Solve 175.25-13.625/1.5^2+0.5^2+0.5^2+1.5^2*2.5

$$175.25- \frac{ 13.625 }{ { 1.5 }^{ 2 } + { 0.5 }^{ 2 } + { 0.5 }^{ 2 } + { 1.5 }^{ 2 } } \times 2.5$$

Evaluate

$$168.4375$$

Solution Steps

Calculate 1.5 to the power of 2 and get 2.25.

$$175.25-\frac{13.625}{2.25+0.5^{2}+0.5^{2}+1.5^{2}}\times 2.5$$

Calculate 0.5 to the power of 2 and get 0.25.

$$175.25-\frac{13.625}{2.25+0.25+0.5^{2}+1.5^{2}}\times 2.5$$

Add 2.25 and 0.25 to get 2.5.

$$175.25-\frac{13.625}{2.5+0.5^{2}+1.5^{2}}\times 2.5$$

Calculate 0.5 to the power of 2 and get 0.25.

$$175.25-\frac{13.625}{2.5+0.25+1.5^{2}}\times 2.5$$

Add 2.5 and 0.25 to get 2.75.

$$175.25-\frac{13.625}{2.75+1.5^{2}}\times 2.5$$

Calculate 1.5 to the power of 2 and get 2.25.

$$175.25-\frac{13.625}{2.75+2.25}\times 2.5$$

Add 2.75 and 2.25 to get 5.

$$175.25-\frac{13.625}{5}\times 2.5$$

Expand \frac{13.625}{5} by multiplying both numerator and the denominator by 1000.

$$175.25-\frac{13625}{5000}\times 2.5$$

Reduce the fraction \frac{13625}{5000} to lowest terms by extracting and canceling out 125.

$$175.25-\frac{109}{40}\times 2.5$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$175.25-\frac{109}{40}\times \frac{5}{2}$$

Multiply \frac{109}{40} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$175.25-\frac{109\times 5}{40\times 2}$$

Do the multiplications in the fraction \frac{109\times 5}{40\times 2}.

$$175.25-\frac{545}{80}$$

Reduce the fraction \frac{545}{80} to lowest terms by extracting and canceling out 5.

$$175.25-\frac{109}{16}$$

Convert decimal number 175.25 to fraction \frac{17525}{100}. Reduce the fraction \frac{17525}{100} to lowest terms by extracting and canceling out 25.

$$\frac{701}{4}-\frac{109}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{701}{4} and \frac{109}{16} to fractions with denominator 16.

$$\frac{2804}{16}-\frac{109}{16}$$

Since \frac{2804}{16} and \frac{109}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2804-109}{16}$$

Subtract 109 from 2804 to get 2695.

$$\frac{2695}{16}$$

Factor

$$\frac{5 \cdot 11 \cdot 7 ^ {2}}{2 ^ {4}} = 168\frac{7}{16} = 168.4375$$