📚 Grade 6 Math Test Answers | 六年级数学测试答案解析
This article provides a full set of model answers for a typical Grade 6 mathematics test. Each section includes sample questions, final answers, and clear explanations to help students check their work and understand the key steps. Use the answers to review your test and identify any topics that need more practice.
本文提供一套典型六年级数学测试的完整参考答案。每个部分包含例题、最终答案和清晰的解析，帮助学生检查自己的解答并理解关键步骤。请使用这些答案来复习测试，并找出需要加强练习的知识点。
1. How to Use These Answers | 如何使用这份答案
Each section below follows the same pattern: the question, the final answer, and the reasoning that links them. Try the question first on paper, then compare both your answer and your method with the model solution. A correct final answer with a shaky method usually means the topic still needs practice.
下面每个小节都遵循同样的结构：题目、最终答案，以及连接两者的推理过程。请先在纸上独立完成，再把自己的答案和解题方法与范例对照。如果最终答案对了但方法不稳，通常说明这个知识点还需要继续练习。
Answers are written in their simplest form unless the question asks otherwise. In a real test, marks are usually given for correct working even when the final answer contains a small slip, so always show your steps.
除非题目另有要求，答案一律写成最简形式。在真实测试中，即使最终答案有小失误，只要过程正确通常也能得分，所以一定要写出步骤。
- Check the final answer first, then the method. | 先核对最终答案，再检查解题方法。
- Mark every question you got wrong and label the reason: careless, concept, or speed. | 把做错的题标注出来，并写明原因：粗心、概念不清或速度不够。
- Re-do wrong questions after two days without looking at the answer. | 隔两天后不看答案重做错题。
2. Whole Number Computation: Multiplication | 整数运算：乘法
Question: calculate 248 × 37. Answer: 9,176.
题目：计算 248 × 37。答案：9,176。
,736 = 9,176. A quick estimate confirms the size of the answer, because 250 × 40 = 10,000.
把 37 拆分为 30 和 7。先计算 248 × 30 = 7,440，再计算 248 × 7 = 1,736。把两个积相加：7,440 + 1,736 = 9,176。用估算可以快速检验数量级，因为 250 × 40 = 10,000。
the tens column. Losing that carry is the single most frequent source of lost marks here.
常见错误是在某一位乘积超过 9 时忘记进位。在 248 × 7 中，个位是 8 × 7 = 56，应写 6 并向十位进 5。漏掉这个进位是这一部分最常见的失分原因。
Strategy check: place value, carrying, and lining up digits are the three things to verify before moving on.
检查要点：数位对齐、进位处理、数字书写是否整齐，这是继续下一题前必须确认的三件事。
3. Whole Number Computation: Division | 整数运算：除法
Question: divide 1,872 by 24. Answer: 78.
题目：计算 1,872 ÷ 24。答案：78。
ith no remainder. Always check a division by multiplying the quotient back by the divisor.
因为 24 × 70 = 1,680，24 × 8 = 192，所以 1,680 + 192 = 1,872。因此商为 70 + 8 = 78，没有余数。做完除法后务必用商乘以除数进行验算。
n the question allows: for example, a remainder of 6 with divisor 24 is 6/24 = 1/4 = 0.25.
如果出现余数，要把它写清楚，并在题目允许时写成分数或小数：例如除数是 24、余数是 6，就是 6/24 = 1/4 = 0.25。
Long division errors usually come from misaligned columns when bringing down the next digit. Work on squared paper and keep one digit per square.
长除法出错通常是把下一位落下来时列没有对齐。建议使用方格纸，一个格子写一个数字。
4. Fractions: Addition and Subtraction | 分数：加法与减法
Question: add 3/4 and 2/5. Answer: 23/20, or 1 3/20 as a mixed number.
题目：计算 3/4 + 2/5。答案：23/20，或写成带分数 1 3/20。
5 = 8/20. Add the numerators: 15 + 8 = 23, giving 23/20. As a mixed number this is 1 3/20.
先找公分母。4 和 5 的最小公倍数是 20，所以 3/4 = 15/20，2/5 = 8/20。分子相加：15 + 8 = 23，得到 23/20。写成带分数就是 1 3/20。
0. Never add or subtract denominators; only numerators change once the denominators match.
减法步骤相同，但要特别注意符号：3/4 − 2/5 = 15/20 − 8/20 = 7/20。分母绝不相加减；通分之后，只有分子参与运算。
Always give the answer in its simplest form, and convert an improper fraction to a mixed number if the question asks for one.
答案一定要化成最简形式；如果题目要求带分数，还要把假分数转成带分数。
5. Decimals: Converting to Fractions | 小数：化为分数
Question: convert 0.625 into a fraction in its simplest form. Answer: 5/8.
题目：把 0.625 化为最简分数。答案：5/8。
minator by their highest common factor, 125: 625 ÷ 125 = 5 and 1000 ÷ 125 = 8, giving 5/8.
把 0.625 写作 625/1000，因为末位数字位于千分位。分子分母同时除以它们的最大公因数 125：625 ÷ 125 = 5，1000 ÷ 125 = 8，得到 5/8。
| Decimal | 小数 | Fraction | 分数 | Percent | 百分数 |
| 0.5 | 1/2 | 50% |
| 0.25 | 1/4 | 25% |
| 0.75 | 3/4 | 75% |
| 0.2 | 1/5 | 20% |
| 0.625 | 5/8 | 62.5% |
Recognising common decimal-fraction equivalents saves time in a timed test, and it makes percentage questions much faster to handle.
熟记常见的小数与分数换算可以节省考试时间，也能让百分数题目处理起来快得多。
6. Multiplying and Dividing Fractions | 分数乘除法
merators together and denominators together, then simplify. For example, 2/3 × 4/5 = 8/15.
分数相乘时，分子乘分子、分母乘分母，然后再化简。例如 2/3 × 4/5 = 8/15。
ion, multiply by its reciprocal. For example, 2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2.
除以一个分数，等于乘以它的倒数。例如 2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2。
factor of 2, and the 3 and the 9 share a factor of 3, so the product reduces to 3/2 immediately.
相乘之前先约分：在 2/3 × 9/4 中，2 与 4 有公因数 2，3 与 9 有公因数 3，所以乘积可以直接约成 3/2。
7. Ratio and Proportion | 比与比例
Question: share 48 sweets between two students in the ratio 3 : 5. Answer: 18 and 30.
题目：把 48 颗糖按 3 : 5 分给两名学生。答案：18 颗和 30 颗。
Multiply each share by 6 to get 3 × 6 = 18 and 5 × 6 = 30. Check by adding: 18 + 30 = 48.
先把比的各项相加：3 + 5 = 8。因此一份是 48 ÷ 8 = 6。各份分别乘 6，得到 3 × 6 = 18 和 5 × 6 = 30。用加法验算：18 + 30 = 48。
, then 10 pens cost 6 ÷ 4 × 10 = 15 yuan. Find the value of one unit first, then scale up.
比例题常以放缩的形式出现：如果 4 支笔 6 元，那么 10 支笔是 6 ÷ 4 × 10 = 15 元。先求出一个单位的量，再按倍数放大。
8. Percentages | 百分数
Question: find 15% of 250. Answer: 37.5.
题目：求 250 的 15%。答案：37.5。
Break 15% into 10% and 5%. Since 10% of 250 = 25 and 5% 12.5, the total is 25 + 12.5 = 37.5. Alternatively, multiply directly: 250 × 0.15 = 37.5.
把 15% 拆成 10% 和 5%。250 的 10% = 25，5% 是它的一半 = 12.5，合计 25 + 12.5 = 37.5。也可以直接相乘：250 × 0.15 = 37.5。
ercentage, divide the numerator by the denominator and multiply by 100: 3/8 = 0.375 = 37.5%. To go backwards, divide by 100 and simplify.
把分数化成百分数，就用分子除以分母再乘 100：3/8 = 0.375 = 37.5%。反过来则除以 100 后化简。
nge is a favourite exam item: change = (new value − original value) ÷ original value × 100%.
百分数变化是考试常考题型：变化率 = （新值 − 原值）÷ 原值 × 100%。
9. Expressions and Equations | 代数式与方程
Question: solve 3x + 7 = 25. Answer: x = 6.
题目：解方程 3x + 7 = 25。答案：x = 6。
6. Substitute back to check: 3 × 6 + 7 = 18 + 7 = 25, which matches the original equation.
两边同时减 7：3x = 18。两边同时除以 3：x = 6。代回原式检验：3 × 6 + 7 = 18 + 7 = 25，与原方程一致。
Whatever you do to one side of an equation, you must do to the other. Keep the equals signs lined up vertically so the balance stays visible.
等式一边做什么运算，另一边必须做同样的运算。把等号竖直对齐书写，等量关系就一目了然。
ms only: 5a + 3b − 2a + b = 3a + 4b. The terms a and b cannot be combined with each other.
化简代数式时，只能合并同类项：5a + 3b − 2a + b = 3a + 4b。字母 a 与 b 的项不能相互合并。
10. Area, Perimeter and Volume | 面积、周长与体积
th; triangle area = 1/2 × base × height; circle circumference = 2πr and circle area = πr².
长方形面积 = 长 × 宽；三角形面积 = 1/2 × 底 × 高；圆的周长 = 2πr，圆的面积 = πr²。
base of 5 cm by 4 cm and a height of 10 cm. Find its volume. Answer: 5 × 4 × 10 = 200 cm³.
题目：一个长方体的底面是 5 cm × 4 cm，高为 10 cm，求体积。答案：5 × 4 × 10 = 200 cm³。
Volume = base area × height | 体积 = 底面积 × 高
Units matter: perimeter is measured in cm, area in cm², and volume in cm³. Writing the wrong unit can cost a mark even when the number is right.
单位很重要：周长用 cm，面积用 cm²，体积用 cm³。即使数字算对，单位写错也可能丢分。
11. Statistics and Averages | 统计与平均数
Question: find the mean, median and mode of 4, 7, 9, 12, 18. Answer: mean 10, median 9, no mode.
题目：求 4、7、9、12、18 的平均数、中位数和众数。答案：平均数 10，中位数 9，没有众数。
he median is the middle value once the data is in order, which is 9. Each value appears only once, so there is no mode.
总和是 4 + 7 + 9 + 12 + 18 = 50，共有 5 个数，所以平均数是 50 ÷ 5 = 10。数据排列后位于中间的数是中位数，即 9。每个数只出现一次，因此没有众数。
ian is the mean of the two middle values: for 3, 5, 8, 10 the median is (5 + 8) ÷ 2 = 6.5.
当数据个数为偶数时，中位数是中间两个数的平均数：对于 3、5、8、10，中位数是 (5 + 8) ÷ 2 = 6.5。
ges can be used in reverse too: if five tests average 82, the total is 82 × 5 = 410 marks.
平均数也可以反向使用：如果五次测验的平均分是 82，那么总分就是 82 × 5 = 410 分。
12. Common Mistakes and Checking Strategies | 常见错误与检查策略
Most lost marks in Grade 6 tests come from a small set of repeated errors rather than from topics the student never learned.
六年级测试中的失分，大多来自少数几类重复性错误，而不是学生完全没学过的知识点。
- Fraction arithmetic without a common denominator. | 分数运算时没有先通分。
- Decimal points misplaced in multiplication and division. | 乘除法中小数点位置写错。
- Ratio parts added incorrectly, or one part not multiplied by every share. | 比的份数相加出错，或没有把每一份都乘上倍数。
- Units omitted in area, volume and measurement answers. | 面积、体积和测量类答案漏写单位。
- Equations solved on one side only, breaking the balance. | 解方程时只在一侧运算，破坏了等量关系。
The strongest checking habit is estimating before you calculate and verifying after you finish. For division, multiply back; for equations, substitute the value; for fractions, check that the answer is in simplest form.
最有效的检查习惯是：计算前先估算，计算后再验算。除法用乘法倒推，方程把解代回，分数则确认结果已是最简形式。
Finally, rework every incorrect question from this paper after two days. If you can reach the correct answer without looking at the model solution, the topic has moved from short-term memory into real understanding, and that is what the next test will measure.
最后，请在两天后把这份试卷里所有做错的题重做一遍。如果你能在不看参考答案的情况下算出正确答案，就说明这个知识点已经从短期记忆变成了真正的理解，而这正是下一次测试要考查的东西。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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