KS3 Mathematics: p147_1 Practice Set | KS3数学：练习题集p147_1

📚 KS3 Mathematics: p147_1 Practice Set | KS3数学：练习题集p147_1

Welcome to a focused revision session built around the concepts covered in Practice Set p147_1 from the Cambridge KS3 Mathematics curriculum. This set is designed to strengthen your understanding of fractions, decimals, percentages, and their real-world applications. By working through these core ideas, you will build confidence in number operations and problem-solving skills. Let’s dive in and master the fundamentals step by step.

欢迎来到围绕剑桥KS3数学课程中练习题集 p147_1 所涵盖概念的专项复习。这一套练习旨在巩固你对分数、小数、百分数以及它们在实际情境中运用的理解。通过梳理这些核心概念，你将逐步建立对数字运算和问题解决能力的信心。让我们一步步掌握基础。

1. Understanding Fractions | 理解分数

A fraction represents a part of a whole. It is written as a/b, where a is the numerator and b is the denominator. The denominator tells us how many equal parts the whole is divided into, while the numerator tells us how many of those parts we are considering. For example, 3/4 of a pizza means the pizza is divided into 4 equal slices and you have 3 of them.

分数表示整体的一部分。它写作 a/b，其中 a 是分子，b 是分母。分母告诉我们整体被分成了多少等份，分子则表示我们取了多少份。例如，一个披萨的 3/4 意味着披萨被分成 4 等份，而你拥有其中的 3 份。

2. Equivalent Fractions | 等值分数

Equivalent fractions are different fractions that represent the same value. You can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number. For instance, 1/2 is equivalent to 2/4, 3/6, and 50/100. Recognising equivalent fractions is essential for simplifying and comparing fractions.

等值分数是表示相同值但形式不同的分数。你可以通过将分子和分母同时乘以或除以同一个非零数来找到等值分数。例如，1/2 等价于 2/4、3/6 和 50/100。识别等值分数对于化简分数和比较分数至关重要。

3. Simplifying Fractions | 化简分数

To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF) until no number except 1 can divide both. For example, to simplify 8/12, the GCF of 8 and 12 is 4, so divide both by 4 to get 2/3. A simplified fraction is in its lowest terms and is often the preferred form in final answers.

要化简一个分数，将分子和分母同时除以它们的最大公因数（GCF），直到除了 1 之外没有其他数能同时整除它们。例如，化简 8/12，8 和 12 的最大公因数是 4，因此分子分母同除以 4 得到 2/3。化简后的分数是最简形式，通常是最终答案的首选写法。

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4. Converting Between Fractions and Decimals | 分数与小数的转换

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/5 = 3 ÷ 5 = 0.6. When the division does not terminate, you may get a recurring decimal, such as 1/3 = 0.333…, often written as 0.3 with a dot above the 3. Knowing common conversions like 1/2 = 0.5 and 1/4 = 0.25 saves time in calculations.

要将分数转换为小数，用分子除以分母。例如，3/5 = 3 ÷ 5 = 0.6。当除法不能除尽时，你会得到循环小数，如 1/3 = 0.333…，通常写作在 3 上方带一个点的 0.3。熟记 1/2 = 0.5、1/4 = 0.25 等常见转换可以节省计算时间。

5. Converting Decimals to Percentages and Vice Versa | 小数与百分数的转换

A percentage is a fraction out of 100. To convert a decimal to a percentage, multiply by 100 and add the % sign. For example, 0.75 × 100 = 75%. To change a percentage to a decimal, divide by 100 (or move the decimal point two places to the left). So 8% becomes 0.08. These conversions underpin many KS3 topics, including probability and data interpretation.

百分数是一种分母为 100 的分数。要将小数转换为百分数，乘以 100 并加上百分号。例如，0.75 × 100 = 75%。要将百分数转换为小数，除以 100（或将小数点向左移动两位）。因此 8% 变成 0.08。这些转换是许多 KS3 主题的基础，包括概率和数据解读。

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6. Ordering Fractions, Decimals and Percentages | 分数、小数和百分数的排序

To compare different forms, first convert all numbers to the same representation – usually decimals or common denominators. For example, to order 1/4, 0.3, and 20%, convert to decimals: 1/4 = 0.25, 20% = 0.2. So the order from smallest to largest is 20% (0.2), 1/4 (0.25), then 0.3. Using a number line helps visualise the comparisons.

为了比较不同形式的数，先将所有数转换为同一种表达方式——通常是小数或相同的分母。例如，要排序 1/4、0.3 和 20%，先转换为小数：1/4 = 0.25，20% = 0.2。因此从小到大依次为 20%（0.2）、1/4（0.25），之后是 0.3。使用数轴有助于将比较过程形象化。

7. Adding and Subtracting Fractions | 分数的加减

To add or subtract fractions, they must share the same denominator. If denominators differ, find a common denominator (often the least common multiple). For 1/3 + 1/6, the common denominator is 6: convert 1/3 to 2/6, then add to get 3/6 = 1/2. Always simplify your final answer and, for mixed numbers, convert to improper fractions first if it makes the calculation easier.

分数相加减时，它们必须有相同的分母。如果分母不同，先找到公分母（通常是最小公倍数）。对于 1/3 + 1/6，公分母为 6：将 1/3 转换为 2/6，然后相加得到 3/6 = 1/2。最后一定要化简答案；对于带分数，如果有助于计算，可以先转换为假分数。

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8. Multiplying Fractions | 分数的乘法

Multiply fractions by multiplying the numerators together and the denominators together. For example, 2/3 × 4/5 = (2×4)/(3×5) = 8/15. When multiplying a fraction by a whole number, write the whole number as a fraction over 1: 3 × 2/7 = 3/1 × 2/7 = 6/7. Simplify the product where possible, and look for cross-cancellation before multiplying to make numbers smaller.

分数乘法是将分子相乘作为新分子，分母相乘作为新分母。例如，2/3 × 4/5 = (2×4)/(3×5) = 8/15。当分数与整数相乘时，将整数写成分母为 1 的分数：3 × 2/7 = 3/1 × 2/7 = 6/7。尽量对乘积进行化简，并在相乘前寻找交叉约分的机会以简化数字。

9. Dividing Fractions | 分数的除法

To divide by a fraction, multiply by its reciprocal (swap the numerator and denominator). For instance, 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8, which can be left as an improper fraction or written as 1⅞. Remember that dividing by a fraction is the same as multiplying by its flip – often summarised as ‘Keep, Change, Flip’.

除以一个分数，等于乘以它的倒数（交换分子和分母）。例如，3/4 ÷ 2/5 变为 3/4 × 5/2 = 15/8，可以保留假分数或者写成带分数 1⅞。记住，除以一个分数等同于乘以它的倒数——通常概括为“保留、变号、翻转”。

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10. Percentage of an Amount | 求一个数的百分之几

To find a percentage of an amount, convert the percentage to a fraction or decimal and multiply. For 30% of 200, use 30/100 × 200 = 3/10 × 200 = 60. Alternatively, find 10% first by dividing by 10, and then scale up. For mental percentages, break the percentage into easy chunks, e.g. 15% = 10% + 5%.

要求一个数量的百分之几，先把百分数转换为分数或小数再相乘。求 200 的 30%，用 30/100 × 200 = 3/10 × 200 = 60。也可以先除以 10 找出 10%，再进行缩放。对于心算百分数，可以将百分数拆分成方便计算的部分，例如 15% = 10% + 5%。

11. Problem-Solving: Mixed Applications | 解决问题：混合应用

The p147_1 practice set often includes word problems that blend fractions, decimals, and percentages. Approach these by reading carefully, identifying the operation needed, and converting all numbers to a consistent form. For example, if a shop offers a 25% discount on a £60 item, find the sale price by calculating 25% of 60 (£15) and subtracting from the original price (£45). Always check your answer makes sense in context.

练习题集 p147_1 通常会包含融合分数、小数和百分数的应用题。解答这些题目时，仔细阅读，确定所需的运算，并将所有数字转换为一致的形式。例如，如果一家商店对一件 60 英镑的商品打七五折（即折扣 25%），先计算 60 的 25%（15 英镑），再从原价中减去，得出售价 45 英镑。始终要结合情境检查答案是否合理。

12. Quick Revision Checklist | 快速复习清单

• Can you explain what numerator and denominator mean? 你能解释分子和分母的含义吗？
• Do you know how to find equivalent fractions and simplify to lowest terms? 你知道如何找到等值分数并化简到最简形式吗？
• Can you fluently convert between fractions, decimals, and percentages? 你能熟练地在分数、小数和百分数之间转换吗？
• Are you confident adding, subtracting, multiplying, and dividing fractions? 你有信心进行分数的加、减、乘、除运算吗？
• Can you find a percentage of an amount using different methods? 你能用不同方法求一个数量的百分之几吗？

Use this checklist to identify topics that need extra practice; revisiting them will help you tackle p147_1 exercises with ease.

利用这份清单找出需要额外练习的主题；回顾这些主题将帮助你轻松应对 p147_1 中的练习。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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