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受欢迎的初等代数 >

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

解答

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

解答

2 \frac{2}{7}

+1

十进制

2.28571 \dots

求解步骤

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

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

计算括号内的值

(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{9}{4} \div \frac{7}{4} + 1

乘除（左右）

\frac{9}{4} \div \frac{7}{4} : \frac{9}{7}

\frac{9}{4} \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{9}{4} \cdot \frac{4}{7}

交叉约分:

4

= \frac{9}{7}

= \frac{9}{7} + 1

加减（左右）

\frac{9}{7} + 1 : \frac{16}{7}

\frac{9}{7} + 1

\frac{9}{7} + 1 = \frac{16}{7}

\frac{9}{7} + 1

将项转换为分式:

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

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

1 \cdot 7 + 9 = 16

1 \cdot 7 + 9

数字相乘:

1 \cdot 7 = 7

= 7 + 9

数字相加:

7 + 9 = 16

= 16

= \frac{16}{7}

= \frac{16}{7}

= \frac{16}{7}

将假分式转换为带分数:

\frac{16}{7} = 2 \frac{2}{7}

\frac{16}{7} = 2

余数

2

\frac{16}{7}

将问题写为长除法形式

7 \overline{∣ 16}

将

16

除以

7

以得到

2

将

16

除以

7

以得到

2

2 7 \overline{∣ 16}

将商数

(2)

乘以除数

7

2 7 \overline{∣ 16} \underline{14}

从

16

减去

14

2 7 \overline{∣ 16} \underline{14} 2

2 7 \overline{∣ 16} \underline{14} 2

长除

\frac{16}{7}

的解是

2

，余数是

2

2 余数 2

转换为带分数: 商

\frac{余数}{除数}

\frac{16}{7} = 2 \frac{2}{7}

= 2 \frac{2}{7}

= 2 \frac{2}{7}

流行的例子

1 0^{3} - 9^{3}

65-45+(-8)-(-43)+7

65 - 45 + (- 8) - (- 43) + 7

(1)^{2} - 6 (1) + 9

(6^{3} \times 4)^{3}

3 \times (- 1) + 1