Solve 2+1/4/frac{4{7}}-frac{4sqrt{2}}{2}

$$2 + \frac { \frac { 1 } { 4 } } { \frac { 4 } { 7 } } - \frac { 4 \sqrt { 2 } } { 2 }$$

Evaluate

$$\frac{39}{16}-2\sqrt{2}\approx -0.390927125$$

Solution Steps

Divide \frac{1}{4} by \frac{4}{7} by multiplying \frac{1}{4} by the reciprocal of \frac{4}{7}.

$$2+\frac{1}{4}\times \frac{7}{4}-\frac{4\sqrt{2}}{2}$$

Multiply \frac{1}{4} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{1\times 7}{4\times 4}-\frac{4\sqrt{2}}{2}$$

Do the multiplications in the fraction \frac{1\times 7}{4\times 4}.

$$2+\frac{7}{16}-\frac{4\sqrt{2}}{2}$$

Convert 2 to fraction \frac{32}{16}.

$$\frac{32}{16}+\frac{7}{16}-\frac{4\sqrt{2}}{2}$$

Since \frac{32}{16} and \frac{7}{16} have the same denominator, add them by adding their numerators.

$$\frac{32+7}{16}-\frac{4\sqrt{2}}{2}$$

Add 32 and 7 to get 39.

$$\frac{39}{16}-\frac{4\sqrt{2}}{2}$$

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

$$\frac{39}{16}-2\sqrt{2}$$

Factor

$$\frac{39 - 32 \sqrt{2}}{16} = -0.3909271247461903$$