The words for numbers · 数字用词
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| factor/ˈfæktə/ | 因数 | yīn shù |
| integer/ˈɪntɪdʒə/ | 整数 | zhěng shù |
| rational number/ˈræʃənl ˈnʌmbə/ | 有理数 | yǒu lǐ shù |
| irrational number/ɪˈræʃənl ˈnʌmbə/ | 无理数 | wú lǐ shù |
| prime number/praɪm ˈnʌmbə/ | 质数 | zhì shù |
| significant figures/sɪɡˈnɪfɪkənt ˈfɪɡəz/ | 有效数字 | yǒu xiào shù zì |
| highest common factor/ˈhaɪɪst ˈkɒmən ˈfæktə/ | 最大公因数 | zuì dà gōng yīn shù |
| lowest common multiple/ˈləʊɪst ˈkɒmən ˈmʌltɪpl/ | 最小公倍数 | zuì xiǎo gōng bèi shù |
Explain a number as well as calculate it
- A factor 因数 divides a number exactly; a multiple is obtained by multiplying it by an integer. Naming the relationship helps another person check a calculation.
- A terminology logbook can combine a definition and example. Follow your centre's brief for submitted work; these original practice tasks do not establish official assessment weights.
解释一个数并计算它
- 因数 因数能整除一个数；倍数是通过乘以整数得到的。命名这种关系有助于他人检查计算。
- 术语记录本可以结合定义和示例。请遵循您所在中心的提交要求；这些原始练习任务不确立正式评估权重。
Distinguish number families
- An integer 整数 includes zero and negative whole numbers. A rational number 有理数 is a ratio of integers with a nonzero denominator; an irrational number 无理数 cannot be written that way.
- A prime number 质数 is a positive integer greater than 1 with exactly two positive factors. A terminating or eventually repeating decimal is rational; an irrational decimal neither terminates nor eventually repeats.
区分数的家族
- 整数 整数包括零和负整数。有理数 有理数是分母非零的整数之比；无理数 无理数无法写成这种方式。
- 质数 质数是大于1的正整数，且恰好有两个正因数。有限小数或最终循环小数是有理数；无理小数既不终止也不最终循环。
Sort each number into its family · 将每个数字归类到其所属家族
Say which family a number belongs to, and why. · 指出一个数属于哪个家族，并说明原因。
Why is 1 not a prime number? · 为什么 1 不是质数？
A prime is a positive integer greater than 1 with exactly two positive factors. The number 1 has only one positive factor. · 素数是大于1的正整数，恰好有两个正因数。数字1只有一个正因数。
Match each term to its definition. · 将每个术语与其定义匹配。
Use precise definitions; a finite displayed approximation does not establish whether the underlying exact number is rational. · 使用精确定义；有限显示的近似值不能证明底层精确数值是有理数。
Work through operations in order
- Calculate brackets and powers first. Multiplication and division share a level and go left to right; addition and subtraction share the next level.
- In $18-3(4-7)$ the bracket is negative 3, so the product is negative 9. Subtracting that negative gives 27, not 9.
按顺序进行运算
- 先计算括号和幂。乘法和除法处于同一层级，从左到右进行；加法和减法处于下一层级。
- 在 $18-3(4-7)$ 中，括号内是负3，所以乘积为负9。减去该负数得到27，而不是9。
Evaluate 5 + 3 × 2² − 4. · 计算 5 + 3 × 2² − 4。
Indices first (2² = 4), then multiplication (3 × 4 = 12), then left to right: 5 + 12 − 4 = 13. · 先算指数 (2² = 4)，再算乘法 (3 × 4 = 12)，最后从左到右：5 + 12 − 4 = 13。
Keep the percentage base visible
- Increase by 15% uses multiplier 1.15; decrease by 15% uses 0.85. Reverse a change by dividing by its multiplier.
- Significant figures 有效数字 state retained precision, not proof of measurement accuracy. $0.004072$ becomes $0.00407$ to three significant figures; keep unrounded values for intermediate steps.
保持百分比基数可见
- 增加15%使用乘数1.15；减少15%使用0.85。通过除以对应乘数来逆转变化。
- 有效数字 有效数字表示保留的精度，而非测量准确性的证明。$0.004072$ 变为 $0.00407$ 以保留三位有效数字；中间步骤应保留未舍入的值。
A price of 240 rises by 15%, then the new price falls by 15%. What is the final price? · 某商品价格 240 上涨 15% 后，新价格又下降 15%。最终价格是多少？
240 × 1.15 = 276, then 276 × 0.85 = 234.60. The two percentages act on different amounts, so you do not return to 240. · 240 × 1.15 = 276，然后 276 × 0.85 = 234.60。两个百分比作用于不同的金额，所以不会回到 240。
Write 0.004072 to three significant figures. · 将 0.004072 保留三位有效数字。
Significant figures start at the first non-zero digit, so 4, 0 and 7 are the three. The leading zeros only fix the size. · 有效数字从第一个非零数字开始，即 4、0 和 7 是三个有效数字。前面的零仅用于定位小数点位置。
A price that rises 20% and then falls 20% returns to its original value. · 一个价格上涨 20% 后又下跌 20%，会恢复到原价。
It falls to 96% of the original: 1.20 × 0.80 = 0.96. The second percentage acts on the larger amount. · 它降至原价的 96%：1.20 × 0.80 = 0.96。第二个百分比作用于较大的金额。
Find the lowest common multiple of 24 and 36. · 求 24 和 36 的最小公倍数。
24 = 2³ × 3 and 36 = 2² × 3². Take the higher power of each prime: 2³ × 3² = 72. · 24 = 2³ × 3 且 36 = 2² × 3²。取每个质数的最高次幂：2³ × 3² = 72。
Factors connect with repeating schedules. For positive integers 24 and 36, $24=2^3\times3$ and $36=2^2\times3^2$. The highest common factor 最大公因数 uses the shared lower powers, giving 12. The lowest common multiple 最小公倍数 uses the highest powers needed, giving 72. Two cycles of 24 and 36 minutes next coincide after 72 minutes.
因数与重复日程相关。 对于正整数24和36，$24=2^3\times3$ 和 $36=2^2\times3^2$。最大公因数 最大公因数使用共享的低次幂，结果为12。最小公倍数 最小公倍数使用所需的高次幂，结果为72。24分钟和36分钟的两次周期将在72分钟后再次重合。
Compare cost per item before comparing offers. Divide total cost by item count, with the same units for each offer. A lower unit price may require a higher total purchase. Sheet 1.1 combines arithmetic, schedules and reverse percentages.
比较单价前先比较优惠方案。 用总成本除以商品数量，确保每个方案的单位一致。较低的单价可能需要更高的总购买量。表1.1结合了算术、日程和反向百分比。
A 20% fall followed by a 20% rise multiplies by $0.8\times1.2=0.96$. The second percentage uses a different base. Name that base before deciding whether two changes cancel.
下降20%后上升20%相当于乘以 $0.8\times1.2=0.96$。第二个百分比使用了不同的基数。在决定两个变化是否抵消之前，请先命名该基数。