Solve 9/11(1/2-4/1)-3/4(frac{1}{2}-frac{3}{8})=-frac{5}{13}

$$\frac { 9 } { 11 } ( \frac { 1 } { 2 } - \frac { 4 } { 1 } ) - \frac { 3 } { 4 } ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) = - \frac { 5 } { 13 }$$

Verify

Solution Steps

Anything divided by one gives itself.

$$\frac{9}{11}\left(\frac{1}{2}-4\right)-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{9}{11}\left(\frac{1}{2}-\frac{8}{2}\right)-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Since \frac{1}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{11}\times \frac{1-8}{2}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Subtract 8 from 1 to get -7.

$$\frac{9}{11}\left(-\frac{7}{2}\right)-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Multiply \frac{9}{11} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(-7\right)}{11\times 2}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Do the multiplications in the fraction \frac{9\left(-7\right)}{11\times 2}.

$$\frac{-63}{22}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Fraction \frac{-63}{22} can be rewritten as -\frac{63}{22} by extracting the negative sign.

$$-\frac{63}{22}-\frac{3}{4}\left(\frac{1}{2}-\frac{3}{8}\right)=-\frac{5}{13}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$-\frac{63}{22}-\frac{3}{4}\left(\frac{4}{8}-\frac{3}{8}\right)=-\frac{5}{13}$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{63}{22}-\frac{3}{4}\times \frac{4-3}{8}=-\frac{5}{13}$$

Subtract 3 from 4 to get 1.

$$-\frac{63}{22}-\frac{3}{4}\times \frac{1}{8}=-\frac{5}{13}$$

Multiply \frac{3}{4} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{63}{22}-\frac{3\times 1}{4\times 8}=-\frac{5}{13}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 8}.

$$-\frac{63}{22}-\frac{3}{32}=-\frac{5}{13}$$

Least common multiple of 22 and 32 is 352. Convert -\frac{63}{22} and \frac{3}{32} to fractions with denominator 352.

$$-\frac{1008}{352}-\frac{33}{352}=-\frac{5}{13}$$

Since -\frac{1008}{352} and \frac{33}{352} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1008-33}{352}=-\frac{5}{13}$$

Subtract 33 from -1008 to get -1041.

$$-\frac{1041}{352}=-\frac{5}{13}$$

Least common multiple of 352 and 13 is 4576. Convert -\frac{1041}{352} and -\frac{5}{13} to fractions with denominator 4576.

$$-\frac{13533}{4576}=-\frac{1760}{4576}$$

Compare -\frac{13533}{4576} and -\frac{1760}{4576}.

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