8 = 0.375 = 37.5% 15% of 240 = 36
4. Ratio and Proportion | 比与比例
n in the form 1 : n are especially useful for comparing prices, speeds and recipe amounts.
比用于比较同类的量。用两个数的最大公因数同时除，即可化简：24 : 36 = 2 :
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