The words for numbers
| English | Chinese | Pinyin |
|---|---|---|
| factor | 因数 | yīn shù |
| integer | 整数 | zhěng shù |
| rational number | 有理数 | yǒu lǐ shù |
| irrational number | 无理数 | wú lǐ shù |
| prime number | 质数 | zhì shù |
| significant figures | 有效数字 | yǒu xiào shù zì |
| highest common factor | 最大公因数 | zuì dà gōng yīn shù |
| lowest common multiple | 最小公倍数 | zuì xiǎo gōng bèi shù |
You already know this. Now say it in English
- You can find a factor 因数 of 24. Can you say what a factor is, in one English sentence?
- GAC004 tests both, and the terminology logbook is worth real marks.
- The mathematics of unit 1 is revision. The language is not.
The number families
- An integer 整数 is a whole number, positive or negative, including zero.
- A rational number 有理数 can be written as a fraction of two integers. $0.75 = \frac{3}{4}$ is rational.
- An irrational number 无理数 cannot. $\pi$ and $\sqrt{2}$ are the two examples every paper uses.
- A prime number 质数 has exactly two factors: itself and 1. So 1 is not prime — it has only one factor.
Sort each number into its family
Say which family a number belongs to, and why.
Why is 1 not a prime number?
A prime has exactly two factors, itself and 1. For the number 1 those are the same factor, so it has only one.
Match each term to its definition.
These four definitions are logbook material — write each one in your own words, not copied.
Order of operations
- Brackets, then indices, then multiplication and division, then addition and subtraction.
- Within one level, work left to right.
- $3 + 4 \times 2^2 = 3 + 4 \times 4 = 3 + 16 = 19$, not $(3+4) \times 4$.
Evaluate 5 + 3 × 2² − 4.
Indices first (2² = 4), then multiplication (3 × 4 = 12), then left to right: 5 + 12 − 4 = 13.
Say the rule out loud in English as you work: "indices before multiplication". The logbook is marked on your own wording, and a rule you can say is a rule you can apply under pressure.
A price of 240 rises by 15%, then the new price falls by 15%. What is the final price?
240 × 1.15 = 276, then 276 × 0.85 = 234.60. The two percentages act on different amounts, so you do not return to 240.
Write 0.004072 to three significant figures.
Significant figures start at the first non-zero digit, so 4, 0 and 7 are the three. The leading zeros only fix the size.
A price that rises 20% and then falls 20% returns to its original value.
It falls to 96% of the original: 1.20 × 0.80 = 0.96. The second percentage acts on the larger amount.
Find the lowest common multiple of 24 and 36.
24 = 2³ × 3 and 36 = 2² × 3². Take the higher power of each prime: 2³ × 3² = 72.
Percentage change
- An increase of 15% multiplies by $1.15$. A decrease of 15% multiplies by $0.85$.
- To reverse a change, divide by the multiplier — never subtract the same percentage.
- Significant figures 有效数字 say how precisely a value is known: $0.004\,072$ to 3 s.f. is $0.004\,07$.
A price rises 15%, then falls 15%. It does not return to where it started. $240 \times 1.15 \times 0.85 = 234.60$, because the two percentages act on different amounts. This is the single most common arithmetic error in the module.
Find the HCF and LCM of 24 and 36.
Write each as prime factors: $24 = 2^3 \times 3$ and $36 = 2^2 \times 3^2$.
For the highest common factor 最大公因数, take the lower power of each shared prime: $2^2 \times 3 = 12$.
For the lowest common multiple 最小公倍数, take the higher power of every prime present: $2^3 \times 3^2 = 72$.
Check: $12 \times 72 = 864 = 24 \times 36$ ✓ — the product of the HCF and LCM always equals the product of the two numbers.