Solve (-25/9+120/11):148/49-12/9:(-6)=

$$( - 2 \frac { 5 } { 9 } + 1 \frac { 20 } { 11 } ) : 14 \frac { 8 } { 49 } - 1 \frac { 2 } { 9 } : ( - 6 ) =$$

Evaluate

$$\frac{45809}{206118}\approx 0.22224648$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\frac{-\frac{18+5}{9}+\frac{1\times 11+20}{11}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Add 18 and 5 to get 23.

$$\frac{-\frac{23}{9}+\frac{1\times 11+20}{11}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Multiply 1 and 11 to get 11.

$$\frac{-\frac{23}{9}+\frac{11+20}{11}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Add 11 and 20 to get 31.

$$\frac{-\frac{23}{9}+\frac{31}{11}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Least common multiple of 9 and 11 is 99. Convert -\frac{23}{9} and \frac{31}{11} to fractions with denominator 99.

$$\frac{-\frac{253}{99}+\frac{279}{99}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Since -\frac{253}{99} and \frac{279}{99} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-253+279}{99}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Add -253 and 279 to get 26.

$$\frac{\frac{26}{99}}{\frac{14\times 49+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Multiply 14 and 49 to get 686.

$$\frac{\frac{26}{99}}{\frac{686+8}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Add 686 and 8 to get 694.

$$\frac{\frac{26}{99}}{\frac{694}{49}}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Divide \frac{26}{99} by \frac{694}{49} by multiplying \frac{26}{99} by the reciprocal of \frac{694}{49}.

$$\frac{26}{99}\times \frac{49}{694}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Multiply \frac{26}{99} times \frac{49}{694} by multiplying numerator times numerator and denominator times denominator.

$$\frac{26\times 49}{99\times 694}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Do the multiplications in the fraction \frac{26\times 49}{99\times 694}.

$$\frac{1274}{68706}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Reduce the fraction \frac{1274}{68706} to lowest terms by extracting and canceling out 2.

$$\frac{637}{34353}-\frac{\frac{1\times 9+2}{9}}{-6}$$

Express \frac{\frac{1\times 9+2}{9}}{-6} as a single fraction.

$$\frac{637}{34353}-\frac{1\times 9+2}{9\left(-6\right)}$$

Multiply 1 and 9 to get 9.

$$\frac{637}{34353}-\frac{9+2}{9\left(-6\right)}$$

Add 9 and 2 to get 11.

$$\frac{637}{34353}-\frac{11}{9\left(-6\right)}$$

Multiply 9 and -6 to get -54.

$$\frac{637}{34353}-\frac{11}{-54}$$

Fraction \frac{11}{-54} can be rewritten as -\frac{11}{54} by extracting the negative sign.

$$\frac{637}{34353}-\left(-\frac{11}{54}\right)$$

The opposite of -\frac{11}{54} is \frac{11}{54}.

$$\frac{637}{34353}+\frac{11}{54}$$

Least common multiple of 34353 and 54 is 206118. Convert \frac{637}{34353} and \frac{11}{54} to fractions with denominator 206118.

$$\frac{3822}{206118}+\frac{41987}{206118}$$

Since \frac{3822}{206118} and \frac{41987}{206118} have the same denominator, add them by adding their numerators.

$$\frac{3822+41987}{206118}$$

Add 3822 and 41987 to get 45809.

$$\frac{45809}{206118}$$

Factor

$$\frac{19 \cdot 2411}{2 \cdot 3 ^ {3} \cdot 11 \cdot 347} = 0.2222464801715522$$