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受欢迎的初等代数 >

5+2\div (1+(1\div 2)\div (2-1\div 4))

解答

5 + 2 \div (1 + (1 \div 2) \div (2 - 1 \div 4))

解答

6 \frac{5}{9}

+1

十进制

6.55555 \dots

求解步骤

5 + 2 \div (1 + (1 \div 2) \div (2 - 1 \div 4))

遵循 PEMDAS 运算顺序

计算括号内的值

(1 + (1 \div 2) \div (2 - 1 \div 4)) : \frac{9}{7}

1 + (1 \div 2) \div (2 - 1 \div 4)

计算括号内的值

(1 \div 2) : \frac{1}{2}

1 \div 2

1 \div 2 = \frac{1}{2}

= \frac{1}{2}

= 1 + \frac{1}{2} \div (2 - 1 \div 4)

计算括号内的值

(2 - 1 \div 4) : \frac{7}{4}

2 - 1 \div 4

乘除（左右）

1 \div 4 : \frac{1}{4}

1 \div 4

1 \div 4 = \frac{1}{4}

= \frac{1}{4}

= 2 - \frac{1}{4}

加减（左右）

2 - \frac{1}{4} : \frac{7}{4}

2 - \frac{1}{4}

2 - \frac{1}{4} = \frac{7}{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 = 7

2 \cdot 4 - 1

数字相乘:

2 \cdot 4 = 8

= 8 - 1

数字相减:

8 - 1 = 7

= 7

= \frac{7}{4}

= \frac{7}{4}

= \frac{7}{4}

= 1 + \frac{1}{2} \div \frac{7}{4}

乘除（左右）

\frac{1}{2} \div \frac{7}{4} : \frac{2}{7}

\frac{1}{2} \div \frac{7}{4}

使用分式法则:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{1}{2} \cdot \frac{4}{7}

交叉约去公约数:

2

= \frac{2}{7}

= 1 + \frac{2}{7}

加减（左右）

1 + \frac{2}{7} : \frac{9}{7}

1 + \frac{2}{7}

1 + \frac{2}{7} = \frac{9}{7}

1 + \frac{2}{7}

将项转换为分式:

1 = \frac{1 \cdot 7}{7}

= \frac{1 \cdot 7}{7} + \frac{2}{7}

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{1 \cdot 7 + 2}{7}

1 \cdot 7 + 2 = 9

1 \cdot 7 + 2

数字相乘:

1 \cdot 7 = 7

= 7 + 2

数字相加:

7 + 2 = 9

= 9

= \frac{9}{7}

= \frac{9}{7}

= \frac{9}{7}

= 5 + 2 \div \frac{9}{7}

乘除（左右）

2 \div \frac{9}{7} : \frac{14}{9}

2 \div \frac{9}{7}

将项转换为分式:

2 = \frac{2}{1}

= \frac{2}{1} \div \frac{9}{7}

使用分式法则:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2}{1} \cdot \frac{7}{9}

分式相乘:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 7}{1 \cdot 9}

数字相乘:

2 \cdot 7 = 14

= \frac{14}{1 \cdot 9}

数字相乘:

1 \cdot 9 = 9

= \frac{14}{9}

= 5 + \frac{14}{9}

加减（左右）

5 + \frac{14}{9} : \frac{59}{9}

5 + \frac{14}{9}

5 + \frac{14}{9} = \frac{59}{9}

5 + \frac{14}{9}

将项转换为分式:

5 = \frac{5 \cdot 9}{9}

= \frac{5 \cdot 9}{9} + \frac{14}{9}

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{5 \cdot 9 + 14}{9}

5 \cdot 9 + 14 = 59

5 \cdot 9 + 14

数字相乘:

5 \cdot 9 = 45

= 45 + 14

数字相加:

45 + 14 = 59

= 59

= \frac{59}{9}

= \frac{59}{9}

= \frac{59}{9}

将假分式转换为带分数:

\frac{59}{9} = 6 \frac{5}{9}

\frac{59}{9} = 6

余数

5

\frac{59}{9}

将问题写为长除法形式

9 \overline{∣ 59}

将

59

除以

9

以得到

6

将

59

除以

9

以得到

6

6 9 \overline{∣ 59}

将商数

(6)

乘以除数

9

6 9 \overline{∣ 59} \underline{54}

从

59

减去

54

6 9 \overline{∣ 59} \underline{54} 5

6 9 \overline{∣ 59} \underline{54} 5

长除

\frac{59}{9}

的解是

6

，余数是

5

6 余数 5

转换为带分数: 商

\frac{余数}{除数}

\frac{59}{9} = 6 \frac{5}{9}

= 6 \frac{5}{9}

= 6 \frac{5}{9}

流行的例子

2-5× 2+3\div 6

(20-12)\div (-2)