Solve 4/2(2+4/3)-4=5/4(1-1/5)

$$\frac{ 4 }{ 2 } (2+ \frac{ 4 }{ 3 } )-4= \frac{ 5 }{ 4 } (1- \frac{ 1 }{ 5 } )$$

Verify

Solution Steps

Divide 4 by 2 to get 2.

$$2\left(2+\frac{4}{3}\right)-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$2\left(\frac{6}{3}+\frac{4}{3}\right)-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Since \frac{6}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$2\times \frac{6+4}{3}-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Add 6 and 4 to get 10.

$$2\times \frac{10}{3}-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Express 2\times \frac{10}{3} as a single fraction.

$$\frac{2\times 10}{3}-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Multiply 2 and 10 to get 20.

$$\frac{20}{3}-4=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{20}{3}-\frac{12}{3}=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Since \frac{20}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-12}{3}=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

Subtract 12 from 20 to get 8.

$$\frac{8}{3}=\frac{5}{4}\left(1-\frac{1}{5}\right)$$

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

$$\frac{8}{3}=\frac{5}{4}\left(\frac{5}{5}-\frac{1}{5}\right)$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}=\frac{5}{4}\times \frac{5-1}{5}$$

Subtract 1 from 5 to get 4.

$$\frac{8}{3}=\frac{5}{4}\times \frac{4}{5}$$

Cancel out \frac{5}{4} and its reciprocal \frac{4}{5}.

$$\frac{8}{3}=1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{8}{3}=\frac{3}{3}$$

Compare \frac{8}{3} and \frac{3}{3}.

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