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受欢迎的初等代数 >

(10\div 5/6)\div 3 1/6

解答

(10 \div \frac{5}{6}) \div 3 \frac{1}{6}

解答

3 \frac{15}{19}

+1

十进制

3.78947 \dots

求解步骤

(10 \div \frac{5}{6}) \div 3 \frac{1}{6}

将带分数转换为假分式:

3 \frac{1}{6} = \frac{19}{6}

3 \frac{1}{6}

将带分数转换为假分式:

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

3 \frac{1}{6} = \frac{3 \cdot 6 + 1}{6}

= \frac{19}{6}

= (10 \div \frac{5}{6}) \div \frac{19}{6}

遵循 PEMDAS 运算顺序

计算括号内的值

(10 \div \frac{5}{6}) : 12

10 \div \frac{5}{6}

乘除（左右）

将项转换为分式:

10 = \frac{10}{1}

= \frac{10}{1} \div \frac{5}{6}

使用分式法则:

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

= \frac{10}{1} \cdot \frac{6}{5}

交叉约去公约数:

5

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

分式相乘:

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

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

数字相乘:

2 \cdot 6 = 12

= \frac{12}{1 \cdot 1}

数字相乘:

1 \cdot 1 = 1

= \frac{12}{1}

使用法则

\frac{a}{1} = a

= 12

= 12 \div \frac{19}{6}

乘除（左右）

12 \div \frac{19}{6} : \frac{72}{19}

12 \div \frac{19}{6}

将项转换为分式:

12 = \frac{12}{1}

= \frac{12}{1} \div \frac{19}{6}

使用分式法则:

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

= \frac{12}{1} \cdot \frac{6}{19}

分式相乘:

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

= \frac{12 \cdot 6}{1 \cdot 19}

数字相乘:

12 \cdot 6 = 72

= \frac{72}{1 \cdot 19}

数字相乘:

1 \cdot 19 = 19

= \frac{72}{19}

= \frac{72}{19}

将假分式转换为带分数:

\frac{72}{19} = 3 \frac{15}{19}

\frac{72}{19} = 3

余数

15

\frac{72}{19}

将问题写为长除法形式

19 \overline{∣ 72}

将

72

除以

19

以得到

3

将

72

除以

19

以得到

3

3 19 \overline{∣ 72}

将商数

(3)

乘以除数

19

3 19 \overline{∣ 72} \underline{57}

从

72

减去

57

3 19 \overline{∣ 72} \underline{57} 15

3 19 \overline{∣ 72} \underline{57} 15

长除

\frac{72}{19}

的解是

3

，余数是

15

3 余数 15

转换为带分数: 商

\frac{余数}{除数}

\frac{72}{19} = 3 \frac{15}{19}

= 3 \frac{15}{19}

= 3 \frac{15}{19}

流行的例子

1× 2\div 2+4\div 2+6\div 2× 3

1 \times 2 \div 2 + 4 \div 2 + 6 \div 2 \times 3

7-3*(-4)-27\div (-9)

7 - 3 \cdot (- 4) - 27 \div (- 9)

- 2 (1) - 2

-1× 4-(3-5+6)-5× 6

- 1 \times 4 - (3 - 5 + 6) - 5 \times 6

5 \cdot 3^{4}