📚 Year 7 Essential Maths 7 Core Answers: Worked Solutions for Key Topics | Year 7 数学 Essential Maths 7 Core 核心答案解析
This revision guide gives clear, model answers for the core question types in Year 7 Essential Maths 7 Core. Use it to check your method, not just your final answer, because marks are awarded for working.
本复习指南为 Year 7 数学 Essential Maths 7 Core 的核心题型提供清晰、规范的答案示范。请用它来检查解题方法，而不只是核对最终答案，因为评分时会看重解题过程。
1. Place Value and Rounding | 位值与四舍五入
Write the value of the digit 7 in 37 452. The digit 7 is in the thousands column, so its value is 7 000.
写出 37 452 中数字 7 的值。数字 7 位于千位，因此它的值是 7 000。
In 5 308, the value of the digit 5 is 5 000 because it is in the thousands column. In 4 623, the digit 6 has a value of 600 because it is in the hundreds column.
在 5 308 中，数字 5 的值是 5 000，因为它位于千位。在 4 623 中，数字 6 的值是 600，因为它位于百位。
A reliable method is to read the column heading first, then multiply the digit by that place value. The table below shows the same idea for the three examples.
可靠的方法是先读列标题，再用该数字乘以对应的位值。下表用这三个例子说明同一思路。
| Number | 数字 | Digit | 数字位 | Column | 所在位 | Value | 值 |
| 37 452 | 7 | thousands | 千位 | 7 000 |
| 5 308 | 5 | thousands | 千位 | 5 000 |
| 4 623 | 6 | hundreds | 百位 | 600 |
Round 2 648 to the nearest 10, 100 and 1 000. To the nearest 10 the answer is 2 650, to the nearest 100 it is 2 600, and to the nearest 1 000 it is 3 000.
将 2 648 四舍五入到最接近的 10、100 和 1 000。到最近的 10 是 2 650，到最近的 100 是 2 600，到最近的 1 000 是 3 000。
The rule is to look at the digit to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down. For 2 648: the ones digit is 8, so round up to 2 650; the tens digit is 4, so round down to 2 600; the hundreds digit is 6, so round up to 3 000.
规则是看要保留位的右一位数字。若为 5 或更大，就进位；若为 4 或更小，就舍去。对 2 648：个位是 8，所以进位到 2 650；十位是 4，所以舍去得到 2 600；百位是 6，所以进位到 3 000。
2 648 → 2 650 (nearest 10) | 2 600 (nearest 100) | 3 000 (nearest 1 000)
Order 3 142, 2 986 and 3 099 from smallest to largest. The correct order is 2 986, 3 099, 3 142.
将 3 142、2 986 和 3 099 从小到大排列。正确顺序是 2 986、3 099、3 142。
Compare thousands first: 2 986 has 2 thousands, so it is smallest. The other two both have 3 thousands, so compare hundreds: 3 099 has 0 hundreds and 3 142 has 1 hundred, so 3 099 comes next and 3 142 is largest.
先比较千位：2 986 有 2 个千，所以最小。另外两个都有 3 个千，再比较百位：3 099 的百位是 0，3 142 的百位是 1，所以 3 099 排第二，3 142 最大。
2. Addition and Subtraction of Integers | 整数加减法
te 5 and carry the 1. Continue with the tens, hundreds and thousands columns to get 9 305.
计算 5 426 + 3 879。个位相加：6 + 9 = 15，写 5，进 1。继续计算十位、百位和千位，得到 9 305。
ds: 4 + 8 + 1 = 13, write 3, carry 1. Thousands: 5 + 3 + 1 = 9. The final answer is 9 305.
完整竖式过程：个位：6 + 9 = 15，写 5，进 1。十位：2 + 7 + 1 = 10，写 0，进 1。百位：4 + 8 + 1 = 13，写 3，进 1。千位：5 + 3 + 1 = 9。最终答案是 9 305。
5 426 + 3 879 = 9 305
Calculate 7 003 - 2 648. You need to borrow from the thousands column because the hundreds and tens columns have zeros. The answer is 4 355.
计算 7 003 - 2 648。由于百位和十位是 0，需要从千位借位。答案是 4 355。
ndreds column is also 0, so borrow from the thousands. This turns 7 003 into 6 thousands, 9 hundreds, 9 tens and 13 ones. Then 13 - 8 = 5, 9 - 4 = 5, 9 - 6 = 3, and 6 - 2 = 4, giving 4 355.
逐列计算：个位 3 - 8 不够减，需要向十位借 1；但十位是 0，所以要向百位借；百位也是 0，所以再向千位借。这样 7 003 变成 6 个千、9 个百、9 个十和 13 个一。于是 13 - 8 = 5，9 - 4 = 5，9 - 6 = 3，6 - 2 = 4，得到 4 355。
Always check subtraction by adding: 4 355 + 2 648 = 7 003, so the answer is correct.
减法一定要用加法检查：4 355 + 2 648 = 7 003，所以答案正确。
250 + 875 = 2 125 books. The difference between the two types is 1 250 - 875 = 375 books.
一个图书馆有 1 250 本小说类图书和 875 本非小说类图书。图书总数是 1 250 + 875 = 2 125 本。两类图书的差是 1 250 - 875 = 375 本。
1 250 + 875 = 2 125 books | 1 250 - 875 = 375 books
3. Multiplication, Division and Order of Operations | 乘法、除法与运算顺序
6, split 26 into 20 + 6: 348 × 20 = 6 960 and 348 × 6 = 2 088. Then 6 960 + 2 088 = 9 048.
乘法可以用竖式，也可以用拆分法。计算 348 × 26 时，把 26 拆成 20 + 6：348 × 20 = 6 960，348 × 6 = 2 088。然后 6 960 + 2 088 = 9 048。
348 × 26 = 9 048
For division, use short division or the bus-stop method. For 4 725 ÷ 15, ask how many 15s are in 47 (3, remainder 2), then bring down 2 to make 22 (1, remainder 7), then bring down 5 to make 75 (5). The answer is 315.
除法可以用短除法或长除法。计算 4 725 ÷ 15 时，先看 47 里面有几个 15（3 个，余 2），把 2 落下来成 22（1 个，余 7），再把 5 落下来成 75（5 个）。答案是 315。
4 725 ÷ 15 = 315
or 24 + 6 × 5, do the multiplication first: 24 + 30 = 54. For (24 + 6) × 5, do the bracket first: 30 × 5 = 150.
运算顺序遵循 BIDMAS：括号、指数、除法与乘法（从左到右）、加法与减法（从左到右）。计算 24 + 6 × 5 时，先算乘法：24 + 30 = 54。计算 (24 + 6) × 5 时，先算括号：30 × 5 = 150。
d 20 - (8 - 3) × 2 = 20 - 5 × 2 = 20 - 10 = 10. Indices are powers, so 3² means 3 × 3 = 9.
更多例子：3² + 4 × 2 = 9 + 8 = 17。以及 20 - (8 - 3) × 2 = 20 - 5 × 2 = 20 - 10 = 10。指数就是幂，所以 3² 表示 3 × 3 = 9。
4. Negative Numbers and Number Lines | 负数与数轴
ft on the number line. So 5 + (-8) = -3. Adding a positive number moves right: -4 + 9 = 5.
加一个负数相当于在数轴上向左移动。所以 5 + (-8) = -3。加一个正数向右移动：-4 + 9 = 5。
gative number moves right, because two negatives make a positive: -6 - (-2) = -6 + 2 = -4.
减一个正数向左移动：-7 - 3 = -10。减一个负数向右移动，因为负负得正：-6 - (-2) = -6 + 2 = -4。
5 + (-8) = -3 | -4 + 9 = 5 | -7 - 3 = -10 | -6 - (-2) = -4
ve × negative = positive. For example, (-3) × 4 = -12, (-3) × (-4) = 12, and -20 ÷ 5 = -4.
乘除法要使用符号法则：正 × 正 = 正；正 × 负 = 负；负 × 负 = 正。例如 (-3) × 4 = -12，(-3) × (-4) = 12，-20 ÷ 5 = -4。
is -6 °C and rises by 11 °C, the new temperature is -6 + 11 = 5 °C. If a bank balance is -£45 and £20 is paid in, the new balance is -£45 + £20 = -£25.
温度和钱款情境在 Year 7 题目中很常见。如果温度是 -6 °C，上升 11 °C，新温度是 -6 + 11 = 5 °C。如果银行余额是 -£45，又存入 £20，新余额是 -£45 + £20 = -£25。
5. Factors, Multiples, Primes and Index Notation | 因数、倍数、质数与指数记法
prime factorisation writes a number as a product of primes: 36 = 2 × 2 × 3 × 3 = 2² × 3².
36 的因数是 1、2、3、4、6、9、12、18 和 36。质因数分解就是把一个数写成质数的乘积：36 = 2 × 2 × 3 × 3 = 2² × 3²。
common multiple (LCM) of 24 and 36 is 72. A quick check: 24 × 36 = 864, and 864 ÷ 12 = 72.
24 和 36 的最大公因数是 12。24 和 36 的最小公倍数是 72。快速检验：24 × 36 = 864，864 ÷ 12 = 72。
Prime numbers below 20 are 2, 3, 5, 7, 11, 13, 17 and 19. Remember that 1 is not prime, and 2 is the only even prime number.
20 以内的质数是 2、3、5、7、11、13、17 和 19。记住 1 不是质数，2 是唯一的偶质数。
iting repeated multiplication. For example, 3⁴ = 3 × 3 × 3 × 3 = 81, 5² = 25, and 2⁵ = 32.
指数记法是重复乘法的简写。例如 3⁴ = 3 × 3 × 3 × 3 = 81，5² = 25，2⁵ = 32。
36 = 2² × 3² | HCF(24, 36) = 12 | LCM(24, 36) = 72
6. Fractions, Decimals and Percentages | 分数、小数与百分数
or by the denominator. Then multiply by 100 for a percentage. For example, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 7/10 = 0.7 = 70%, and 5/8 = 0.625 = 62.5%.
把分数化成小数，用分子除以分母。再乘以 100 就得到百分数。例如 3/4 = 0.75 = 75%，1/5 = 0.2 = 20%，7/10 = 0.7 = 70%，5/8 = 0.625 = 62.5%。
5/6. To multiply fractions, multiply numerators and denominators: 3/4 × 8/9 = 24/36 = 2/3.
分数相加要先通分。计算 2/3 + 1/6 时，把 2/3 化成 4/6，然后 4/6 + 1/6 = 5/6。分数相乘时，分子乘分子、分母乘分母：3/4 × 8/9 = 24/36 = 2/3。
ion, multiply by its reciprocal. So 3 ÷ 1/2 = 3 × 2 = 6, and 2/5 ÷ 3/4 = 2/5 × 4/3 = 8/15.
除以一个分数，等于乘它的倒数。所以 3 ÷ 1/2 = 3 × 2 = 6，2/5 ÷ 3/4 = 2/5 × 4/3 = 8/15。
a percentage of an amount, convert the percentage to a decimal or use simple parts. For 15% of 240: 10% is 24 and 5% is 12, so 15% is 24 + 12 = 36. For 35% of 80: 10% is 8, 30% is 24, and 5% is 4, so 35% is
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