Solve |9/2+4/3|*sqrt{4/11*9/25*frac{1}{11}}

$$| \frac { 9 } { 2 } + \frac { 4 } { 3 } | \cdot \sqrt { \frac { 4 } { 11 } \cdot \frac { 9 } { 25 } \cdot \frac { 1 } { 11 } }$$

Evaluate

$$\frac{7}{11}\approx 0.636363636$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{4}{3} to fractions with denominator 6.

$$|\frac{27}{6}+\frac{8}{6}|\sqrt{\frac{4}{11}\times \frac{9}{25}\times \frac{1}{11}}$$

Since \frac{27}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$|\frac{27+8}{6}|\sqrt{\frac{4}{11}\times \frac{9}{25}\times \frac{1}{11}}$$

Add 27 and 8 to get 35.

$$|\frac{35}{6}|\sqrt{\frac{4}{11}\times \frac{9}{25}\times \frac{1}{11}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{35}{6} is \frac{35}{6}.

$$\frac{35}{6}\sqrt{\frac{4}{11}\times \frac{9}{25}\times \frac{1}{11}}$$

Multiply \frac{4}{11} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{6}\sqrt{\frac{4\times 9}{11\times 25}\times \frac{1}{11}}$$

Do the multiplications in the fraction \frac{4\times 9}{11\times 25}.

$$\frac{35}{6}\sqrt{\frac{36}{275}\times \frac{1}{11}}$$

Multiply \frac{36}{275} times \frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{6}\sqrt{\frac{36\times 1}{275\times 11}}$$

Do the multiplications in the fraction \frac{36\times 1}{275\times 11}.

$$\frac{35}{6}\sqrt{\frac{36}{3025}}$$

Rewrite the square root of the division \frac{36}{3025} as the division of square roots \frac{\sqrt{36}}{\sqrt{3025}}. Take the square root of both numerator and denominator.

$$\frac{35}{6}\times \frac{6}{55}$$

Multiply \frac{35}{6} times \frac{6}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 6}{6\times 55}$$

Cancel out 6 in both numerator and denominator.

$$\frac{35}{55}$$

Reduce the fraction \frac{35}{55} to lowest terms by extracting and canceling out 5.

$$\frac{7}{11}$$

Factor

$$\frac{7}{11} = 0.6363636363636364$$