Solve 1-0,5/1-90frac{1{5}}=1+0,5/1-frac{1{2}}

$$\frac { 1 - 0,5 } { 1 - 90 \frac { 1 } { 5 } } = \frac { 1 + 0,5 } { 1 - \frac { 1 } { 2 } }$$

Verify

Solution Steps

Subtract 0,5 from 1 to get 0,5.

$$\frac{0,5}{1-\frac{90\times 5+1}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Multiply 90 and 5 to get 450.

$$\frac{0,5}{1-\frac{450+1}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Add 450 and 1 to get 451.

$$\frac{0,5}{1-\frac{451}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{0,5}{\frac{5}{5}-\frac{451}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Since \frac{5}{5} and \frac{451}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{0,5}{\frac{5-451}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Subtract 451 from 5 to get -446.

$$\frac{0,5}{-\frac{446}{5}}=\frac{1+0,5}{1-\frac{1}{2}}$$

Divide 0,5 by -\frac{446}{5} by multiplying 0,5 by the reciprocal of -\frac{446}{5}.

$$0,5\left(-\frac{5}{446}\right)=\frac{1+0,5}{1-\frac{1}{2}}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}\left(-\frac{5}{446}\right)=\frac{1+0,5}{1-\frac{1}{2}}$$

Multiply \frac{1}{2} times -\frac{5}{446} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-5\right)}{2\times 446}=\frac{1+0,5}{1-\frac{1}{2}}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 446}.

$$\frac{-5}{892}=\frac{1+0,5}{1-\frac{1}{2}}$$

Fraction \frac{-5}{892} can be rewritten as -\frac{5}{892} by extracting the negative sign.

$$-\frac{5}{892}=\frac{1+0,5}{1-\frac{1}{2}}$$

Add 1 and 0,5 to get 1,5.

$$-\frac{5}{892}=\frac{1,5}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{892}=\frac{1,5}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{892}=\frac{1,5}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$-\frac{5}{892}=\frac{1,5}{\frac{1}{2}}$$

Divide 1,5 by \frac{1}{2} by multiplying 1,5 by the reciprocal of \frac{1}{2}.

$$-\frac{5}{892}=1,5\times 2$$

Multiply 1,5 and 2 to get 3.

$$-\frac{5}{892}=3$$

Convert 3 to fraction \frac{2676}{892}.

$$-\frac{5}{892}=\frac{2676}{892}$$

Compare -\frac{5}{892} and \frac{2676}{892}.

$$\text{false}$$