Solve 1/4*(4.85div5/10-3.6+6.15*33/5)

$$\frac { 1 } { 4 } \times ( 4.85 \div \frac { 5 } { 10 } - 3.6 + 6.15 \times 3 \frac { 3 } { 5 } )$$

Evaluate

$$7.06$$

Solution Steps

Divide 4.85 by \frac{5}{10} by multiplying 4.85 by the reciprocal of \frac{5}{10}.

$$\frac{1}{4}\left(\frac{4.85\times 10}{5}-3.6+6.15\times \frac{3\times 5+3}{5}\right)$$

Multiply 4.85 and 10 to get 48.5.

$$\frac{1}{4}\left(\frac{48.5}{5}-3.6+6.15\times \frac{3\times 5+3}{5}\right)$$

Expand \frac{48.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{1}{4}\left(\frac{485}{50}-3.6+6.15\times \frac{3\times 5+3}{5}\right)$$

Reduce the fraction \frac{485}{50} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}\left(\frac{97}{10}-3.6+6.15\times \frac{3\times 5+3}{5}\right)$$

Convert decimal number 3.6 to fraction \frac{36}{10}. Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\left(\frac{97}{10}-\frac{18}{5}+6.15\times \frac{3\times 5+3}{5}\right)$$

Least common multiple of 10 and 5 is 10. Convert \frac{97}{10} and \frac{18}{5} to fractions with denominator 10.

$$\frac{1}{4}\left(\frac{97}{10}-\frac{36}{10}+6.15\times \frac{3\times 5+3}{5}\right)$$

Since \frac{97}{10} and \frac{36}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}\left(\frac{97-36}{10}+6.15\times \frac{3\times 5+3}{5}\right)$$

Subtract 36 from 97 to get 61.

$$\frac{1}{4}\left(\frac{61}{10}+6.15\times \frac{3\times 5+3}{5}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{1}{4}\left(\frac{61}{10}+6.15\times \frac{15+3}{5}\right)$$

Add 15 and 3 to get 18.

$$\frac{1}{4}\left(\frac{61}{10}+6.15\times \frac{18}{5}\right)$$

Convert decimal number 6.15 to fraction \frac{615}{100}. Reduce the fraction \frac{615}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}\left(\frac{61}{10}+\frac{123}{20}\times \frac{18}{5}\right)$$

Multiply \frac{123}{20} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}\left(\frac{61}{10}+\frac{123\times 18}{20\times 5}\right)$$

Do the multiplications in the fraction \frac{123\times 18}{20\times 5}.

$$\frac{1}{4}\left(\frac{61}{10}+\frac{2214}{100}\right)$$

Reduce the fraction \frac{2214}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\left(\frac{61}{10}+\frac{1107}{50}\right)$$

Least common multiple of 10 and 50 is 50. Convert \frac{61}{10} and \frac{1107}{50} to fractions with denominator 50.

$$\frac{1}{4}\left(\frac{305}{50}+\frac{1107}{50}\right)$$

Since \frac{305}{50} and \frac{1107}{50} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}\times \frac{305+1107}{50}$$

Add 305 and 1107 to get 1412.

$$\frac{1}{4}\times \frac{1412}{50}$$

Reduce the fraction \frac{1412}{50} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\times \frac{706}{25}$$

Multiply \frac{1}{4} times \frac{706}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 706}{4\times 25}$$

Do the multiplications in the fraction \frac{1\times 706}{4\times 25}.

$$\frac{706}{100}$$

Reduce the fraction \frac{706}{100} to lowest terms by extracting and canceling out 2.

$$\frac{353}{50}$$

Factor

$$\frac{353}{2 \cdot 5 ^ {2}} = 7\frac{3}{50} = 7.06$$