Fractions, Decimals and Percentages | 分数、小数和百分数

📚 Fractions, Decimals and Percentages | 分数、小数和百分数

Fractions, decimals and percentages are three different ways of writing the same number. In KS3 Cambridge Mathematics, you need to convert between them, compare them and use them in real-life problems such as discounts, interest and data interpretation.

分数、小数和百分数是同一个数的三种不同写法。在 KS3 剑桥数学中，你需要掌握它们之间的相互转换、比较大小，并能在折扣、利息和数据解释等实际问题中运用。

1. Equivalent Fractions | 等值分数

Equivalent fractions have the same value even though they have different numerators and denominators. You can create an equivalent fraction by multiplying or dividing both parts by the same whole number, other than zero.

等值分数虽然分子和分母不同，但表示的数值相同。你可以通过将分子和分母同时乘或除以同一个非零整数来得到等值分数。

2/3 = (2 × 4)/(3 × 4) = 8/12

Dividing is just as important when you simplify a fraction. For example, 6/8 = 3/4 because both 6 and 8 are divided by 2.

在化简分数时，除以同一个数也同样重要。例如 6/8 = 3/4，因为 6 和 8 都除以了 2。

Always check that you multiply or divide both the numerator and denominator by the same number, otherwise the value of the fraction will change.

一定要检查分子和分母是否同时乘或除以了同一个数，否则分数的值会改变。

2. Simplifying Fractions | 分数化简

To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). The fraction is in simplest form when the only common factor of the numerator and denominator is 1.

化简分数时，将分子和分母同时除以它们的最大公因数 (HCF)。当分子和分母的唯一公因数是 1 时，分数就是最简形式。

18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4

You can simplify in several steps if you do not spot the HCF immediately. For instance, 18/24 = 9/12 = 3/4.

如果一时没有找到最大公因数，也可以分几步化简。例如 18/24 = 9/12 = 3/4。

Remember that simplifying does not change the value of the fraction; it only makes the numbers smaller and easier to use.

请记住，化简不会改变分数的值，它只是让数字更小、更容易使用。

3. Converting Fractions to Decimals | 分数转小数

To change a fraction to a decimal, divide the numerator by the denominator. Some fractions give terminating decimals, while others give recurring decimals.

将分数化成小数，用分子除以分母。有些分数会得到有限小数，有些则会得到循环小数。

3/8 = 3 ÷ 8 = 0.375

If the denominator is a power of 10, such as 10, 100 or 1000, you can write the decimal directly from the place value.

如果分母是 10、100 或 1000 这样的 10 的幂，你可以根据数位直接写出小数。

7/100 = 0.07 and 13/1000 = 0.013

For fractions whose denominator is not a power of 10, use short division or a calculator when allowed.

对于分母不是 10 的幂的分数，可以使用短除法，或者在允许的情况下使用计算器。

4. Converting Decimals to Fractions | 小数转分数

To change a terminating decimal to a fraction, write the decimal as a fraction with denominator 10, 100, 1000, and so on. Then simplify if possible.

将有限小数化成分数时，先按小数位数写成分母为 10、100、1000 等的分数，然后进行化简。

0.45 = 45/100 = 9/20

For recurring decimals, the method is more advanced at KS3, but you should recognise common ones such as 0.333… = 1/3 and 0.666… = 2/3.

对于循环小数，KS3 阶段的方法更复杂，但你应该认识常见的循环小数，如 0.333… = 1/3 和 0.666… = 2/3。

Always count the number of decimal places to decide what denominator to use. One decimal place means 10, two means 100, three means 1000.

一定要根据小数位数来决定分母：一位小数用 10，两位用 100，三位用 1000。

5. Converting Fractions and Decimals to Percentages | 分数和小数转百分数

A percentage is a fraction out of 100. To convert a fraction to a percentage, find an equivalent fraction with denominator 100, or multiply the fraction by 100%.

百分数表示以 100 为分母的分数。将分数化成百分数，可以找到分母为 100 的等值分数，也可以将分数乘以 100%。

3/5 = 3 ÷ 5 × 100% = 60%

To convert a decimal to a percentage, multiply by 100% and add the percent symbol.

将小数化成百分数，乘以 100% 并加上百分号。

0.375 = 0.375 × 100% = 37.5%

Multiplying by 100% is the same as moving the decimal point two places to the right.

乘以 100% 相当于把小数点向右移动两位。

6. Converting Percentages to Fractions and Decimals | 百分数转分数和小数

To convert a percentage to a fraction, write it over 100 and simplify. For example, 35% = 35/100 = 7/20.

将百分数化成分数，先写成分母为 100 的分数，再化简。例如 35% = 35/100 = 7/20。

To convert a percentage to a decimal, divide by 100. This is the same as moving the decimal point two places to the left.

将百分数化成小数，除以 100。这相当于把小数点向左移动两位。

6.5% = 0.065

Be careful with percentages smaller than 1%, such as 0.5% = 0.005, because the decimal position is easy to confuse.

要特别小心小于 1% 的百分数，例如 0.5% = 0.005，因为小数点的位置很容易弄错。

7. Ordering Fractions, Decimals and Percentages | 排序

When ordering mixed forms, convert all numbers to the same form first. Decimals are usually the easiest for comparison.

在比较混合形式时，先统一成同一种形式，通常化成小数最便于比较。

3/5 = 0.6, 62% = 0.62, 0.58

Then compare the decimals place by place. In this example, 0.58 < 0.6 < 0.62.

然后逐位比较小数。在这个例子中，0.58 < 0.6 < 0.62。

In ascending order, the numbers are written as 0.58, 3/5, 62%. Descending order would be 62%, 3/5, 0.58.

按升序排列为 0.58、3/5、62%。按降序排列则为 62%、3/5、0.58。

Write your final answer in the original forms unless the question tells you otherwise.

除非题目另有要求，最终答案要用原来的形式表示。

8. Percentage of an Amount | 求一个数的百分数

To find a percentage of an amount, write the percentage as a fraction or decimal, then multiply by the amount.

求一个数的百分数，先将百分数写成分数或小数，再与这个数相乘。

15% of 80 = 0.15 × 80 = 12

For harder percentages, break the amount into easier parts, such as 10% and 5%.

对于较难的百分数，可拆成更简单的部分，如 10% 和 5%。

22% of 60 = (20% + 2%) of 60 = 12 + 1.2 = 13.2

This method is especially useful in non-calculator questions because 10% and 5% are easy to find mentally.

这种方法在非计算器题目中特别有用，因为 10% 和 5% 可以很容易地心算。

9. Percentage Increase and Decrease | 百分数增减

Use a multiplier to work out percentage change. For an increase, add the percentage to 100% and change to a decimal. For a decrease, subtract from 100%.

用乘数来计算百分数变化。增加时用

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

Fractions, Decimals and Percentages | 分数、小数和百分数