Essential Maths 7C Homework Answers: Common Mistakes | Essential Maths 7C 作业答案易错点总结

📚 Essential Maths 7C Homework Answers: Common Mistakes | Essential Maths 7C 作业答案易错点总结

In Essential Maths 7C, you tackle negative numbers, fractions, algebra, geometry and statistics. When checking your homework answers, a few mistakes crop up again and again. Understanding these common errors will help you avoid losing marks and build stronger skills. This article walks you through the top pitfalls, with clear examples and corrections for each one.

在 Essential Maths 7C 中，你会接触到负数、分数、代数、几何和统计。批改作业答案时，有些错误总会反复出现。彻底弄清这些常见错误，能帮你避免失分，打下更扎实的数学基础。本文为你梳理了最频繁的易错点，每一个都配有具体的例子和正确的解法。

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1. Adding and Subtracting Negative Numbers | 负数加减法

When you see an expression like 4 + (-7), the ‘+’ and ‘-‘ signs sit next to each other. Many pupils mistakenly ignore the negative sign and work out 4 + 7 = 11. The correct interpretation is to rewrite it as a subtraction: 4 – 7 = -3. The same logic applies when you have a larger positive number being subtracted from a smaller one, such as 3 – 8: the answer must be negative, -5, not 5.

当看到 4 + (-7) 这样的式子时，加号和负号紧挨在一起。很多同学会忽略那个负号，直接算成 4 + 7 = 11。正确的理解是把它改写为减法：4 – 7 = -3。同样的道理也适用于较小的数减去较大的数，比如 3 – 8：答案必须是负数，即 -5，而不是 5。

Subtracting a negative number is another major sticking point. Take 5 – (-2): the double negative turns into addition, so you get 5 + 2 = 7. A typical mistake is to write 5 – (-2) = 3, as if the minus sign only removes the bracket. Remember that ‘minus a negative’ is the same as adding the positive version of that number.

减去负数则是另一大易错点。以 5 – (-2) 为例：两个负号会转化为加法，因此得到 5 + 2 = 7。一个典型错误是把 5 – (-2) 算成 3，好像减号只是去掉了括号一样。请牢记，“减去一个负数”就等于加上这个数的相反数（正数）。

Finally, when combining several terms, always move left to right with the signs treated carefully. For -3 – 4 + 2, you start at -3, subtract 4 to reach -7, then add 2 to land at -5. Errors often occur when students try to reorder the terms without keeping the correct sign attached to each number.

最后，当有多个项相加减时，一定要从左到右，小心处理每个数的符号。以 -3 – 4 + 2 为例，从 -3 开始，减 4 得 -7，再加 2 得到 -5。常见错误是学生在没有把符号跟随数字一起移动的情况下就随意交换了顺序。

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2. Multiplying and Dividing Negative Numbers | 负数乘除法

With multiplication, two negatives always give a positive. So (-4) × (-6) = 24. Yet many students still write -24, especially in timed conditions. A quick check is to cover the signs first: 4 × 6 = 24, then decide the sign: negative × negative = positive. Similarly, a negative times a positive gives a negative, e.g. (-5) × 3 = -15.

在乘法中，负负得正。所以 (-4) × (-6) = 24。但很多学生还是会写成 -24，尤其是在限时作答时。一个快速检验的方法是先忽略符号算 4×6=24，再定符号：负×负=正。同理，负×正得负，例如 (-5)×3 = -15。

Division follows exactly the same sign rules. (-18) ÷ 3 = -6, and (-24) ÷ (-4) = 6. A frequent slip occurs when a division is written as a fraction, such as -12/4. Some pupils read it as ’12 divided by 4 and then put a minus sign’, which is correct, but they then incorrectly add that minus to the denominator as well, treating it as 12/(-4) when the original denominator is positive.

除法也遵循完全相同的符号规则。(-18) ÷ 3 = -6，(-24) ÷ (-4) = 6。一个常见失误出现在除法写成分数形式的时候，比如 -12/4。有些同学会理解为“12 除以 4 再带上负号”，这是对的，但他们有时会错误地把分母也当成负数，而当原来的分母实际上是正数时，就会得出错误的正负号。

When chains of multiplication and division appear together, work strictly from left to right unless brackets tell you otherwise. For 12 ÷ (-3) × 2, first do 12 ÷ (-3) = -4, then multiply by 2 to get -8. Many learners mistakenly do the multiplication first and get 12 ÷ (-6) = -2. Stick to the left-to-right rule.

当乘除混合运算连在一起时，除非有括号说明，否则必须严格按照从左到右的顺序计算。比如 12 ÷ (-3) × 2，先算 12 ÷ (-3) = -4，再乘 2 得到 -8。许多学生错误地先算了乘法，得出 12 ÷ (-6) = -2。请一定坚持从左到右的规则。

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3. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分数的互化

Converting a simple fraction like 3/8 to a decimal often trips students up. They might guess 0.3 or 0.38 instead of performing the division 3 ÷ 8 = 0.375. Always use long division or a known equivalent fraction (3/8 = 375/1000) to get the exact decimal. A decimal that stops is a terminating decimal; many fractions give recurring decimals unless the denominator’s prime factors are only 2 and 5.

把 3/8 这样的简单分数化成小数时，常有学生直接猜测 0.3 或 0.38，而不去做除法 3 ÷ 8 = 0.375。要养成用长除法或者利用等值分数（3/8 = 375/1000）得出精确小数的习惯。只含质因数 2 和 5 的分母会得到有限小数，否则就会出现循环小数。

When turning a decimal into a percentage, remember that multiplying by 100 moves the decimal point two places to the right. So 0.07 becomes 7%, not 0.7% or 70%. A common error with 0.7 is to write 7% instead of 70%. Similarly, 1.2 as a percentage is 120%, not 12%.

把小数化成百分数时，记住乘 100 就是把小数点向右移动两位。因此 0.07 变成 7%，而不是 0.7% 或 70%。面对 0.7 时，常见错误是写成 7% 而不是 70%。同样的，1.2 化成百分数是 120%，而不是 12%。

For conversions in the opposite direction, a percentage to a fraction, write the percentage over 100 and simplify. 45% = 45/100 = 9/20. Students often stop at 45/100 and lose marks for not simplifying. Always check if the fraction can be cancelled down.

反过来由百分数化成分数时，先将百分数写成 100 分之几，再约分。45% = 45/100 = 9/20。很多学生止步于 45/100，因为没有继续化简而被扣分。每次都要检查分数能否约简。

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4. Collecting Like Terms in Algebra | 代数中的合并同类项

Like terms have exactly the same variable part. For 3a + 2b + 4a – b, you can group the a terms: 3a + 4a = 7a, and the b terms: 2b – b = 1b or just b. The most frequent slip is trying to combine unlike terms, such as writing 3a + 2b as 5ab. Letters that are different cannot be added together like ordinary numbers.

同类项是指字母部分完全相同的项。对于 3a + 2b + 4a – b，可以把含 a 的项合并：3a + 4a = 7a，含 b 的项合并：2b – b = b。最常见的差错是把不同类项强行合并，比如将 3a + 2b 写成了 5ab。字母不同的项不能像普通数字那样相加。

Another pitfall is ignoring the sign in front of a term. When simplifying 5x – 3y + 2x + y, you should get 7x – 2y. Some pupils write 7x – 4y because they treat the last y as negative instead of positive. Always read the expression exactly as it is written: + y is plus y, not minus y.

另一个易错点是忽略项前面的符号。化简 5x – 3y + 2x + y 时，应得到 7x – 2y。有的学生会写成 7x – 4y，因为他们把最后的 y 误当作了 -y。请务必按照原式解读：+ y 就是加 y，不是减 y。

When terms include powers, such as x² and x, they are not like terms. So 2x² + 3x cannot be simplified to 5x² or 5x. Only terms with exactly the same variable and the same exponent can be collected together.

当项带指数时，比如 x² 和 x，它们也不是同类项。因此 2x² + 3x 不能简化为 5x² 或 5x。只有字母和指数都完全相同的项，才能合并。

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5. Solving One-Step and Two-Step Equations | 解一步和两步方程

A one-step equation like x + 7 = 12 requires the inverse operation: subtract 7 from both sides to get x = 5. The mistake here is often to add 7 to 12, giving x = 19. Remember, whatever operation you do to one side must be done to the other, and you must undo the operation that is applied to x.

像 x + 7 = 12 这样的一步方程，需要用逆运算来解：两边同时减 7，得到 x = 5。这里的常见错误是把 7 加到 12 上，得出 x = 19。记住，对等式一边做了什么操作，另一边也必须做同样的操作，而且必须对 x 施加逆运算。

For two-step equations such as 2x – 3 = 9, the correct order is to undo the subtraction first: add 3 to both sides to give 2x = 12, then divide by 2 to obtain x = 6. Many learners incorrectly divide by 2 first, rewriting it as x – 3 = 4.5, which leads to an incorrect answer. Always reverse the order of operations: addition/subtraction before multiplication/division.

对于 2x – 3 = 9 这样的两步方程，正确的顺序是先处理减法：两边加 3 得 2x = 12，然后除以 2 得到 x = 6。不少学生错误地先除以 2，把式子变成 x – 3 = 4.5，最终得出错误答案。一定要逆着运算顺序来：先处理加减，后处理乘除。

When a negative sign is in front of x, like -x = 4, multiply or divide both sides by -1 to get x = -4. Pupils sometimes leave the answer as x = 4 or write minus x equals 4 without solving for positive x. The goal is always to end with ‘x = …’.

当 x 前面有负号时，比如 -x = 4，两边同乘或同除以 -1，得到 x = -4。一些学生会直接把答案写成 x = 4，或者停留在 -x = 4 这一步，而不求出 x。解题的目标永远是要把 x 单独放在等号一边，得到“x = …”的形式。

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6. Perimeter and Area of Rectangles and Triangles | 长方形和三角形的周长与面积

For a rectangle, perimeter = 2 × (length + width). A common mistake is to calculate length + width and stop, forgetting to double it. If a rectangle is 8 cm by 5 cm, its perimeter is 2×(8+5) = 26 cm, not 13 cm. For area of a rectangle, multiply length by width: 8 × 5 = 40 cm². Be sure to use the correct unit: perimeter is in cm, area in cm².

长方形的周长 = 2 × (长 + 宽)。常见错误是只算了长加宽就停住了，忘记再乘 2。如果一个长方形长 8 cm、宽 5 cm，它的周长是 2×(8+5)=26 cm，而不是 13 cm。长方形的面积则是长乘宽：8×5=40

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