Solve [(0,3*2,5+3/4)(3/5+0,6)]:[(3-0,6)*(0,75-4/7)]-1,3

$$[ ( 0,3 \times 2,5 + \frac { 3 } { 4 } ) ( \frac { 3 } { 5 } + 0,6 ) ] : [ ( 3 - 0,6 ) \times ( 0,75 - \frac { 4 } { 7 } ) ] - 1,3$$

Evaluate

$$2,9$$

Solution Steps

Multiply 0,3 and 2,5 to get 0,75.

$$\frac{\left(0,75+\frac{3}{4}\right)\left(\frac{3}{5}+0,6\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Convert decimal number 0,75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\left(\frac{3}{4}+\frac{3}{4}\right)\left(\frac{3}{5}+0,6\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

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

$$\frac{\frac{3+3}{4}\left(\frac{3}{5}+0,6\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Add 3 and 3 to get 6.

$$\frac{\frac{6}{4}\left(\frac{3}{5}+0,6\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\left(\frac{3}{5}+0,6\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Convert decimal number 0,6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{2}\left(\frac{3}{5}+\frac{3}{5}\right)}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Since \frac{3}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}\times \frac{3+3}{5}}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Add 3 and 3 to get 6.

$$\frac{\frac{3}{2}\times \frac{6}{5}}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Multiply \frac{3}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 6}{2\times 5}}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Do the multiplications in the fraction \frac{3\times 6}{2\times 5}.

$$\frac{\frac{18}{10}}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{5}}{\left(3-0,6\right)\left(0,75-\frac{4}{7}\right)}-1,3$$

Subtract 0,6 from 3 to get 2,4.

$$\frac{\frac{9}{5}}{2,4\left(0,75-\frac{4}{7}\right)}-1,3$$

Convert decimal number 0,75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{9}{5}}{2,4\left(\frac{3}{4}-\frac{4}{7}\right)}-1,3$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{4}{7} to fractions with denominator 28.

$$\frac{\frac{9}{5}}{2,4\left(\frac{21}{28}-\frac{16}{28}\right)}-1,3$$

Since \frac{21}{28} and \frac{16}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{5}}{2,4\times \frac{21-16}{28}}-1,3$$

Subtract 16 from 21 to get 5.

$$\frac{\frac{9}{5}}{2,4\times \frac{5}{28}}-1,3$$

Convert decimal number 2,4 to fraction \frac{24}{10}. Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{5}}{\frac{12}{5}\times \frac{5}{28}}-1,3$$

Multiply \frac{12}{5} times \frac{5}{28} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{5}}{\frac{12\times 5}{5\times 28}}-1,3$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{9}{5}}{\frac{12}{28}}-1,3$$

Reduce the fraction \frac{12}{28} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{9}{5}}{\frac{3}{7}}-1,3$$

Divide \frac{9}{5} by \frac{3}{7} by multiplying \frac{9}{5} by the reciprocal of \frac{3}{7}.

$$\frac{9}{5}\times \frac{7}{3}-1,3$$

Multiply \frac{9}{5} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 7}{5\times 3}-1,3$$

Do the multiplications in the fraction \frac{9\times 7}{5\times 3}.

$$\frac{63}{15}-1,3$$

Reduce the fraction \frac{63}{15} to lowest terms by extracting and canceling out 3.

$$\frac{21}{5}-1,3$$

Convert decimal number 1,3 to fraction \frac{13}{10}.

$$\frac{21}{5}-\frac{13}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{21}{5} and \frac{13}{10} to fractions with denominator 10.

$$\frac{42}{10}-\frac{13}{10}$$

Since \frac{42}{10} and \frac{13}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{42-13}{10}$$

Subtract 13 from 42 to get 29.

$$\frac{29}{10}$$

Factor

$$\frac{29}{2 \cdot 5} = 2\frac{9}{10} = 2.9$$