Solve 0.7*12/11-6.6*3/7-2.2div7/3+0.7*9/11+3.3divfrac{7}{8}

$$0.7 \times 1 \frac { 2 } { 11 } - 6.6 \times \frac { 3 } { 7 } - 2.2 \div \frac { 7 } { 3 } + 0.7 \times \frac { 9 } { 11 } + 3.3 \div \frac { 7 } { 8 }$$

Evaluate

$$1.4$$

Solution Steps

Multiply 1 and 11 to get 11.

$$0.7\times \frac{11+2}{11}-6.6\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Add 11 and 2 to get 13.

$$0.7\times \frac{13}{11}-6.6\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{7}{10}\times \frac{13}{11}-6.6\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Multiply \frac{7}{10} times \frac{13}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 13}{10\times 11}-6.6\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Do the multiplications in the fraction \frac{7\times 13}{10\times 11}.

$$\frac{91}{110}-6.6\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Convert decimal number 6.6 to fraction \frac{66}{10}. Reduce the fraction \frac{66}{10} to lowest terms by extracting and canceling out 2.

$$\frac{91}{110}-\frac{33}{5}\times \frac{3}{7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Multiply \frac{33}{5} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{91}{110}-\frac{33\times 3}{5\times 7}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Do the multiplications in the fraction \frac{33\times 3}{5\times 7}.

$$\frac{91}{110}-\frac{99}{35}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Least common multiple of 110 and 35 is 770. Convert \frac{91}{110} and \frac{99}{35} to fractions with denominator 770.

$$\frac{637}{770}-\frac{2178}{770}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Since \frac{637}{770} and \frac{2178}{770} have the same denominator, subtract them by subtracting their numerators.

$$\frac{637-2178}{770}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Subtract 2178 from 637 to get -1541.

$$-\frac{1541}{770}-\frac{2.2}{\frac{7}{3}}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Divide 2.2 by \frac{7}{3} by multiplying 2.2 by the reciprocal of \frac{7}{3}.

$$-\frac{1541}{770}-2.2\times \frac{3}{7}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Convert decimal number 2.2 to fraction \frac{22}{10}. Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{1541}{770}-\frac{11}{5}\times \frac{3}{7}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Multiply \frac{11}{5} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1541}{770}-\frac{11\times 3}{5\times 7}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Do the multiplications in the fraction \frac{11\times 3}{5\times 7}.

$$-\frac{1541}{770}-\frac{33}{35}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Least common multiple of 770 and 35 is 770. Convert -\frac{1541}{770} and \frac{33}{35} to fractions with denominator 770.

$$-\frac{1541}{770}-\frac{726}{770}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Since -\frac{1541}{770} and \frac{726}{770} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1541-726}{770}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Subtract 726 from -1541 to get -2267.

$$-\frac{2267}{770}+0.7\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$-\frac{2267}{770}+\frac{7}{10}\times \frac{9}{11}+\frac{3.3}{\frac{7}{8}}$$

Multiply \frac{7}{10} times \frac{9}{11} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{2267}{770}+\frac{7\times 9}{10\times 11}+\frac{3.3}{\frac{7}{8}}$$

Do the multiplications in the fraction \frac{7\times 9}{10\times 11}.

$$-\frac{2267}{770}+\frac{63}{110}+\frac{3.3}{\frac{7}{8}}$$

Least common multiple of 770 and 110 is 770. Convert -\frac{2267}{770} and \frac{63}{110} to fractions with denominator 770.

$$-\frac{2267}{770}+\frac{441}{770}+\frac{3.3}{\frac{7}{8}}$$

Since -\frac{2267}{770} and \frac{441}{770} have the same denominator, add them by adding their numerators.

$$\frac{-2267+441}{770}+\frac{3.3}{\frac{7}{8}}$$

Add -2267 and 441 to get -1826.

$$\frac{-1826}{770}+\frac{3.3}{\frac{7}{8}}$$

Reduce the fraction \frac{-1826}{770} to lowest terms by extracting and canceling out 22.

$$-\frac{83}{35}+\frac{3.3}{\frac{7}{8}}$$

Divide 3.3 by \frac{7}{8} by multiplying 3.3 by the reciprocal of \frac{7}{8}.

$$-\frac{83}{35}+3.3\times \frac{8}{7}$$

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

$$-\frac{83}{35}+\frac{33}{10}\times \frac{8}{7}$$

Multiply \frac{33}{10} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{83}{35}+\frac{33\times 8}{10\times 7}$$

Do the multiplications in the fraction \frac{33\times 8}{10\times 7}.

$$-\frac{83}{35}+\frac{264}{70}$$

Reduce the fraction \frac{264}{70} to lowest terms by extracting and canceling out 2.

$$-\frac{83}{35}+\frac{132}{35}$$

Since -\frac{83}{35} and \frac{132}{35} have the same denominator, add them by adding their numerators.

$$\frac{-83+132}{35}$$

Add -83 and 132 to get 49.

$$\frac{49}{35}$$

Reduce the fraction \frac{49}{35} to lowest terms by extracting and canceling out 7.

$$\frac{7}{5}$$

Factor

$$\frac{7}{5} = 1\frac{2}{5} = 1.4$$