Mathematics Grade 5 Test Answers | 数学五年级测试答案详解

📚 Mathematics Grade 5 Test Answers | 数学五年级测试答案详解

Welcome to this Grade 5 mathematics test answer guide. In the following sections, you will find worked solutions and clear explanations for the most common question types in a Year 5 or Grade 5 maths assessment, covering number, fractions, decimals, geometry, measurement, and data handling. Use this guide to check your answers, correct mistakes, and strengthen your problem-solving skills.

欢迎使用本五年级数学测试答案指南。以下各节将提供五年级数学测评中最常见题型的详细解答与清晰解释，涵盖整数、分数、小数、几何、测量和数据处理。请使用本指南核对答案、纠正错误并强化解题能力。

1. Place Value and Number Sense | 位值与数感

In Grade 5 tests, place-value questions often ask you to identify the value of a digit in a large number or to write numbers in expanded form. For example, in 47,306, the digit 4 has a value of 40,000 because it is in the ten-thousands place.

在五年级测试中，位值题常要求识别大数中某一位数字的值，或写出数的展开式。例如在 47,306 中，数字 4 的值为 40,000，因为它位于万位。

Another common task is rounding. To round 68,492 to the nearest thousand, look at the hundreds digit (4). Since 4 is less than 5, round down to 68,000.

另一个常见任务是四舍五入。将 68,492 四舍五入到千位时，看百位数字 4。因为 4 小于 5，所以舍去，得到 68,000。

When comparing numbers, write them with the same number of digits by adding leading zeros if needed. For example, 34,205 > 9,999 because 34,205 has five digits while 9,999 has only four.

比较大小时，如果需要，可以用前导零将数字写成相同位数。例如 34,205 > 9,999，因为 34,205 是五位数，而 9,999 只有四位。

A common mistake is confusing the place values of adjacent digits. Remember that each place to the left is ten times greater, so the 4 in 47,306 is not 4 but 40,000.

一个常见错误是混淆相邻数位的位值。请记住，每向左移动一位，数值就扩大到十倍，因此 47,306 中的 4 不是 4，而是 40,000。

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2. Addition and Subtraction of Whole Numbers | 整数加减法

For addition, align digits by place value and carry when a column total is 10 or more. Calculate 5,286 + 3,947. Start with the ones: 6 + 7 = 13, write 3 and carry 1. Continue to get 9,233.

做加法时，按位值对齐数字，当某一列总和为 10 或以上时进位。计算 5,286 + 3,947：从个位开始，6 + 7 = 13，写 3 进 1。继续计算得到 9,233。

For subtraction, align digits and borrow when the top digit is smaller. Find 7,305 − 2,468. In the ones column, 5 − 8 requires borrowing from the tens. Since the tens digit is 0, borrow from the hundreds. The answer is 4,837.

做减法时，对齐数字，当上一位数字较小时借位。计算 7,305 − 2,468：个位上 5 − 8 需要从十位借位。由于十位是 0，需从百位借位。答案是 4,837。

You can check subtraction by adding the answer to the number you subtracted. 4,837 + 2,468 = 7,305, so the result is correct.

你可以通过将答案与减数相加来检验减法。4,837 + 2,468 = 7,305，所以结果正确。

Always write one digit per column and keep columns straight. Misaligned columns are a frequent source of careless errors in tests.

永远每列写一个数字，并保持列对齐。列未对齐是考试中粗心错误的常见来源。

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3. Multiplication and Division | 乘法与除法

Multiply multi-digit numbers using the standard algorithm or the area model. Example: 34 × 27. First multiply 34 × 7 = 238, then 34 × 20 = 680, and add: 238 + 680 = 918.

使用标准算法或面积模型进行多位数乘法。例如 34 × 27：先计算 34 × 7 = 238，再计算 34 × 20 = 680，然后相加：238 + 680 = 918。

In division, interpret remainders carefully. For 437 ÷ 5, the quotient is 87 with remainder 2, because 5 × 87 = 435 and 437 − 435 = 2. You can also write this as 87 r 2 or 87 2/5.

在除法中，要仔细理解余数。计算 437 ÷ 5，商为 87 余 2，因为 5 × 87 = 435，而 437 − 435 = 2。也可以写成 87 余 2 或 87 2/5。

When dividing by 10, 100 or 1,000, move the decimal point left by the number of zeros. 8,400 ÷ 100 = 84.

除以 10、100 或 1,000 时，将小数点向左移动相应位数。8,400 ÷ 100 = 84。

Remember that multiplication and division are inverse operations. If 24 × 6 = 144, then 144 ÷ 6 = 24.

请记住，乘法和除法互为逆运算。如果 24 × 6 = 144，那么 144 ÷ 6 = 24。

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4. Factors, Multiples and Primes | 因数、倍数与质数

A factor divides a number exactly with no remainder. The factor pairs of 24 are 1×24, 2×12, 3×8 and 4×6, so the factors are 1, 2, 3, 4, 6, 8, 12, 24.

因数能整除一个数且没有余数。24 的因数对为 1×24、2×12、3×8 和 4×6，所以因数为 1、2、3、4、6、8、12、24。

Multiples are the results of multiplying a number by whole numbers. The first five multiples of 9 are 9, 18, 27, 36, 45.

倍数是一个数乘以整数得到的结果。9 的前五个倍数为 9、18、27、36、45。

Prime numbers have exactly two factors: 1 and themselves. The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19. Note that 2 is the only even prime.

质数只有两个因数：1 和它本身。小于 20 的质数为 2、3、5、7、11、13、17、19。注意 2 是唯一的偶质数。

Do not confuse factors with multiples. Factors divide a number, while multiples are made by multiplying the number by integers. For example, 4 is a factor of 12, but 12 is a multiple of 4.

不要混淆因数与倍数。因数能整除一个数，而倍数是由该数乘以整数得到的。例如，4 是 12 的因数，但 12 是 4 的倍数。

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5. Fractions: Equivalence and Operations | 分数：等值与运算

Equivalent fractions represent the same quantity. Multiply or divide the numerator and denominator by the same non-zero number. For example, 2/3 = 8/12 because 2×4 = 8 and 3×4 = 12.

等值分数表示相同的量。将分子和分母同时乘以或除以同一个非零数即可。例如 2/3 = 8/12，因为 2×4 = 8 且 3×4 = 12。

To add fractions with unlike denominators, find a common denominator. For 1/4 + 1/6, the lowest common denominator is 12. Rewrite as 3/12 + 2/12 = 5/12.

异分母分数相加时，先找公分母。计算 1/4 + 1/6，最小公分母为 12。改写为 3/12 + 2/12 = 5/12。

When multiplying fractions, multiply numerators and denominators directly. 2/5 × 3/4 = (2×3)/(5×4) = 6/20, which simplifies to 3/10.

分数相乘时，分子乘分子，分母乘分母。2/5 × 3/4 = (2×3)/(5×4) = 6/20，化简为 3/10。

To divide by a fraction, multiply by its reciprocal. 3/5 ÷ 2/3 = 3/5 × 3/2 = 9/10.

除以一个分数，等于乘以它的倒数。3/5 ÷ 2/3 = 3/5 × 3/2 = 9/10。

Always write fractions in simplest form unless the question asks otherwise. For example, 4/8 should be simplified to 1/2.

除非题目另有要求，分数应写成最简形式。例如，4/8 应化简为 1/2。

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6. Decimals: Comparing and Calculating | 小数：比较与计算

Compare decimals by aligning decimal points and comparing digits from left to right. 0.75 > 0.7 because in the hundredths place, 5 is greater than 0 (or compare 0.75 and 0.70).

比较小数时，对齐小数点并从左到右逐位比较。0.75 > 0.7，因为在百分位上，5 大于 0（或比较 0.75 和 0.70）。

Add and subtract decimals using column method, keeping decimal points aligned. Example: 2.35 + 4.8 = 7.15 because you write 4.8 as 4.80 and add 2.35 + 4.80.

小数的加减法使用竖式，保持小数点对齐。例如 2.35 + 4.8 = 7.15，因为你可以把 4.8 写作 4.80，然后计算 2.35 + 4.80。

Multiply decimals as whole numbers, then place the decimal point according to the total decimal places in the factors. 0.6 × 0.4 = 0.24 (one decimal

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