Solve 5(-23/27)+4div7=11(-23/27)+9div10

$$5(- \frac{ 23 }{ 27 } )+4 \div 7=11(- \frac{ 23 }{ 27 } )+9 \div 10$$

Verify

Solution Steps

Express 5\left(-\frac{23}{27}\right) as a single fraction.

$$\frac{5\left(-23\right)}{27}+\frac{4}{7}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Multiply 5 and -23 to get -115.

$$\frac{-115}{27}+\frac{4}{7}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Fraction \frac{-115}{27} can be rewritten as -\frac{115}{27} by extracting the negative sign.

$$-\frac{115}{27}+\frac{4}{7}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Least common multiple of 27 and 7 is 189. Convert -\frac{115}{27} and \frac{4}{7} to fractions with denominator 189.

$$-\frac{805}{189}+\frac{108}{189}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Since -\frac{805}{189} and \frac{108}{189} have the same denominator, add them by adding their numerators.

$$\frac{-805+108}{189}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Add -805 and 108 to get -697.

$$-\frac{697}{189}=11\left(-\frac{23}{27}\right)+\frac{9}{10}$$

Express 11\left(-\frac{23}{27}\right) as a single fraction.

$$-\frac{697}{189}=\frac{11\left(-23\right)}{27}+\frac{9}{10}$$

Multiply 11 and -23 to get -253.

$$-\frac{697}{189}=\frac{-253}{27}+\frac{9}{10}$$

Fraction \frac{-253}{27} can be rewritten as -\frac{253}{27} by extracting the negative sign.

$$-\frac{697}{189}=-\frac{253}{27}+\frac{9}{10}$$

Least common multiple of 27 and 10 is 270. Convert -\frac{253}{27} and \frac{9}{10} to fractions with denominator 270.

$$-\frac{697}{189}=-\frac{2530}{270}+\frac{243}{270}$$

Since -\frac{2530}{270} and \frac{243}{270} have the same denominator, add them by adding their numerators.

$$-\frac{697}{189}=\frac{-2530+243}{270}$$

Add -2530 and 243 to get -2287.

$$-\frac{697}{189}=-\frac{2287}{270}$$

Least common multiple of 189 and 270 is 1890. Convert -\frac{697}{189} and -\frac{2287}{270} to fractions with denominator 1890.

$$-\frac{6970}{1890}=-\frac{16009}{1890}$$

Compare -\frac{6970}{1890} and -\frac{16009}{1890}.

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