📚 Fractions, Decimals and Percentages: Core Skills | 分数、小数和百分比：核心技能
In Cambridge KS3 mathematics, fractions, decimals and percentages are three connected ways of representing parts of a whole. This article reviews the core skills you need to convert, compare and calculate confidently.
在剑桥 KS3 数学中，分数、小数和百分比是表示整体部分数量的三种相互关联的方式。本文回顾你需要自信地转换、比较和计算的核心技能。
1. Understanding the Three Forms | 理解三种表示形式
A fraction such as 3/4 means 3 parts out of 4 equal parts. The top number is the numerator and the bottom number is the denominator.
像 3/4 这样的分数表示 4 等份中的 3 份。上面的数字是分子，下面的数字是分母。
A decimal such as 0.75 uses place value: the digit 7 is in the tenths column and the digit 5 is in the hundredths column.
像 0.75 这样的小数使用位值：数字 7 在十分位，数字 5 在百分位。
A percentage such as 75% means 75 out of 100, so it is another way of writing the fraction 75/100 or the decimal 0.75.
像 75% 这样的百分比表示 100 份中的 75 份，因此它是分数 75/100 或小数 0.75 的另一种写法。
2. Converting Between Fractions and Decimals | 分数与小数之间的转换
To change a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 means 3 ÷ 8, which gives 0.375.
要把分数转换为小数，用分子除以分母。例如，3/8 表示 3 ÷ 8，得到 0.375。
r 100: 7/20 = 35/100 = 0.35. This is often faster when the denominator is a factor of 100.
对于像 7/20 这样的分数，先化成分母为 100 的等值分数：7/20 = 35/100 = 0.35。当分母是 100 的因数时，这样通常更快。
n, write the decimal over its place value and simplify. For example, 0.36 = 36/100 = 9/25.
要把小数转换为分数，将小数写在对应位值的分母上并化简。例如，0.36 = 36/100 = 9/25。
3. Converting Decimals to Percentages and Back | 小数与百分比的转换
To change a decimal to a percentage, multiply by 100 and add the % sign. For example, 0.62 = 0.62 × 100% = 62%.
要把小数转换为百分比，乘以 100 并加上 % 符号。例如，0.62 = 0.62 × 100% = 62%。
To change a percentage to a decimal, divide by 100 and remove the % sign. For example, 8% = 8 ÷ 100 = 0.08.
要把百分比转换为小数，除以 100 并去掉 % 符号。例如，8% = 8 ÷ 100 = 0.08。
Remember that percentages greater than 100% represent amounts more than the original whole, such as 120% = 1.2.
请记住，大于 100% 的百分比表示超过原始整体的数量，例如 120% = 1.2。
4. Comparing and Ordering Quantities | 比较和排序数量
When comparing fractions, decimals and percentages, convert all values to the same form. Decimals are often the most convenient for ordering.
比较分数、小数和百分比时，将所有数值转换为同一种形式。小数通常最便于排序。
Example: Order 0.45, 2/5 and 48% from smallest to largest. Convert 2/5 = 0.4 and 48% = 0.48, so the order is 0.4, 0.45, 0.48.
示例：将 0.45、2/5 和 48% 从小到大排列。将 2/5 转换为 0.4，48% 转换为 0.48，因此顺序为 0.4、0.45、0.48。
On a number line, values to the left are smaller and values to the right are larger. This visual check can prevent sign and order mistakes.
在数轴上，靠左的数值较小，靠右的数值较大。这种直观检查可以防止符号和顺序方面的错误。
5. Adding and Subtracting Fractions | 分数的加法和减法
t have the same denominator. For example, 1/4 + 2/4 = 3/4, because the denominators match.
分数相加或相减时，它们必须有相同的分母。例如，1/4 + 2/4 = 3/4，因为分母相同。
inator (LCD). To calculate 1/3 + 1/6, rewrite 1/3 as 2/6, then add: 2/6 + 1/6 = 3/6 = 1/2.
如果分母不同，求出最小公分母 (LCD)。计算 1/3 + 1/6 时，将 1/3 改写为 2/6，然后相加：2/6 + 1/6 = 3/6 = 1/2。
d the fractional parts separately. Example: 2 1/4 + 1 1/2 = (2 + 1) + (1/4 + 2/4) = 3 3/4.
对于带分数，分别相加整数部分和分数部分。示例：2 1/4 + 1 1/2 = (2 + 1) + (1/4 + 2/4) = 3 3/4。
6. Multiplying and Dividing Fractions | 分数的乘法和除法
ators together and the denominators together. Example: 2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15.
分数相乘时，分子与分子相乘，分母与分母相乘。示例：2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15。
× 5/9, cancel 5 with 10 and 3 with 9 to get (3÷3)/(10÷5) × (5÷5)/(9÷3) = 1/2 × 1/3 = 1/6.
如果可能，在相乘前先约分。在 3/10 × 5/9 中，将 5 与 10 约分，3 与 9 约分，得到 (3÷3)/(10÷5) × (5÷5)/(9÷3) = 1/2 × 1/3 = 1/6。
ivide by a fraction, multiply by its reciprocal. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1
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