From fbe42abb2fb903f723feb4e6c652f411717c86d7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E8=B5=B5=E9=91=AB?= <7176466@qq.com> Date: Fri, 19 Aug 2022 12:38:20 +0800 Subject: [PATCH] =?UTF-8?q?=E6=96=B0=E5=A2=9E?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 分数.md | 63 +++++++++++++++++++++++++++++++++ 图片/分数.png | Bin 0 -> 47063 bytes 知识点/MathJax数学公式.md | 72 +++++++++++++++++++------------------- 3 files changed, 99 insertions(+), 36 deletions(-) create mode 100644 分数.md create mode 100644 图片/分数.png diff --git a/分数.md b/分数.md new file mode 100644 index 0000000..bd7d8c9 --- /dev/null +++ b/分数.md @@ -0,0 +1,63 @@ +# 分数 + +分数(英语:Fraction)是用分式(分数式)表达成 $\dfrac{a}{b}$ 的数($a,b\in Z,b\neq 0$)。在上式之中, $b$ 称为分母(Denominator)而 $a$ 称为分子(Numerator),可视为某件事物平均分成 $b$ 份中占 $a$ 份,读作“ $b$ 分之 $a$ ”。中间的线称为分数线。有时人们会用 $a/b$ 来表示分数。 + +![](图片/分数.png) + +## 分数大小的比较 + + 分母相同,分子大的分数大; + 分子相同,分母小的分数大。 + +## 分数运算 + +### 约分、扩分及通分 + +一个分数**约分**后或**扩分**后,其分数与原来之分数的值相等,称为等值分数。 + +#### 约分 + +“约分”是将一个分数的分子和分母同除以一个比1大的整数(它们的公约数)。 约分后的分数和原来分数的值相等。 + +$\dfrac{3}{6}=\dfrac{1}{2}$ (前面的分数的分子和分母皆除以三) + +#### 扩分 + +“扩分”是将一个分数的分子和分母同乘以比1大的数。扩分后的分数和原来分数的值相等。 + +$\dfrac{1}{2}=\dfrac{2}{4}$ (前面的分数的分子和分母皆乘以二) + +#### 通分 + +“通分”是利用约分或扩分,将两个分母不同的分数,分别化为同分母的分数。 + +例如: + +$\dfrac{2}{5}=\dfrac{2\times7}{5\times7}=\dfrac{14}{35}$ + +$\dfrac{3}{7}=\dfrac{3\times5}{7\times5}=\dfrac{15}{35}$ + +所以 $\dfrac{2}{5} \lt \dfrac{3}{7}$ + +### 加减法 + +分数做加减法时,计算前先通分,得数要做约分以简化结果。例如: + +例如: + +$ \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{1 + 1}{4} = \dfrac{2}{4} = \dfrac{1}{2} $ + +$ \dfrac{1}{5} + \dfrac{1}{3} = \dfrac{3}{15} + \dfrac{5}{15} = \dfrac{3 + 5}{15} = \dfrac{8}{15} $ + +$ \dfrac{3}{7} - \dfrac{2}{5} = \dfrac{15}{35} - \dfrac{14}{35} = \dfrac{15-14}{35} = \dfrac{1}{35}$ + +### 乘除法 + +- 除以一个分数相当于乘以该分数的“**倒数**”。 +- 分数做乘法时,先分子和分母分别相乘,后通过约分将结果简化。 + +注:分数的倒数是指分子分母调换后的分数,$\dfrac{a}{b} \xrightarrow{倒数} \dfrac{b}{a}$ + +例如: + +$ \dfrac{1}{5} \div \dfrac{7}{10} = \dfrac{1}{5} \times 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