📚 Math G5 – Practice Workbook | 数学 G5 练习册
This Grade 5 practice workbook consolidates core skills across number, fractions, decimals, measurement, geometry, and data. Each section combines a short explanation with worked examples and targeted practice points. Regular use of this workbook helps learners build fluency and confidence before assessments.
本五年级练习册旨在巩固数、分数、小数、测量、几何与数据等核心技能。每个小节都包含简短讲解、示例和针对性练习要点。坚持使用本练习册可以帮助学习者在测评前提升熟练度与自信心。
1. Place Value and Number Sense | 位值与数感
In Grade 5, place value extends to millions and to thousandths. Learners should read, write, order, and round multi-digit whole numbers as well as decimals to three decimal places.
在五年级，位值扩展到百万位和千分位。学习者应能读写、排序和取整多位数整数以及三位小数。
A strong place-value foundation supports mental calculation. For example, in 3,482 the digit 4 has a value of 400, while in 0.04 it has a value of four hundredths.
扎实的位值基础有助于心算。例如，在 3,482 中，数字 4 的值是 400；而在 0.04 中，它的值是四个百分之一。
3,482 = 3 × 1000 + 4 × 100 + 8 × 10 + 2 × 1
Practice point: write 6,205,030 in expanded form, and round 47.586 to the nearest tenth. Recognising each digit's position prevents errors when comparing or estimating.
练习要点：将 6,205,030 写成展开式，并将 47.586 取整到十分位。识别每个数字的位置可以避免比较或估算时出错。
2. Whole Number Operations | 整数四则运算
By Grade 5, learners use standard algorithms for addition, subtraction, multiplication, and division with larger numbers. They should check answers using inverse operations and estimation.
到五年级，学习者能使用标准竖式进行较大数的加、减、乘、除。他们应能用逆运算和估算检查答案。
eaking one factor into expanded form is a useful strategy: 23 × 14 = (23 × 10) + (23 × 4).
对于乘法，将一个因数拆成展开式是常用策略：23 × 14 = (23 × 10) + (23 × 4)。
23 × 14 = 230 + 92 = 322
s should be expressed as a mixed number or decimal when appropriate: 47 ÷ 5 = 9 r 2 = 9.4.
带余数的除法在适当时应表示为带分数或小数：47 ÷ 5 = 9 r 2 = 9.4。
| Addition: sum, total, altogether | 加法：和、总共、一共 |
| Subtraction: difference, how many left | 减法：差、还剩多少 |
| Multiplication: product, times, groups of | 乘法：积、乘以、几组 |
| Division: quotient, share equally, per | 除法：商、平均分、每 |
3. Factors, Multiples, and Primes | 因数、倍数与质数
Grade 5 introduces factor pairs, common factors, common multiples, and prime numbers. A prime number has exactly two distinct factors: 1 and itself.
五年级引入因数对、公因数、公倍数和质数。质数恰好有两个不同的因数：1 和它本身。
The prime numbers below 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Note that 1 is not prime, and 2 is the only even prime.
20 以下的质数有 2、3、5、7、11、13、17 和 19。注意 1 不是质数，2 是唯一的偶质数。
To find the greatest common factor (GCF) of 24 and 36, list the factors: 24 has 1, 2, 3, 4, 6, 8, 12, 24; 36 has 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCF is 12.
求 24 和 36 的最大公因数，可先列出因数：24 有 1、2、3、4、6、8、12、24；36 有 1、2、3、4、6、9、12、18、36。最大公因数是 12。
GCF(24, 36) = 12, LCM(4, 6) = 12
Multiples are made by repeated addition: the first five multiples of 7 are 7, 14, 21, 28, 35.
倍数通过重复相加得到：7 的前五个倍数是 7、14、21、28、35。
4. Fractions: Comparing and Equivalent Forms | 分数：比较与等值形式
the numerator and denominator by the same non-zero number. For example, 2/3 = 4/6 = 8/12.
等值分数通过将分子和分母同时乘以或除以同一个非零数得到。例如，2/3 = 4/6 = 8/12。
a/b = (a × n)/(b × n), n ≠ 0
a common denominator. Compare 3/5 and 2/3: 3/5 = 9/15 and 2/3 = 10/15, so 2/3 is greater.
比较异分母分数时，先将它们改写为同分母。比较 3/5 和 2/3：3/5 = 9/15，2/3 = 10/15，所以 2/3 更大。
verted to mixed numbers: 17/5 = 3 2/5 because 5 fits into 17 three times with remainder 2.
假分数可以化为带分数：17/5 = 3 2/5，因为 17 除以 5 得 3 余 2。
g and subtracting fractions requires a common denominator: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
分数加减需要公分母：1/4 + 1/6 = 3/12 + 2/12 = 5/12。
5. Decimal Operations | 小数运算
and by powers of ten. Align decimal points when adding or subtracting: 3.45 + 2.7 = 6.15.
五年级的小数包括加、减、乘以及除以整数和除以 10 的幂。加减时要对齐小数点：3.45 + 2.7 = 6.15。
ve the decimal point one, two, or three places to the right. For example, 0.37 × 100 = 37.
小数乘以 10、100 或 1000 时，将小数点向右移动一位、两位或三位。例如，0.37 × 100 = 37。
0.37 × 100 = 37, 4.9 × 10 = 49
mber can produce a terminating or repeating decimal: 5 ÷ 8 = 0.625, while 2 ÷ 3 = 0.666...
除以整数可得到有限小数或循环小数：5 ÷ 8 = 0.625，而 2 ÷ 3 = 0.666...
| 1/2 = 0.5 | 1/4 = 0.25 | 3/4 = 0.75 |
| 1/5 = 0.2 | 1/8 = 0.125 | 1/10 = 0.1 |
6. Percentages and Conversions | 百分数与换算
Percent means 'out of 100.' In Grade 5, learners relate percentages to fractions and decimals: 25% = 25/100 = 1/4 = 0.25.
百分数表示 '每一百份中的多少'。在五年级，学习者将百分数与分数和小数关联：25% = 25/100 = 1/4 = 0.25。
Percent = (part ÷ whole) × 100%
ercentage of a quantity, convert the percentage to a decimal and multiply. For example, 30% of 80 = 0.3 × 80 = 24.
求一个量的百分之几，可将百分数化为小数再相乘。例如，80 的 30% = 0.3 × 80 = 24。
Percentage increase and decrease can be introduced through shopping contexts: a £40 item with a 15% discount saves £6, so the sale price is £34.
可以通过购物情境引入百分比增减：一件 40 英镑的商品打 15% 折扣省下 6 英镑，因此售价为 34 英镑。
Common conversions to memorise: 50% = 1/2, 10% = 1/10, 20% = 1/5, 75% = 3/4.
需要记住的常见换算：50% = 1/2、10% = 1/10、20% = 1/5、75% = 3/4。
7. Measurement and Unit Conversion | 测量与单位换算
ntral in Grade 5: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 L = 1000 mL.
公制单位换算是五年级的重点：1 千米 = 1000 米，1 米 = 100 厘米，1 厘米 = 10 毫米，1 千克 = 1000 克，1 升 = 1000 毫升。
, multiply; to convert smaller to larger, divide. For example, 2.5 m = 2.5 × 100 = 250 cm.
从较大单位换算到较小单位用乘法；从较小单位换算到较大单位用除法。例如，2.5 米 = 2.5 × 100 = 250 厘米。
r: 1 hour = 60 minutes, 1 minute = 60 seconds. Therefore 150 minutes = 2 hours 30 minutes.
时间换算也出现：1 小时 = 60 分钟，1 分钟 = 60 秒。因此 150 分钟 = 2 小时 30 分钟。
| Length: 1 cm = 10 mm | 长度：1 厘米 = 10 毫米 |
| Mass: 1 kg = 1000 g | 质量：1 千克 = 1000 克 |
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