📚 Year 7 Maths Essential Maths 7H Homework Answers | Year 7 数学 Essential Maths 7H 作业答案
Welcome to this Year 7 Maths homework support article. It covers the key skills in Essential Maths 7H, with worked examples and answers for the most common homework questions. Each section gives a typical question, the correct answer, and the step-by-step method you need to show in your exercise book.
欢迎阅读本篇 Year 7 数学作业辅导文章。本文涵盖 Essential Maths 7H 的核心技能，针对最常见的作业题提供典型例题、正确答案和分步解题方法，帮助你规范书写过程。
1. How to Use This Homework Answer Guide | 如何使用本作业答案指南
This article supports Year 7 students working through Essential Maths 7H, the higher-level pupil book in the Essential Maths series. Every section below takes one skill that appears constantly in homework, shows a typical question in the style the book uses, gives the correct answer, and then explains the method you should write down in your exercise book. In Year 7, marks are awarded for method as well as for the final answer, so copying an answer without the working will not help you in the end-of-topic test.
本文面向使用 Essential Maths 7H（该系列中的高阶用书）的 Year 7 学生。下面每一节都选取一项在作业中反复出现的技能，给出与教材风格一致的典型题目、正确答案，并说明你在练习本上应当写下的解题过程。Year 7 的评分既看过程也看结果，只抄答案不写过程，对单元测试没有帮助。
The best way to use the guide is to attempt each question first with the book closed, then check your answer against the worked solution. If your answer matches but your method is different, your method is usually still valid - marks are given for correct reasoning, not for one approved route.
使用本指南的最佳方式是：先合上书本独立完成题目，再对照解答检查。若答案一致而方法不同，你的方法通常同样有效——给分看的是推理是否正确，而不是只有唯一标准解法。
A short checklist for every homework question: write the question number; show one line of working per step; keep equals signs aligned in a column; write units (cm, kg, £, °); and box or underline your final answer so it is easy to find.
每道作业题的简明清单：写清题号；每一步写一行过程；等号上下对齐成一列；答案带上单位（cm、kg、£、°）；最后把答案加框或下划线，方便查找。
2. Place Value and Ordering Integers | 位值与整数排序
In Year 7, you must be able to read, write and order whole numbers and decimals. Homework questions often ask you to arrange a set of numbers in ascending or descending order, or to write a number in words.
在 Year 7，你需要能够读写整数与小数并比较大小。作业题常要求将一组数字按升序或降序排列，或将数字写成文字形式。
Place value is the value a digit has because of its position. In the number 4 706. 85, the digit 4 means 4 thousands (4 000), the 7 means 7 hundreds (700), the 0 means 0 tens, the 6 means 6 units (6), the 8 means 8 tenths (0.8) and the 5 means 5 hundredths (0.05).
位值是指一个数字因其所在位置而具有的值。在数 4 706.85 中，4 表示 4 个千（4 000），7 表示 7 个百（700），0 表示 0 个十，6 表示 6 个一，8 表示 8 个十分之一（0.8），5 表示 5 个百分之一（0.05）。
| Thousands | Hundreds | Tens | Units | Tenths | Hundredths |
|---|---|---|---|---|---|
| 4 | 7 | 0 | 6 | 8 | 5 |
Model question: Write these numbers in order from smallest to largest: 905, 509, 950, 590, 59.
示例题： 将下列各数从小到大排列：905、509、950、590、59。
Answer: 59, 509, 590, 905, 950. Compare the hundreds digits first. The only two-digit number is 59, so it is the smallest. Among the hundreds, 5 is less than 9, so 509 and 590 come before 905 and 950. Then compare the tens digits to order 509 before 590 and 905 before 950.
答案： 59、509、590、905、950。先比较百位数字。唯一的两位数是 59，因此它最小。在三位数中，百位 5 小于 9，所以 509 和 590 排在 905 和 950 之前。再比较十位，509 在 590 前，905 在 950 前。
Another typical question: Write 6 084 in words.
另一道典型题： 用英文写出 6 084。
Answer: Six thousand and eighty-four. In British English, use 'and' before the tens or units when the hundreds part is present, but do not use 'and' between thousands and hundreds.
答案： Six thousand and eighty-four。英式英语中，当百位之后还有十位或个位时使用 'and'，但千位与百位之间不用 'and'。
3. Rounding, Estimating and Checking Answers | 四舍五入、估算与检验
Rounding questions almost always tell you the accuracy required: nearest whole number, nearest ten, one decimal place, two decimal places, or one significant figure. The method is the same every time: find the digit in the required place, look at the digit immediately to its right, and round up if that digit is 5 or more, otherwise keep the digit the same.
四舍五入题几乎总会说明精确到哪一位：最接近的整数、十位、一位小数、两位小数，或一位有效数字。方法每次都一样：找到要求数位上的数字，看它右边紧邻的一位，若该位 ≥ 5 就进位，否则保持原数字不变。
Model question: Round 4.678 to (a) 2 decimal places, (b) 1 decimal place, (c) the nearest whole number.
示例题： 将 4.678 分别保留：(a) 两位小数，(b) 一位小数，(c) 最接近的整数。
Answer: (a) 4.68 - the third decimal is 8, so round up. (b) 4.7 - the second decimal is 7, so round up. (c) 5 - the first decimal is 6, so round up.
答案： (a) 4.68——第三位小数是 8，进位。(b) 4.7——第二位小数是 7，进位。(c) 5——第一位小数是 6，进位。
Estimating is the fastest check you have in an exam. Round every number to one significant figure, do the calculation mentally, and compare with your exact answer.
估算是最快的检查手段。把每个数取一位有效数字，心算一遍，再与精确答案比较。
3.9 × 21.4 ≈ 4 × 20 = 80
If your exact answer is 83.46, the estimate confirms it. If your exact answer is 834.6, you have made a place-value error somewhere.
若精确答案是 83.46，估算结果可以佐证。若精确答案是 834.6，说明某处出现了位值错误。
4. Negative Numbers and the Number Line | 负数与数轴
Negative numbers appear in Year 7 as temperature, bank balances, and coordinates. The number line is the safest tool: moving right is adding, moving left is subtracting. A negative sign in front of a bracket changes every sign inside.
负数在 Year 7 中以温度、银行余额和坐标等形式出现。数轴是最稳妥的工具：向右移动是加，向左移动是减。括号前的负号会改变括号内每一项的符号。
Model question: Work out (a) −7 + 5, (b) 3 − 8, (c) −4 × −3, (d) −20 ÷ 5.
示例题： 计算 (a) −7 + 5，(b) 3 − 8，(c) −4 × −3，(d) −20 ÷ 5。
Answer: (a) −2, because you start at −7 and move 5 to the right. (b) −5, because you start at 3 and move 8 to the left. (c) 12, because a negative times a negative is positive. (d) −4, because a negative divided by a positive is negative.
答案： (a) −2：从 −7 出发向右移 5 格。(b) −5：从 3 出发向左移 8 格。(c) 12：负负得正。(d) −4：负数除以正数得负数。
Sign rules worth memorising:
值得背诵的符号法则：
- (+) × (+) = (+) (+) ÷ (+) = (+)
- (−) × (−) = (+) (−) ÷ (−) = (+)
- (+) × (−) = (−) (+) ÷ (−) = (−)
- (−) × (+) = (−) (−) ÷ (+) = (−)
For ordering, remember that further left on the number line means smaller: −12 < −5 < 0 < 3.
比较大小时要记住：数轴上越靠左越小，即 −12 < −5 < 0 < 3。
5. The Four Operations with Decimals | 小数的四则运算
Decimal arithmetic is where most careless marks are lost. Line up decimal points for addition and subtraction, ignore decimal points while multiplying and count the total decimal places at the end, and make the divisor a whole number before dividing.
小数运算是丢分最多的地方。加减法要把小数点对齐；乘法先忽略小数点计算，最后数出总的小数位数；除法要先把除数变成整数。
Model question: Work out (a) 3.6 + 4.75, (b) 9.2 − 4.65, (c) 2.4 × 0.7, (d) 8.4 ÷ 0.6.
示例题： 计算 (a) 3.6 + 4.75，(b) 9.2 − 4.65，(c) 2.4 × 0.7，(d) 8.4 ÷ 0.6。
Answer: 8 and there are two decimal places in total, so the answer has two decimal places. (d) 14 - multiply both numbers by 10 to get 84 ÷ 6 = 14.
答案： (a) 8.35——把 3.60 写在 4.75 上方相加。(b) 4.55——把 9.20 写在 4.65 上方相减，需跨小数点借位。(c) 1.68——先算 24 × 7 = 168，两个乘数共有两位小数，故结果保留两位小数。(d) 14——两数同乘 10，得 84 ÷ 6 = 14。
Count the decimal places carefully - 2.4 has one and 0.7 has one, so the answer needs two.
一个能救回不少分数的提醒：2.4 × 0.7 不是 16.8。务必数清小数位数——2.4 有一位，0.7 有一位，所以结果要有两位小数。
6. Fractions, Decimals and Percentages | 分数、小数与百分数
You must be able to move between fractions, decimals and percentages without a calculator. To turn a fraction into a decimal, divide the numerator by the denominator. To turn a decimal into a percentage, multiply by 100.
你必须能够在不用计算器的情况下在分数、小数和百分数之间转换。分数化小数：分子除以分母。小数化百分数：乘以 100。
Model question: Complete the table.
示例题： 完成下表。
| Fraction | Decimal | Percentage |
|---|---|---|
| ⅜ | 0.375 | 37.5% |
| 9⁄25 | 0.36 | 36% |
| 9⁄20 | 0.45 | 45% |
Answer: ⅜ = 3 ÷ 8 = 0.375 = 37.5%. 0.36 = 36⁄100 = 9⁄25 = 36%. 45% = 45⁄100 = 9⁄20 = 0.45.
答案： ⅜ = 3 ÷ 8 = 0.375 = 37.5%。0.36 = 36⁄100 = 9⁄25 = 36%。45% = 45⁄100 = 9⁄20 = 0.45。
Learn these by heart, they appear in almost every homework exercise: ½ = 0.5 = 50%; ¼ = 0.25 = 25%; ¾ = 0.75 = 75%; ⅕ = 0.2 = 20%; ⅛ = 0.125 = 12.5%; ⅓ = 0.333... ≈ 33.3%; ⅔ ≈ 66.7%; 1⁄10 = 0.1 = 10%.
以下转换几乎每次作业都会用到，务必背熟：½ = 0.5 = 50%；¼ = 0.25 = 25%；¾ = 0.75 = 75%；⅕ = 0.2 = 20%；⅛ = 0.125 = 12.5%；⅓ = 0.333… ≈ 33.3%；⅔ ≈ 66.7%；1⁄10 = 0.1 = 10%。
7. Ratio, Proportion and Sharing | 比、比例与按比分配
Ratio questions come in three types: simplifying, sharing an amount in a given ratio, and solving a proportion such as scaling a recipe. Always find the value of one part first when sharing.
比的问题有三类：化简比、按比分配总量、以及配比缩放这类比例问题。按比分配时，永远先求出一份的值。
Model question: Share £240 in the ratio 3 : 5.
示例题： 将 £240 按 3 : 5 分配。
Answer: Add the parts: 3 + 5 = 8 parts. One part = 240 ÷ 8 = £30. So the shares are 3 × 30 = £90 and 5 × 30 = £150. Check: 90 + 150 = 240, which is the original amount.
答案： 先求总份数：3 + 5 = 8 份。一份 = 240 ÷ 8 = £30。两份分别为 3 × 30 = £90 和 5 × 30 = £150。检验：90 + 150 = 240，与总量一致。
Another typical question: Simplify the ratio 18 : 24 and write the ratio 1 : 4 as a percentage.
另一道典型题： 化简比 18 : 24，并把比 1 : 4 写成百分数。
Answer: second part, 1 : 4 means 1 part out of 5 altogether, so the percentage is 1 ÷ 5 × 100 = 20%.
答案： 两数同除以最大公因数 6，得 3 : 4。第二问中 1 : 4 表示共 5 份中的 1 份，故百分数为 1 ÷ 5 × 100 = 20%。
8. Algebra: Collecting Terms and Substitution | 代数：合并同类项与代入求值
Algebra in Year 7 starts with writing expressions, collecting like terms, expanding a single bracket, and substituting numbers into a formula. Like terms have exactly the same letters and powers, so 5a and 3a are like terms but 5a and 5a² are not.
Year 7 的代数从列式、合并同类项、去单个括号以及代入公式求值开始。同类项必须字母与指数完全相同，因此 5a 与 3a 是同类项，而 5a 与 5a² 不是。
Model question: mplify (a) 5a + 3b − 2a + 4b, (b) 3(2x + 5), and (c) find the value of 3x² − 5 when x = 4.
示例题： 化简 (a) 5a + 3b − 2a + 4b，(b) 3(2x + 5)，(c) 当 x = 4 时求 3x² − 5 的值。
Answer: − 5 = 3 × 16 − 5 = 48 − 5 = 43. Square before multiplying - this order of operations is where most errors happen.
答案： (a) 5a − 2a = 3a，3b + 4b = 7b，故答案为 3a + 7b。(b) 括号内每一项都乘 3：3 × 2x = 6x，3 × 5 = 15，故答案为 6x + 15。(c) 3 × 4² − 5 = 3 × 16 − 5 = 48 − 5 = 43。要先算平方再乘——这里的运算顺序是多数错误的来源。
Remember the order of operations: brackets, indices, division and multiplication, addition and subtraction. Writing each step on a new line prevents the most common errors.
牢记运算顺序：括号、乘方、乘除、加减。每一步另起一行书写，可以避免最常见的错误。
9. Solving Linear Equations | 解一元一次方程
Solving an equation means finding the value of the unknown that makes both sides equal. Do the same thing to both sides, and undo the operations in reverse order: deal with addition and subtraction first, then multiplication and division.
解方程就是找出使等式两边相等的未知数的值。等式两边做相同的运算，并按相反的顺序逆运算：先处理加减，再处理乘除。
Model question: Solve (a) 4x + 7 = 31, (b) 5(x − 2) = 35, (c) 3x − 5 = x + 11.
示例题： 解方程 (a) 4x + 7 = 31，(b) 5(x − 2) = 35，(c) 3x − 5 = x + 11。
Answer: × 7 = 35. (c) Subtract x from both sides: 2x − 5 = 11. Add 5: 2x = 16. Divide by 2: x = 8.
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