Solve -3/4*(15/4)^2+3/2*15/4+6

$$- \frac { 3 } { 4 } \times ( \frac { 15 } { 4 } ) ^ { 2 } + \frac { 3 } { 2 } \times \frac { 15 } { 4 } + 6$$

Evaluate

$$\frac{69}{64}=1.078125$$

Solution Steps

Calculate \frac{15}{4} to the power of 2 and get \frac{225}{16}.

$$-\frac{3}{4}\times \frac{225}{16}+\frac{3}{2}\times \frac{15}{4}+6$$

Multiply -\frac{3}{4} times \frac{225}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 225}{4\times 16}+\frac{3}{2}\times \frac{15}{4}+6$$

Do the multiplications in the fraction \frac{-3\times 225}{4\times 16}.

$$\frac{-675}{64}+\frac{3}{2}\times \frac{15}{4}+6$$

Fraction \frac{-675}{64} can be rewritten as -\frac{675}{64} by extracting the negative sign.

$$-\frac{675}{64}+\frac{3}{2}\times \frac{15}{4}+6$$

Multiply \frac{3}{2} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{675}{64}+\frac{3\times 15}{2\times 4}+6$$

Do the multiplications in the fraction \frac{3\times 15}{2\times 4}.

$$-\frac{675}{64}+\frac{45}{8}+6$$

Least common multiple of 64 and 8 is 64. Convert -\frac{675}{64} and \frac{45}{8} to fractions with denominator 64.

$$-\frac{675}{64}+\frac{360}{64}+6$$

Since -\frac{675}{64} and \frac{360}{64} have the same denominator, add them by adding their numerators.

$$\frac{-675+360}{64}+6$$

Add -675 and 360 to get -315.

$$-\frac{315}{64}+6$$

Convert 6 to fraction \frac{384}{64}.

$$-\frac{315}{64}+\frac{384}{64}$$

Since -\frac{315}{64} and \frac{384}{64} have the same denominator, add them by adding their numerators.

$$\frac{-315+384}{64}$$

Add -315 and 384 to get 69.

$$\frac{69}{64}$$

Factor

$$\frac{3 \cdot 23}{2 ^ {6}} = 1\frac{5}{64} = 1.078125$$