Solve 1.8-3.3-4.5:3.75/5.6:2frac{1{3}+2.5}

$$1.8 - \frac { 3.3 - 4.5 : 3.75 } { 5.6 : 2 \frac { 1 } { 3 } + 2.5 }$$

Evaluate

$$\frac{48}{35}\approx 1.371428571$$

Solution Steps

Expand \frac{4.5}{3.75} by multiplying both numerator and the denominator by 100.

$$1.8-\frac{3.3-\frac{450}{375}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Reduce the fraction \frac{450}{375} to lowest terms by extracting and canceling out 75.

$$1.8-\frac{3.3-\frac{6}{5}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Convert decimal number 3.3 to fraction \frac{33}{10}.

$$1.8-\frac{\frac{33}{10}-\frac{6}{5}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{33}{10} and \frac{6}{5} to fractions with denominator 10.

$$1.8-\frac{\frac{33}{10}-\frac{12}{10}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Since \frac{33}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$1.8-\frac{\frac{33-12}{10}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Subtract 12 from 33 to get 21.

$$1.8-\frac{\frac{21}{10}}{\frac{5.6}{\frac{2\times 3+1}{3}}+2.5}$$

Divide 5.6 by \frac{2\times 3+1}{3} by multiplying 5.6 by the reciprocal of \frac{2\times 3+1}{3}.

$$1.8-\frac{\frac{21}{10}}{\frac{5.6\times 3}{2\times 3+1}+2.5}$$

Multiply 5.6 and 3 to get 16.8.

$$1.8-\frac{\frac{21}{10}}{\frac{16.8}{2\times 3+1}+2.5}$$

Multiply 2 and 3 to get 6.

$$1.8-\frac{\frac{21}{10}}{\frac{16.8}{6+1}+2.5}$$

Add 6 and 1 to get 7.

$$1.8-\frac{\frac{21}{10}}{\frac{16.8}{7}+2.5}$$

Expand \frac{16.8}{7} by multiplying both numerator and the denominator by 10.

$$1.8-\frac{\frac{21}{10}}{\frac{168}{70}+2.5}$$

Reduce the fraction \frac{168}{70} to lowest terms by extracting and canceling out 14.

$$1.8-\frac{\frac{21}{10}}{\frac{12}{5}+2.5}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$1.8-\frac{\frac{21}{10}}{\frac{12}{5}+\frac{5}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{12}{5} and \frac{5}{2} to fractions with denominator 10.

$$1.8-\frac{\frac{21}{10}}{\frac{24}{10}+\frac{25}{10}}$$

Since \frac{24}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$1.8-\frac{\frac{21}{10}}{\frac{24+25}{10}}$$

Add 24 and 25 to get 49.

$$1.8-\frac{\frac{21}{10}}{\frac{49}{10}}$$

Divide \frac{21}{10} by \frac{49}{10} by multiplying \frac{21}{10} by the reciprocal of \frac{49}{10}.

$$1.8-\frac{21}{10}\times \frac{10}{49}$$

Multiply \frac{21}{10} times \frac{10}{49} by multiplying numerator times numerator and denominator times denominator.

$$1.8-\frac{21\times 10}{10\times 49}$$

Cancel out 10 in both numerator and denominator.

$$1.8-\frac{21}{49}$$

Reduce the fraction \frac{21}{49} to lowest terms by extracting and canceling out 7.

$$1.8-\frac{3}{7}$$

Convert decimal number 1.8 to fraction \frac{18}{10}. Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 5 and 7 is 35. Convert \frac{9}{5} and \frac{3}{7} to fractions with denominator 35.

$$\frac{63}{35}-\frac{15}{35}$$

Since \frac{63}{35} and \frac{15}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-15}{35}$$

Subtract 15 from 63 to get 48.

$$\frac{48}{35}$$

Factor

$$\frac{3 \cdot 2 ^ {4}}{5 \cdot 7} = 1\frac{13}{35} = 1.3714285714285714$$