# 初中數學/算則練習/分數四則

### 計算要領

• 加減
1. 帶分數整數部分可以直接加減
2. 分數部分先通分使分母相同
3. 通分後，分母不變，分子相加減
• 乘除
1. 帶分數要先化成假分數
2. 乘法時分子乘分字，分母乘分母
3. 要先有「倒數」的觀念才有辦法計算分數除法
4. 除以一個分數，等於乘以這個分數的倒數
• 約分
1. 計算最後的結果，分子和分母可以同除以一個整數，使分子分母數字變小但比例不變

### 例題一

${\displaystyle 36-11-11{\frac {11}{36}}}$

${\displaystyle 36-11-11=14}$

${\displaystyle =14-{\frac {11}{36}}}$

${\displaystyle =13{\frac {36-11}{36}}=13{\frac {25}{36}}}$

### 例題二

${\displaystyle 37{\frac {5}{31}}-5{\frac {11}{31}}}$

${\displaystyle 36{\frac {36}{31}}-5{\frac {11}{31}}}$

${\displaystyle (36-5)+{\frac {36-11}{31}}}$

${\displaystyle =31{\frac {25}{31}}}$

### 例題三

${\displaystyle {\frac {1}{3}}+{\frac {1}{4}}}$

${\displaystyle ={\frac {1{\color {red}\times 4}}{3{\color {red}\times 4}}}+{\frac {1{\color {red}\times 3}}{4{\color {red}\times 3}}}}$

${\displaystyle ={\frac {4}{12}}+{\frac {3}{12}}}$

${\displaystyle ={\frac {4+3}{12}}}$

${\displaystyle ={\frac {7}{12}}}$

### 例題四

${\displaystyle {\frac {18}{11}}-{\frac {1}{2}}}$

${\displaystyle ={\frac {18{\color {red}\times 2}}{11{\color {red}\times 2}}}-{\frac {1{\color {red}\times 11}}{2{\color {red}\times 11}}}}$

${\displaystyle ={\frac {36}{22}}-{\frac {11}{22}}}$

${\displaystyle ={\frac {36-11}{22}}}$

${\displaystyle ={\frac {25}{22}}=1{\frac {3}{22}}}$

${\displaystyle {\frac {18}{11}}-{\frac {1}{2}}}$

${\displaystyle ={\frac {1}{2}}({\frac {36}{11}}-1)}$

${\displaystyle ={\frac {1}{2}}({\frac {36-{\color {orange}11}}{11}})}$

${\displaystyle ={\frac {1}{2}}\times {\frac {25}{11}}={\frac {25}{22}}=1{\frac {3}{22}}}$

### 例題五

${\displaystyle {\frac {1}{3}}\times {\frac {1}{4}}}$

${\displaystyle ={\frac {1\times 1}{3\times 4}}}$

${\displaystyle ={\frac {1}{12}}}$

### 例題六

${\displaystyle {\frac {1}{6}}\div {\frac {1}{8}}}$

${\displaystyle ={\frac {1}{6}}\times {\frac {8}{1}}}$

${\displaystyle ={\frac {1\times 8}{6\times 1}}}$

${\displaystyle ={\frac {8/2}{6/2}}}$

${\displaystyle ={\frac {4}{3}}}$

${\displaystyle =1{\frac {1}{3}}}$

### 練習題

1. ${\displaystyle {\frac {2}{6}}+{\frac {5}{9}}=}$
2. ${\displaystyle {\frac {1}{5}}+(-{\frac {3}{8}})=}$
3. ${\displaystyle -{\frac {1}{8}}+{\frac {3}{7}}=}$
4. ${\displaystyle -{\frac {3}{25}}+(-{\frac {7}{5}})=}$
5. ${\displaystyle (1{\frac {1}{8}})+(2{\frac {2}{3}})=}$
6. ${\displaystyle (-{\frac {7}{27}})\times (1{\frac {1}{8}})=}$
7. ${\displaystyle (-{\frac {3}{7}})\times (-{\frac {2}{3}})=}$
8. ${\displaystyle (2{\frac {1}{4}})\div (-1{\frac {1}{12}})=}$
9. ${\displaystyle (-{\frac {9}{16}})\div (3{\frac {3}{8}})=}$
10. ${\displaystyle (-{\frac {12}{13}})\div (-{\frac {1}{2}})=}$