📚 Grade 5 Maths Test: Core Topics and Practice | 五年级数学测试：核心考点与练习
Grade 5 maths tests bring together all the key skills you have learned in primary school. This revision guide covers number operations, fractions, decimals, geometry, measurement, data handling and problem solving. You will find clear English explanations paired with Chinese translations, plus worked examples and tips for test day. Use this article to check your understanding, practise key methods and build confidence before your exam.
五年级数学测试综合考查小学阶段所学的核心技能。本复习指南涵盖整数运算、分数、小数、几何、测量、数据处理和应用题。每部分都提供清晰的英文讲解和对应的中文翻译，并配有例题和考试技巧。利用本文检查自己的理解、练习关键方法，并在考试前建立信心。
1. Number Sense and Place Value | 数感与位值
Place value tells us the value of each digit in a number based on its position. In 47,352, the digit 4 is in the ten-thousands place and represents 40,000, while the digit 3 is in the hundreds place and represents 300. Understanding place value helps with reading, writing, comparing and rounding large numbers.
位值告诉我们一个数中每个数字根据其位置所表示的值。在 47,352 中，数字 4 在万位，表示 40,000，而数字 3 在百位，表示 300。理解位值有助于读、写、比较和四舍五入较大的数。
Every column is ten times the value of the column on its right. The table below breaks down 47,352 digit by digit.
每一列的数值都是它右边一列的十倍。下表把 47,352 逐位拆解。
| Digit 数字 | Place 位 | Value 数值 |
| 4 | ten thousands 万位 | 40,000 |
| 7 | thousands 千位 | 7,000 |
| 3 | hundreds 百位 | 300 |
| 5 | tens 十位 | 50 |
| 2 | ones 个位 | 2 |
Numbers can be written in standard form, expanded form and word form. For example, the expanded form of 47,352 is 40,000 + 7,000 + 300 + 50 + 2, and its word form is "forty-seven thousand, three hundred and fifty-two".
数字可以用标准形式、展开形式和文字形式书写。例如，47,352 的展开形式是 40,000 + 7,000 + 300 + 50 + 2，文字形式是"四万七千三百五十二"。
than), > (greater than) and = (equal to). So 46,708 < 47,352 and 47,352 > 47,299.
比较数字时，从左到右逐位比较，并使用符号 <（小于）、>（大于）和 =（等于）。因此 46,708 < 47,352，47,352 > 47,299。
Rounding depends on the digit to the right of the target column. To round 47,352 to the nearest thousand, look at the hundreds digit (3), which is less than 5, so the answer is 47,000. To round to the nearest hundred, look at the tens digit (5), so round up to 47,400.
四舍五入取决于目标数位右边的那一位。把 47,352 四舍五入到千位时，看百位数字 3，小于 5，所以答案是 47,000。四舍五入到百位时，看十位数字 5，因此进位得到 47,400。
2. Whole Number Operations | 整数四则运算
Addition and subtraction are usually done with the column method, lining up digits with the same place value. Remember to regroup when a column totals more than 9 in addition, or when you need to borrow in subtraction.
加法和减法通常用竖式计算，把相同数位的数字对齐。加法中某一列超过 9 要进位，减法中不够减要退位。
347 × 26: first 347 × 20 = 6,940, then 347 × 6 = 2,082, and finally 6,940 + 2,082 = 9,022.
乘法可以用长乘法，把两位数乘数拆成十位和个位。计算 347 × 26：先算 347 × 20 = 6,940，再算 347 × 6 = 2,082，最后 6,940 + 2,082 = 9,022。
36. When a division is not exact, write the remainder, for example 47 ÷ 5 = 9 remainder 2.
除法分为短除法（除数不超过 12）和长除法。4,536 ÷ 7 = 648，因为 7 × 648 = 4,536。当不能整除时，要写余数，例如 47 ÷ 5 = 9 余 2。
÷ 7 = 648, then 648 × 7 must equal 4,536. This single habit catches most careless errors.
一定要用逆运算检查答案。如果 4,536 ÷ 7 = 648，那么 648 × 7 必须等于 4,536。这个简单习惯能发现大多数粗心错误。
3. Order of Operations and Estimation | 运算顺序与估算
When a calculation contains several operations, follow the order of operations, often remembered as BIDMAS: Brackets, Indices, Division and Multiplication, then Addition and Subtraction.
当一个算式包含多种运算时，要遵循运算顺序，通常记作 BIDMAS：括号、指数、除法和乘法，最后是加法和减法。
Brackets → Indices → Division/Multiplication → Addition/Subtraction
o right when two operations have the same priority: 20 − 3 × 4 + 8 ÷ 2 = 20 − 12 + 4 = 12.
例如 6 + 4 × 5 = 6 + 20 = 26，而不是 50，因为乘法先于加法。如果加上括号，(6 + 4) × 5 = 10 × 5 = 50。同级运算要从左到右计算：20 − 3 × 4 + 8 ÷ 2 = 20 − 12 + 4 = 12。
× 20 = 4,000, so an exact answer of about 4,158 makes sense, while 41,580 clearly does not.
估算是判断答案是否合理的快捷方法。计算前把每个数四舍五入到方便的值。对于 198 × 21，可以想 200 × 20 = 4,000，所以精确答案约 4,158 是合理的，而 41,580 显然不合理。
4. Fractions | 分数
A fraction shows equal parts of a whole. In the fraction 3/4, the denominator 4 tells you how many equal parts the whole is divided into, and the numerator 3 tells you how many parts are taken.
分数表示整体的若干等份。在分数 3/4 中，分母 4 表示整体被分成多少等份，分子 3 表示取了多少份。
lify a fraction, divide the numerator and denominator by their highest common factor. So 12/18 simplifies to 2/3 because both numbers divide by 6.
等值分数大小相同：1/2 = 2/4 = 5/10 = 50/100。化简分数时，用分子和分母的最大公因数去除。因此 12/18 化简为 2/3，因为两个数都能被 6 整除。
lowest common denominator is 12, so 3/4 = 9/12 and 5/6 = 10/12, which means 5/6 is larger.
比较或排列分数时，先把它们化成同分母。比较 3/4 和 5/6：最小公分母是 12，所以 3/4 = 9/12，5/6 = 10/12，因此 5/6 更大。
2 + 3/12 = 11/12, and 3/4 − 1/6 = 9/12 − 2/12 = 7/12. Never add the denominators together.
分数加减法也用同样的方法。2/3 + 1/4 = 8/12 + 3/12 = 11/12，3/4 − 1/6 = 9/12 − 2/12 = 7/12。千万不要把分母相加。
12/8 = 1 1/2. Mixed numbers should be changed into improper fractions first: 2 1/3 = 7/3.
分数乘整数时，只乘分子：3/8 × 4 = 12/8 = 1 1/2。带分数要先化成假分数：2 1/3 = 7/3。
iding by the denominator and multiplying by the numerator. So 3/5 of 45 = 45 ÷ 5 × 3 = 27.
求一个量的几分之几，就是先除以分母再乘分子。所以 45 的 3/5 = 45 ÷ 5 × 3 = 27。
5. Decimals and Percentages | 小数与百分数
Decimals extend place value to the right of the decimal point: tenths, hundredths and thousandths. The number 3.47 means 3 + 0.4 + 0.07, that is, 3 ones, 4 tenths and 7 hundredths.
小数把位值延伸到小数点右边：十分位、百分位和千分位。3.47 表示 3 + 0.4 + 0.07，即 3 个一、4 个十分之一和 7 个百分之一。
0 is greater than 0.65. To round 4.268 to two decimal places, look at the third decimal digit (8) and round up to 4.27.
比较小数时，先补齐小数位数：0.7 = 0.70，所以 0.70 大于 0.65。把 4.268 保留两位小数时，看第三位小数 8，进位得到 4.27。
imal places: 5.2 × 0.4 gives 52 × 4 = 208, and with two decimal places the answer is 2.08.
小数加减法要对齐小数点：2.45 + 3.7 = 6.15。乘法可以先忽略小数点，最后数总的小数位数：5.2 × 0.4 先算 52 × 4 = 208，共两位小数，答案是 2.08。
by the same power of ten to make the divisor a whole number: 4.8 ÷ 0.6 becomes 48 ÷ 6 = 8.
除以小数时，把两个数同时乘以相同的 10 的幂，使除数变成整数：4.8 ÷ 0.6 变为 48 ÷ 6 = 8。
ntages are three ways of writing the same value. Learn the key conversions: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
分数、小数和百分数是同一个值的三种写法。要熟记关键换算：1/2 = 0.5 = 50%，1/4 = 0.25 = 25%，3/4 = 0.75 = 75%，1/5 = 0.2 = 20%，1/10 = 0.1 = 10%。
To find a percentage of an amount, convert the percentage to a decimal and multiply. 15% of 240 = 0.15 × 240 = 36. A quick mental method is to find 10% by dividing by 10, then 5% by halving that, and add: 24 + 12 = 36.
求一个数的百分之几，把百分数化成小数再相乘。240 的 15% = 0.15 × 240 = 36。心算技巧是先除以 10 得 10%，再取一半得 5%，然后相加：24 + 12 = 36。
6. Factors, Multiples, Primes and Square Numbers | 因数、倍数、质数与平方数
Factors are numbers that divide exactly into another number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Multiples are what you get when you multiply a number by 1, 2, 3 and so on: the multiples of 6 are 6, 12, 18, 24, 30 ...
因数是能整除另一个数的数。24 的因数是 1、2、3、4、6、8、12 和 24。倍数是一个数分别乘 1、2、3……得到的结果：6 的倍数是 6、12、18、24、30……
A prime number has exactly two factors, 1 and itself. The prime numbers below 20 are 2, 3, 5, 7, 11, 13, 17 and 19. The number 1 is not prime, and 2 is the only even prime.
质数恰好有两个因数：1 和它本身。20 以内的质数是 2、3、5、7、11、13、17 和 19。数字 1 不是质数，2 是唯一的偶质数。
The highest common factor (HCF) is the largest factor shared by two numbers. For 18 and 24, the common factors are 1, 2, 3 and 6, so the HCF is 6. The lowest common multiple (LCM) is the smallest multiple shared by two numbers; for 6 and 8 it is 24.
最大公因数（HCF）是两个数共有的最大因数。18 和 24 的公因数是 1、2、3、6，所以最大公因数是 6。最小公倍数（LCM）是两个数共有的最小倍数；6 和 8 的最小公倍数是 24。
Square numbers come from multiplying a number by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Cube numbers come from multiplying a number by itself twice: 1, 8, 27, 64, 125.
平方数是一个数乘它自己：1、4、9、16、25、36、
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