Solve beta2/5+22/35div111/25-3/7

$$\beta \frac { 2 } { 5 } + 2 \frac { 2 } { 35 } \div 1 \frac { 11 } { 25 } - \frac { 3 } { 7 }$$

Evaluate

$$\frac{2\beta }{5}+1$$

Solution Steps

Divide \frac{2\times 35+2}{35} by \frac{1\times 25+11}{25} by multiplying \frac{2\times 35+2}{35} by the reciprocal of \frac{1\times 25+11}{25}.

$$\beta \times \frac{2}{5}+\frac{\left(2\times 35+2\right)\times 25}{35\left(1\times 25+11\right)}-\frac{3}{7}$$

Cancel out 5 in both numerator and denominator.

$$\beta \times \frac{2}{5}+\frac{5\left(2+2\times 35\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 2 and 35 to get 70.

$$\beta \times \frac{2}{5}+\frac{5\left(2+70\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Add 2 and 70 to get 72.

$$\beta \times \frac{2}{5}+\frac{5\times 72}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 5 and 72 to get 360.

$$\beta \times \frac{2}{5}+\frac{360}{7\left(11+25\right)}-\frac{3}{7}$$

Add 11 and 25 to get 36.

$$\beta \times \frac{2}{5}+\frac{360}{7\times 36}-\frac{3}{7}$$

Multiply 7 and 36 to get 252.

$$\beta \times \frac{2}{5}+\frac{360}{252}-\frac{3}{7}$$

Reduce the fraction \frac{360}{252} to lowest terms by extracting and canceling out 36.

$$\beta \times \frac{2}{5}+\frac{10}{7}-\frac{3}{7}$$

Since \frac{10}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

$$\beta \times \frac{2}{5}+\frac{10-3}{7}$$

Subtract 3 from 10 to get 7.

$$\beta \times \frac{2}{5}+\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$\beta \times \frac{2}{5}+1$$

Expand

$$\frac{2\beta }{5}+1$$

Solution Steps

Divide \frac{2\times 35+2}{35} by \frac{1\times 25+11}{25} by multiplying \frac{2\times 35+2}{35} by the reciprocal of \frac{1\times 25+11}{25}.

$$\beta \times \frac{2}{5}+\frac{\left(2\times 35+2\right)\times 25}{35\left(1\times 25+11\right)}-\frac{3}{7}$$

Cancel out 5 in both numerator and denominator.

$$\beta \times \frac{2}{5}+\frac{5\left(2+2\times 35\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 2 and 35 to get 70.

$$\beta \times \frac{2}{5}+\frac{5\left(2+70\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Add 2 and 70 to get 72.

$$\beta \times \frac{2}{5}+\frac{5\times 72}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 5 and 72 to get 360.

$$\beta \times \frac{2}{5}+\frac{360}{7\left(11+25\right)}-\frac{3}{7}$$

Add 11 and 25 to get 36.

$$\beta \times \frac{2}{5}+\frac{360}{7\times 36}-\frac{3}{7}$$

Multiply 7 and 36 to get 252.

$$\beta \times \frac{2}{5}+\frac{360}{252}-\frac{3}{7}$$

Reduce the fraction \frac{360}{252} to lowest terms by extracting and canceling out 36.

$$\beta \times \frac{2}{5}+\frac{10}{7}-\frac{3}{7}$$

Since \frac{10}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

$$\beta \times \frac{2}{5}+\frac{10-3}{7}$$

Subtract 3 from 10 to get 7.

$$\beta \times \frac{2}{5}+\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$\beta \times \frac{2}{5}+1$$