Solve 9/4-(4-9/4)=5(9+1+9/4)/4

$$\frac { 9 } { 4 } - ( 4 - \frac { 9 } { 4 } ) = 5 \frac { ( 9 + 1 + \frac { 9 } { 4 } ) } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 4.

$$9-4\left(4-\frac{9}{4}\right)=5\left(9+1+\frac{9}{4}\right)$$

Convert 4 to fraction \frac{16}{4}.

$$9-4\left(\frac{16}{4}-\frac{9}{4}\right)=5\left(9+1+\frac{9}{4}\right)$$

Since \frac{16}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$9-4\times \frac{16-9}{4}=5\left(9+1+\frac{9}{4}\right)$$

Subtract 9 from 16 to get 7.

$$9-4\times \frac{7}{4}=5\left(9+1+\frac{9}{4}\right)$$

Cancel out 4 and 4.

$$9-7=5\left(9+1+\frac{9}{4}\right)$$

Subtract 7 from 9 to get 2.

$$2=5\left(9+1+\frac{9}{4}\right)$$

Add 9 and 1 to get 10.

$$2=5\left(10+\frac{9}{4}\right)$$

Convert 10 to fraction \frac{40}{4}.

$$2=5\left(\frac{40}{4}+\frac{9}{4}\right)$$

Since \frac{40}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$2=5\times \frac{40+9}{4}$$

Add 40 and 9 to get 49.

$$2=5\times \frac{49}{4}$$

Express 5\times \frac{49}{4} as a single fraction.

$$2=\frac{5\times 49}{4}$$

Multiply 5 and 49 to get 245.

$$2=\frac{245}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}=\frac{245}{4}$$

Compare \frac{8}{4} and \frac{245}{4}.

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