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受欢迎的初等代数 >

(2+1/4)-(2-1/6)

解答

(2 + \frac{1}{4}) - (2 - \frac{1}{6})

解答

\frac{5}{12}

+1

十进制

0.41666 \dots

求解步骤

(2 + \frac{1}{4}) - (2 - \frac{1}{6})

遵循 PEMDAS 运算顺序

计算括号内的值

(2 + \frac{1}{4}) : \frac{9}{4}

2 + \frac{1}{4}

2 + \frac{1}{4} = \frac{9}{4}

2 + \frac{1}{4}

将项转换为分式:

2 = \frac{2 \cdot 4}{4}

= \frac{2 \cdot 4}{4} + \frac{1}{4}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 4 + 1}{4}

2 \cdot 4 + 1 = 9

2 \cdot 4 + 1

数字相乘:

2 \cdot 4 = 8

= 8 + 1

数字相加:

8 + 1 = 9

= 9

= \frac{9}{4}

= \frac{9}{4}

= \frac{9}{4} - (2 - \frac{1}{6})

计算括号内的值

(2 - \frac{1}{6}) : \frac{11}{6}

2 - \frac{1}{6}

2 - \frac{1}{6} = \frac{11}{6}

2 - \frac{1}{6}

将项转换为分式:

2 = \frac{2 \cdot 6}{6}

= \frac{2 \cdot 6}{6} - \frac{1}{6}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 6 - 1}{6}

2 \cdot 6 - 1 = 11

2 \cdot 6 - 1

数字相乘:

2 \cdot 6 = 12

= 12 - 1

数字相减:

12 - 1 = 11

= 11

= \frac{11}{6}

= \frac{11}{6}

= \frac{9}{4} - \frac{11}{6}

加减（左右）

\frac{9}{4} - \frac{11}{6} : \frac{5}{12}

\frac{9}{4} - \frac{11}{6}

\frac{9}{4} - \frac{11}{6} = \frac{5}{12}

\frac{9}{4} - \frac{11}{6}

4, 6

的最小公倍数:

12

4, 6

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

将每个因子乘以它在

4

或

6

中出现的最多次数

= 2 \cdot 2 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 = 12

= 12

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

12

对于

\frac{9}{4} :

将分母和分子乘以

3

\frac{9}{4} = \frac{9 \cdot 3}{4 \cdot 3} = \frac{27}{12}

对于

\frac{11}{6} :

将分母和分子乘以

2

\frac{11}{6} = \frac{11 \cdot 2}{6 \cdot 2} = \frac{22}{12}

= \frac{27}{12} - \frac{22}{12}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{27 - 22}{12}

数字相减:

27 - 22 = 5

= \frac{5}{12}

= \frac{5}{12}

= \frac{5}{12}

流行的例子

1\div 8+1\div 16

1 \div 8 + 1 \div 16

7^2+20× 4-(28+9× 2)

7^{2} + 20 \times 4 - (28 + 9 \times 2)

2^{2} - 3 \cdot 2 + 2

\frac{3}{( - 7 - 2 )}

520+{8-3+[9-(4+2-1)]}

520 + {8 - 3 + [9 - (4 + 2 - 1)]}