📚 Math Practice Animation G-1-2: Common Mistakes Summary | 数学练习动画 G-1-2 易错点总结
This article highlights the most frequent errors students make when working through the Math Practice Animation G-1-2 exercises. By identifying and understanding these pitfalls, you can strengthen your mathematical foundation and avoid losing easy marks. Each section pairs a clear English explanation with a Chinese version, followed by worked examples and memory fixes.
本文总结了学生在数学练习动画 G-1-2 中反复出现的易错点。这些错误往往源于概念混淆、计算跳步或死记硬背。每个知识点都提供了中英双语解析、正确步骤与避坑指南，帮助你在后续练习中做到快而准。
1. Order of Operations (BODMAS/PEMDAS) | 运算顺序
Many learners treat multiplication as ‘stronger’ than division, or addition as ‘stronger’ than subtraction. In fact, multiplication and division share the same priority and are performed left-to-right; the same applies to addition and subtraction. A common error is to insistently multiply first even when division appears earlier in the expression.
很多同学错误地认为乘法总是比除法先算，或者加法比减法先算。实际上乘除同级，从左往右依次处理；加减同理。最常见的翻车现场是看到乘号就抢跑，无视更靠左的除法。
8 ÷ 2 × (1 + 3) = 8 ÷ 2 × 4 = 4 × 4 = 16
If you incorrectly treat ‘2 × 4’ as an indivisible block, you may obtain 8 ÷ 8 = 1, which is wrong. Always follow the left-to-right rule when operations have equal precedence.
如果你错误地把“2 × 4”当成一个整体先算，就会得到 8 ÷ 8 = 1，结果出错。当运算同级时，一定要从左往右依次计算，切勿擅自添加括号。
2. Negative Numbers and Absolute Value | 负数与绝对值
When squaring a negative number, the notation -3² means -(3×3)= -9 because the exponent only applies to the digit 3, not to the minus sign. The parentheses make all the difference: (-3)² = +9. Another slip is forgetting that absolute value strips the negative sign but leaves positive values unchanged.
平方运算时，-3² 表示 -(3×3)= -9，因为指数只作用在 3 上。加上括号则有 (-3)² = 9。另一个高频错误是处理绝对值时直接“去掉负号”但不考虑正数本身不变，或误以为 |x| 会改变正数的符号。
-5² = -25 (-5)² = +25 | -7 | = 7 | 7 | = 7
Always insert brackets when you intend to square a negative base. For absolute value, think of distance from zero: it is always non-negative.
想对一个负数整体平方时，务必加括号。绝对值表示到零点的距离，结果永远不是负数。记牢这两条，符号题就不会被扣分。
3. Fractions: Addition and Subtraction | 分数的加减法
The most tempting shortcut – adding numerators and adding denominators – is completely wrong. To add 1/2 and 1/3 you must find a common denominator (6), convert each fraction, then add the numerators only. Many students mistakenly write (1+1)/(2+3) = 2/5.
分数加减最经典的错误就是分子加分子、分母加分母。计算 1/2 + 1/3 的正确步骤是先找到公分母 6，将分数变成 3/6 和 2/6，再分子相加得 5/6。直接得出 2/5 的同学请立刻纠正这个习惯。
1/2 + 1/3 = 3/6 + 2/6 = 5/6 (not 2/5)
The same rule governs subtraction: keep the common denominator and subtract the numerators. For mixed numbers, convert to improper fractions first.
减法同理，保持分母不变，只对分子做减法。带分数则需要先化成假分数再操作，千万不要在带分数形式下直接通分。
4. Fractions: Multiplication and Division | 分数的乘除法
Multiplication of fractions is straightforward – multiply the numerators and denominators. Division, however, causes mistakes when students forget to flip the second fraction (the divisor). Write the division as multiplication by the reciprocal, then simplify before multiplying.
分数乘法好办，分子乘分子、分母乘分母即可。但很多人栽在除法上：一直用原分数去算，忘记将除数的分子分母颠倒。正确做法是把除法转化为乘除数的倒数，能约分的先约分再乘。
(3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8
Never try to divide fractions by dividing numerators and denominators directly. A quick check: after flipping, cancel any common factors to keep numbers small.
千万不要直接分子除分子、分母除分母。每次做分数除法时，大声告诉自己“颠倒相乘”，然后在运算前先约分，这样既快又不易出错。
5. Decimal Place Value and Rounding | 小数数位与四舍五入
Confusing 0.5 with 0.50 may seem harmless, but trailing zeros indicate precision. When rounding, look one digit beyond the desired place – if it is 5 or more, round up. A typical mistake is to round 2.345 to one decimal place as 2.4, ignoring that the hundredths digit is only 4.
小数点后末尾的零不是装饰：0.5 和 0.50 表示的精确度不同。四舍五入时，要看目标数位的后一位，≥5 才进一。常见错误是看到 2.345 想保留一位小数，直接进成 2.4，其实百分位是 4，应该舍去得到 2.3。
2.345 → 1 decimal place: look at the hundredths digit (4), so 2.3 (not 2.4)
When rounding to significant figures, start counting from the first non-zero digit. Rounding 0.004567 to 2 sf gives 0.0046, not 0.00 or 0.0045.
保留有效数字时，从第一个非零数字开始数。例如 0.004567 保留两位有效数字是 0.0046，而不是四舍五入到小数点后两位。多加练习，把“看后一位”变成肌肉记忆。
6. Percentages: Increase and Decrease | 百分比的增减
Increasing a quantity by 10% and then decreasing the new amount by 10% does not return to the original value. The second percentage acts on a larger base, so the net change is a loss – a classic trap in shopping and finance problems.
先涨 10% 再降 10% 并不能回到原价。第二次的 10% 作用在更大的基数上，最终反而亏了一点。这是应用题和利息计算中最误导人的陷阱之一。
£100 + 10% = £110; £110 – 10% = £99. Net change: -1%.
To combine percentages, use decimal multipliers. A 15% decrease is × 0.85; two successive 10% decreases give × 0.9 × 0.9 = × 0.81, not × 0.8.
处理连续百分比变化时，统一换成小数倍数连乘。减少 10% 不要减两次变成 20%，而是乘 0.9×0.9=0.81。避开直觉误导，养成用乘法公式验证的习惯。
7. Ratio and Proportion | 比与比例
Students often confuse ratio with fraction. A ratio of 2 : 3 means the whole is divided into 2+3 = 5 parts, so the share of the first quantity is 2/5 of the total, not 2/3. Misinterpreting this leads to incorrect distribution of money or ingredients.
比和分数的差异是火坑。2 : 3 意味着总体被分成 2+3=5 份，第一部分占整体的 2/5，而不是 2/3。很多人在分钱、配料时直接把比例当分数，结果越分越离谱。
Divide £50 in ratio 3 : 2 → total parts = 5 → shares: £30 and £20.
For direct proportion, remember that doubling one quantity doubles the other. In inverse proportion, doubling one quantity halves the other. Setting up a table with consistent units avoids cross-multiplying in the wrong direction.
正比例中一个量翻倍另一个也翻倍；反比例则是一个翻倍另一个减半。建议用表格对齐单位，避免交叉相乘时选错对应关系。
8. Algebraic Equations: Both Sides | 代数方程：两边操作
A frequent slip is moving a term to the other side without changing its sign, or dividing only part of an expression. Remember: whatever you do to one side, you must do to the whole of the other side.
移项忘记变号，或者只给部分项做除法，是解方程时最常见的两个错误。等式两边必须做相同的整体操作，否则平衡就被破坏了。
3x + 5 = 2x – 3 → 3x – 2x = -3 – 5 → x = -8
If you ‘move’ +5 without changing it to -5, you’ll get x = -2, which is wrong. When dividing, enclose the whole side in brackets if needed: (6x + 3)/3 = 2x + 1, not 6x/3 + 3.
移项时一定要问自己“这一项原来是什么符号，过去就变什么符号”。加法移过去变减法，乘法移过去变除法。两边同除时，注意每一项都要除，需要时可加括号把整条包起来。
9. Geometry: Angle Facts | 几何：角度知识
Misapplying angle rules is extremely common. Angles on a straight line sum to 180°, but many learners still add them up to 360°. The interior angles of a triangle always add to 180°, and in an isosceles triangle, the base angles are equal – not necessarily the vertex angle.
角度规则背得滚瓜烂熟，一做题就混淆：直线上角之和是 180°，不是 360°。三角形内角和 180°，等腰三角形底角相等，顶角未必等底角。这些基本事实稍不留神就会用错。
Triangle ABC: ∠A + ∠B + ∠C = 180°
In parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior angles sum to 180°. Drawing a quick sketch and marking known angles prevents careless assumptions.
平行线中，同位角相等，内错角相等，同旁内角互补（180°）。哪怕题目没给图，也要随手画一个草稿，标上已知角，一步步推导，减少跳步导致的误判。
10. Units of Measurement Conversion | 单位换算
Area and volume conversions are a major blind spot. Since 1 m = 100 cm, many wrongly assume 1 m² = 100 cm². In fact, 1 m² = (100 cm) × (100 cm) = 10,000 cm². The same principle applies to volume: 1 m³ = 1,000,000 cm³.
长度单位换算是 1 m = 100 cm，但面积常错成 1 m² = 100 cm²，实际上应该是 100×100 = 10,000 cm²。体积 1 m³ = 1,000,000 cm³。这块是失分重灾区。
1 m² = 100 cm × 100 cm = 10,000 cm²
1 liter = 1,000 cm³; 1 gallon ≈ 4.546 liters
Always write the conversion factor squared or cubed as required. For compound units like km/h to m/s, divide by 3.6; to reverse, multiply by 3.6.
面积换算要平方，体积换算要立方。复合单位如 km/h 转 m/s 要除以 3.6，反过来则乘 3.6。可以在草稿纸上写出完整的换算因子再代入，避免漏掉平方立方。
11. Averages: Mean, Median, Mode | 平均数、中位数、众数
Mean is the sum divided by the count. Median requires ordering the data first – forgetting to sort invalidates the median. Mode is the most frequent value; there can be no mode or more than one mode. A common blunder is to calculate the mean when the question asks for the median, or to pick the largest number as the mode.
平均数是总和除以个数，而中位数必须先排序再找中间值。忘记排序是中位数错题的根源。众数是出现次数最多的值，可能没有也可能有多个。最常见的是审题不清：问中位数却算了平均数，或者把最大值当成了众数。
Data: 3, 7, 7, 2, 10 → Sorted: 2, 3, 7, 7, 10 → Median = 7, Mean = 5.8, Mode = 7
For grouped frequency tables, the median is in the interval where cumulative frequency reaches halfway. The mean from a table uses (sum of fx)/(sum of f). Do not confuse the modal class with the class containing the median.
分组数据的中位数要通过累积频率表中位所在区间去找，平均数用 (频数×组中值) 之和除以总频数。众数区间是频数最高的那个区间，不一定是中位所在的组。多读几遍题目，标出问的是哪一个平均值。
12. Graphs: Misreading Scales | 图表：误读刻度
Bar charts, line graphs and scatter plots can deceive if you ignore the scale. A bar that reaches the 4th gridline does not necessarily represent the value 4 if the scale starts at a different number or increments by 0.5. Always check the origin and the step size on each axis.
柱状图、折线图、散点图的坐标刻度最容易骗眼睛。柱子的高度刚好在第四条网格线，不代表数值就是 4，因为坐标起点可能不是零，每格也可能代表 0.5。读图时必须先看坐标轴起点和步长。
Scale starts at 10, increments by 2 → a bar reaching the 3rd line = 10 + 2×2 = 14
When estimating a value between gridlines, use a ruler or count carefully. In scatter graphs with a line of best fit, ensure your answer is read off the line, not from actual data points.
估算刻度之间的值时，用直尺辅助或数小格。散点图中画有最佳拟合线，取值一定要从那根直线上读，而不是从原始散点上读。读错刻度往往让后面所有计算都废掉。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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