📚 Mastering 0.75: Fractions, Decimals and Percentages | 掌握 0.75：分数、小数和百分比
In IGCSE Edexcel Mathematics, one of the core number skills is moving confidently between fractions, decimals and percentages. The number 0.75 appears frequently—as a price, a probability, a test score or a percentage. Mastering the conversion and manipulation of 0.75 not only strengthens your numerical fluency but also equips you to handle a wide range of exam questions, from fraction simplification to percentage change problems. This article will take you through every essential technique, common pitfalls and exam-style applications of 0.75, fully aligned with the Edexcel specification.
在 IGCSE Edexcel 数学中，核心数字技能之一就是在分数、小数和百分比之间自如转换。0.75 这个数字频繁出现——无论是价格、概率、考试分数还是百分比。掌握 0.75 的转换与运算，不仅能提升你的数字流畅度，还能帮你应对从分数化简到百分比增减等各类考题。本文将带你逐一攻克 0.75 的所有必备技巧、常见误区，并结合 Edexcel 考纲进行应用讲解。
1. Understanding the Decimal 0.75 | 理解小数 0.75
The decimal 0.75 is a terminating decimal because it has a finite number of digits after the decimal point. In place value terms, the digit 7 is in the tenths column and the digit 5 is in the hundredths column. This means 0.75 represents 7 tenths and 5 hundredths. A key fact to remember is that every terminating decimal can be expressed as a fraction with a denominator that is a power of 10. In the Edexcel IGCSE, you must be able to interpret the place value of decimals to convert them into fractions quickly and accurately.
小数 0.75 是一个有限小数，因为它的小数点后只有有限的位数。从数位的角度看，7 在十分位，5 在百分位。这意味着 0.75 表示 7 个十分之一和 5 个百分之一。需要记住的关键点是：每个有限小数都可以表示为分母是 10 的幂的分数。在 Edexcel IGCSE 考试中，你必须能够根据小数的数位意义，迅速准确地将它化为分数。
2. Converting 0.75 to a Fraction Directly | 直接将 0.75 转换为分数
To convert 0.75 to a fraction, write it as 75/100 because there are two digits after the decimal point, making the denominator 100. This fraction can then be simplified. In an exam, this method is the fastest for terminating decimals. Always check the denominator: if there had been one decimal place, you would use 10; for three decimal places, use 1000; and so on. The Edexcel IGCSE foundation tier often tests this basic conversion step, but higher tier questions may embed it within more complex calculations.
要将 0.75 转换为分数，可以把它写成 75/100，因为小数点后有两位数字，所以分母是 100。然后就可以对这个分数进行化简。在考试中，对于有限小数来说，这是最快的方法。一定要核对分母：如果只有一位小数，分母用 10；有三位小数，分母用 1000；以此类推。Edexcel IGCSE 基础层经常考查这一基本转换步骤，而高阶层的题目则可能将其嵌套在更复杂的计算中。
3. Simplifying the Fraction: From 75/100 to 3/4 | 分数化简：从 75/100 到 3/4
4. In the Edexcel IGCSE, you are expected to give answers in their simplest form unless stated otherwise. Getting into the habit of cancelling down fractions will prevent loss of accuracy marks.
分数 75/100 可以通过找 75 和 100 的最大公因数 (HCF) 来化简。75 和 100 的最大公因数是 25。把分子和分母同时除以 25：75 ÷ 25 = 3，100 ÷ 25 = 4。化简后的分数是 3/4。在 Edexcel IGCSE 考试中，除非题目另有说明，否则你需要把答案化成最简形式。养成约分习惯可以避免丢失准确性分数。
4. Converting 0.75 to a Percentage | 将 0.75 转换为百分比
To change a decimal to a percentage, multiply by 100. Therefore, 0.75 × 100 = 75%. This is equivalent to finding the fraction 75/100, which literally means '75 out of 100' that moving the decimal point two places to the right converts a decimal to a percentage.
要把小数转换为百分比，只需乘以 100。因此，0.75 × 100 = 75%。这相当于分数 75/100，字面上就是“每一百中占 75”。IGCSE 考试中百分比应用十分广泛，尤其是在饼图、复利和数据处理等课题中。一个常用的技巧是：把小数点向右移动两位，就能将小数直接转换为百分比。
5. 0.75 as a Fraction and Percentage in Equivalent Forms | 0.75 的等值分数与百分比形式
ble to spot that 0.75 = 3/4 allows you to simplify expressions quickly. For example, 0.75x is the same as (3/4)x, which is often easier to manipulate.
理解等值形式可以帮助你识别 0.75 的不同伪装。分数 3/4 与 6/8、9/12、15/20 等无数个分数相等，只需将 3/4 的分子分母同乘一个数即可。在代数和比例推理题中，能一眼看出 0.75 = 3/4，就可以快速化简表达式。比如，0.75x 就等于 (3/4)x，后者处理起来往往更顺手。
6. Representing 0.75 on a Number Line and in Diagrams | 在数轴和图表中表示 0.75
On a number line from 0 to 1, 0.75 lies exactly three-quarters of the way between 0 and 1. You can mark it by dividing the interval into four equal parts. The third mark after 0 is 0.75. Shaded diagrams are common in Edexcel IGCSE: a shape divided into four equal parts with three parts shaded represents 3/4 or 0.75. This links strongly to questions on fractions of shapes and ratio.
在 0 到 1 的数轴上，0.75 正好位于从 0 到 1 路程的四分之三处。可以将区间分为四等份来表示它，0 之后的第三个标记就是 0.75。在 Edexcel IGCSE 中，涂色图形很常见：一个图形被分成四等份，其中三份涂色，就表示 3/4 或 0.75。这与图形分数和比值的题目紧密相关。
7. Operations with 0.75: Addition, Subtraction, Multiplication and Division | 涉及 0.75 的加减乘除运算
0.75 is the same as multiplying by its reciprocal 4/3. So 12 ÷ 0.75 = 12 × (4/3) = 16. In IGCSE problem‑solving, choosing the right form can simplify the arithmetic.
以小数形式进行加减时，要对齐小数点。例如，1.25 + 0.75 = 2.00。使用分数形式 3/4 时，如果其他数字也是分数，就更容易计算。乘法：0.75 × 8 = 6，相当于 (3/4) × 8 = 6。除法：除以 0.75 等于乘它的倒数 4/3。所以 12 ÷ 0.75 = 12 × (4/3) = 16。在 IGCSE 的应用题中，选择合适的表示形式可以简化计算。
8. Finding 75% of an Amount and Percentage Increase/Decrease | 求一个数的 75% 及百分比的增减
To find 75% of a quantity, multiply by 0.75 or by the fraction 3/4. For example, 75% of 200 is 200 × 0.75 = 150. If a quantity increases by 75%, the new value is original × 1.75; if it decreases by 75% estions. Always check whether the question asks for the final amount or just the increase.
要求一个数的 75%，乘以 0.75 或分数 3/4 即可。比如，200 的 75% 是 200 × 0.75 = 150。如果一个量增加了 75%，新值 = 原值 × 1.75；如果减少了 75%，新值 = 原值 × 0.25。这些都是典型的 IGCSE 百分比变化问题。务必看清题目是要求最终值还是仅仅求增加量。
9. Reverse Percentage Calculations Involving 75% | 涉及 75% 的反向百分比计算
Reverse percentages often appear in Edexcel IGCSE higher tier. If a price including a 75% increase is £87.50, we know the new price is 175% al. So original × 1.75 = 87.50, giving original = 87.50 ÷ 1.75 = 50. Similarly, after a 75% sale reduction, an item costs £15; this means the sale price is 25% original = 15 ÷ 0.25 = 60. Using the fraction equivalents can make these steps less error‑prone.
反向百分比在 Edexcel IGCSE 高阶层中很常见。如果某商品包含 75% 涨幅后的价格是 £87.50，那么新价格是原价的 175%。所以原价 × 1.75 = 87.50，得到原价 = 87.50 ÷ 1.75 = 50。类似地，一件商品经 75% 折扣后售价 £15，意味着售价是原价的 25%。原价 × 0.25 = 15，因此原价 = 15 ÷ 0.25 = 60。使用分数等价物（如 3/4 或 1/4）可减少计算错误。
10. Application in Mixed Numbers and Improper Fractions | 在带分数和假分数中的应用
gebra, you may need to work with coefficients such as 0.75x². Writing them as fractions often makes it easier to combine with other fractional coefficients. Practice converting between the two forms quickly.
有时 0.75 是带分数的一部分，比如 2.75。把它化为假分数：2.75 = 2 + 0.75 = 2 + 3/4 = (8/4 + 3/4) = 11/4。在 Edexcel IGCSE 代数中，你可能遇到像 0.75x² 这样的系数。将它们写成分数形式，通常更容易与其他分数系数合并。请多练习两种形式的快速转换。
11. Common Misconceptions and Exam Tips | 常见误区与考试技巧
One common error is to confuse 0.75 with 0.75% – the latter is 0.0075 as a decimal. Another mistake is forgetting to simplify fractions: writing 75/100 instead of 3/4 may not lose marks if unsimplified answers are allowed, but it can cause trouble in later parts of a question. Also, when multiplying and dividing by 0.75, students sometimes forget that dividing by 0.75 gives a larger number. In the exam, always double‑check whether your final answer makes sense in the context of the question.
一个常见错误是混淆 0.75 和 0.75%——后者作为小数是 0.0075。另一个错误是忘记化简分数：把结果写成 75/100 而不是 3/4，虽然有时不扣分，但可能影响后续问题的计算。此外，在乘除以 0.75 时，有些同学会忘记除以 0.75 会得到一个更大的数。考试时，一定要再次检查最终答案是否符合题目情境。
12. Edexcel IGCSE Exam-Style Question Set | Edexcel IGCSE 考试风格例题
Here are some questions to consolidate your understanding. Try them before checking the solutions.
- Express 0.75 as a fraction in its simplest form. (Answer: 3/4)
- A bicycle originally costs £200. In a sale, the price is reduced by 75%. What is the sale price? (Answer: 200 × 0.25 = £50)
- After a 75% increase, the price of a concert ticket is £56. What was the original price? (Answer: 56 ÷ 1.75 = £32)
- Find (3/4) of 280. (Answer: 210)
- Write 0.75 as a percentage, and hence find 75% of 64. (Answer: 75% of 64 = 48)
Practising these classic 0.75 applications directly mirrors Edexcel IGCSE questions and builds confidence.
以下问题有助于巩固你的理解，先自己尝试，再看答案。
- 将 0.75 表示为最简分数。（答案：3/4）
- 一辆自行车原价 £200，打折期降价 75%。打折后的价格是多少？（答案：200 × 0.25 = £50）
- 一张音乐会门票涨价 75% 后为 £56，原价是多少？（答案：56 ÷ 1.75 = £32）
- 计算 280 的 3/4。（答案：210）
- 把 0.75 写成百分数，并求出 64 的 75%。（答案：64 的 75% = 48）
练习这些经典的 0.75 应用题，能直接对标 Edexcel IGCSE 试题，助你树立信心。
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