Solve 83/334+167/200-7+8/40=

$$8 \frac { 3 } { 334 } + 16 \frac { 7 } { 200 } - 7 + \frac { 8 } { 40 } =$$

Evaluate

$$\frac{575949}{33400}\approx 17.243982036$$

Solution Steps

Multiply 8 and 334 to get 2672.

$$\frac{2672+3}{334}+\frac{16\times 200+7}{200}-7+\frac{8}{40}$$

Add 2672 and 3 to get 2675.

$$\frac{2675}{334}+\frac{16\times 200+7}{200}-7+\frac{8}{40}$$

Multiply 16 and 200 to get 3200.

$$\frac{2675}{334}+\frac{3200+7}{200}-7+\frac{8}{40}$$

Add 3200 and 7 to get 3207.

$$\frac{2675}{334}+\frac{3207}{200}-7+\frac{8}{40}$$

Least common multiple of 334 and 200 is 33400. Convert \frac{2675}{334} and \frac{3207}{200} to fractions with denominator 33400.

$$\frac{267500}{33400}+\frac{535569}{33400}-7+\frac{8}{40}$$

Since \frac{267500}{33400} and \frac{535569}{33400} have the same denominator, add them by adding their numerators.

$$\frac{267500+535569}{33400}-7+\frac{8}{40}$$

Add 267500 and 535569 to get 803069.

$$\frac{803069}{33400}-7+\frac{8}{40}$$

Convert 7 to fraction \frac{233800}{33400}.

$$\frac{803069}{33400}-\frac{233800}{33400}+\frac{8}{40}$$

Since \frac{803069}{33400} and \frac{233800}{33400} have the same denominator, subtract them by subtracting their numerators.

$$\frac{803069-233800}{33400}+\frac{8}{40}$$

Subtract 233800 from 803069 to get 569269.

$$\frac{569269}{33400}+\frac{8}{40}$$

Reduce the fraction \frac{8}{40} to lowest terms by extracting and canceling out 8.

$$\frac{569269}{33400}+\frac{1}{5}$$

Least common multiple of 33400 and 5 is 33400. Convert \frac{569269}{33400} and \frac{1}{5} to fractions with denominator 33400.

$$\frac{569269}{33400}+\frac{6680}{33400}$$

Since \frac{569269}{33400} and \frac{6680}{33400} have the same denominator, add them by adding their numerators.

$$\frac{569269+6680}{33400}$$

Add 569269 and 6680 to get 575949.

$$\frac{575949}{33400}$$

Factor

$$\frac{3 \cdot 11 \cdot 31 \cdot 563}{2 ^ {3} \cdot 5 ^ {2} \cdot 167} = 17\frac{8149}{33400} = 17.243982035928145$$