📚 Grade 6 Topic Series 700: Fractions, Decimals and Percentages | 6年级主题系列-700：分数、小数与百分数
Fractions, decimals and percentages are three different ways of representing parts of a whole. In IGCSE Mathematics, you must be able to convert flexibly between these forms and use them accurately in calculations, comparisons and real-life problems.
分数、小数和百分数是表示整体部分的三种不同方式。在 IGCSE 数学中，你必须能够灵活地进行这三种形式之间的换算，并在计算、比较和实际问题中准确使用它们。
1. Understanding Fractions | 理解分数
A fraction is written as a/b, where a is the numerator and b is the denominator. The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.
分数写作 a/b，其中 a 是分子，b 是分母。分母表示整体被分成多少等份，分子表示你取了多少份。
For example, 3/4 means 3 out of 4 equal parts. A unit fraction has 1 as the numerator, such as 1/5 or 1/8. Proper fractions have a numerator smaller than the denominator, improper fractions have a numerator larger than or equal to the denominator, and mixed numbers combine a whole number with a proper fraction.
例如，3/4 表示 4 等份中的 3 份。单位分数的分子为 1，例如 1/5 或 1/8。真分数的分子小于分母，假分数的分子大于或等于分母，带分数由整数和真分数组成。
tor by the denominator. For example, 7/3 = 2⅓ because 7 ÷ 3 gives 2 with a remainder of 1.
假分数可以通过用分子除以分母转换为带分数。例如，7/3 = 2⅓，因为 7 ÷ 3 得 2 余 1。
2. Equivalent Fractions | 等值分数
Equivalent fractions represent the same value even though they look different. You can create an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number.
等值分数表示相同的值，尽管它们看起来不同。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得到等值分数。
fy a fraction, divide the numerator and denominator by their highest common factor, also called the greatest common divisor.
例如，1/2 = 2/4 = 4/8。要化简分数，将分子和分母同时除以它们的最大公因数，也叫最大公约数。
equivalent fractions with a common denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
在加减分数时，首先需要找到具有公分母的等值分数。例如，1/2 + 1/3 = 3/6 + 2/6 = 5/6。
3. Fractions to Decimals | 分数化小数
To convert a fraction to a decimal, divide the numerator by the denominator. You can use short division, long division or a calculator.
要将分数转换为小数，用分子除以分母。你可以使用短除法、长除法或计算器。
3/4 = 3 ÷ 4 = 0.75
0.4. Others produce recurring decimals, such as 1/3 = 0.333... and 2/7 = 0.285714285714...
有些分数产生有限小数，例如 1/8 = 0.125 和 2/5 = 0.4。另一些分数产生循环小数，例如 1/3 = 0.333... 和 2/7 = 0.285714285714...
A recurring decimal is often shown with a dot over the repeating digit or digits. For example, 0.333... can be written as 0.3̇, and 0.272727... can be written as 0.2̇7̇.
循环小数通常在循环数字上方加点表示。例如，0.333... 可以写作 0.3̇，0.272727... 可以写作 0.2̇7̇。
4. Decimals to Fractions | 小数化分数
erator over a power of 10, then simplify. For example, 0.7 = 7/10 and 0.25 = 25/100 = 1/4.
要将有限小数转换为分数，将小数写作分子，分母为 10 的幂，然后化简。例如，0.7 = 7/10，0.25 = 25/100 = 1/4。
For a decimal like 0.875, write it as 875/1000 and simplify by dividing both numerator and denominator by 125 to get 7/8.
对于像 0.875 这样的小数，将其写作 875/1000，然后将分子分母同时除以 125 化简，得到 7/8。
For example, let x = 0.666..., then 10x = 6.666..., so 10x - x = 6, giving x = 6/9 = 2/3.
对于循环小数，设一个方程并相减以消去循环部分。例如，设 x = 0.666...，则 10x = 6.666...，所以 10x - x = 6，得到 x = 6/9 = 2/3。
5. Percentages as Fractions and Decimals | 百分数作为分数和小数
A percentage is a fraction with denominator 100. The symbol % means 'out of 100'. Therefore, 45% = 45/100 = 9/20 and 45% = 0.45.
百分数是分母为 100 的分数。符号 % 表示“每一百份中的”。因此，45% = 45/100 = 9/20，并且 45% = 0.45。
ivide by 100. To convert a decimal to a percentage, multiply by 100. For example, 0.06 = 6% and 1.2 = 120%.
要将百分数转换为小数，除以 100。要将小数转换为百分数，乘以 100。例如，0.06 = 6%，1.2 = 120%。
Percentages can be greater than 100%, which represents a value larger than the whole. For example, 150% means 1.5 times the original amount.
百分数可以大于 100%，这表示一个大于整体的值。例如，150% 表示原数量的 1.5 倍。
6. Converting Between All Three Forms | 三种形式之间的换算
You need to be able to move quickly between fractions, decimals and percentages. The key conversions are listed below.
你需要能够在分数、小数和百分数之间快速转换。关键换算如下所示。
| Fraction 分数 | Decimal 小数 | Percentage 百分数 |
| 1/2 | 0.5 | 50% |
| 1/4 |
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