Evaluate (((7/4)^2-7/4*3/2)/5)/12-(11/24)/(1/2)

$\frac{\frac{{(\frac{7}{4})}^{2} - \frac{7}{4} \cdot \frac{3}{2}}{5}}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Step 1

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$\frac{{(\frac{7}{4})}^{2} - \frac{7}{4} \cdot \frac{3}{2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Simplify the numerator.

Apply the product rule to $\frac{7}{4}$ .

$\frac{\frac{7^{2}}{4^{2}} - \frac{7}{4} \cdot \frac{3}{2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Raise $7$ to the power of $2$ .

$\frac{\frac{49}{4^{2}} - \frac{7}{4} \cdot \frac{3}{2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Raise $4$ to the power of $2$ .

$\frac{\frac{49}{16} - \frac{7}{4} \cdot \frac{3}{2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $- \frac{7}{4} \cdot \frac{3}{2}$ .

Multiply $\frac{3}{2}$ by $\frac{7}{4}$ .

$\frac{\frac{49}{16} - \frac{3 \cdot 7}{2 \cdot 4}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $3$ by $7$ .

$\frac{\frac{49}{16} - \frac{21}{2 \cdot 4}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $2$ by $4$ .

$\frac{\frac{49}{16} - \frac{21}{8}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

To write $- \frac{21}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{49}{16} - \frac{21}{8} \cdot \frac{2}{2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{21}{8}$ by $\frac{2}{2}$ .

$\frac{\frac{49}{16} - \frac{21 \cdot 2}{8 \cdot 2}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $8$ by $2$ .

$\frac{\frac{49}{16} - \frac{21 \cdot 2}{16}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Combine the numerators over the common denominator.

$\frac{\frac{49 - 21 \cdot 2}{16}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Simplify the numerator.

Multiply $- 21$ by $2$ .

$\frac{\frac{49 - 42}{16}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Subtract $42$ from $49$ .

$\frac{\frac{7}{16}}{5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{16} \cdot \frac{1}{5} \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $\frac{7}{16} \cdot \frac{1}{5}$ .

Multiply $\frac{7}{16}$ by $\frac{1}{5}$ .

$\frac{7}{16 \cdot 5} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $16$ by $5$ .

$\frac{7}{80} \cdot \frac{1}{12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $\frac{7}{80} \cdot \frac{1}{12}$ .

Multiply $\frac{7}{80}$ by $\frac{1}{12}$ .

$\frac{7}{80 \cdot 12} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply $80$ by $12$ .

$\frac{7}{960} - \frac{\frac{11}{24}}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{960} - (\frac{11}{24} \cdot 2)$

Cancel the common factor of $2$ .

Factor $2$ out of $24$ .

$\frac{7}{960} - (\frac{11}{2 (12)} \cdot 2)$

Cancel the common factor.

$\frac{7}{960} - (\frac{11}{2 \cdot 12} \cdot 2)$

Rewrite the expression.

$\frac{7}{960} - \frac{11}{12}$

Step 2

To write $- \frac{11}{12}$ as a fraction with a common denominator, multiply by $\frac{80}{80}$ .

$\frac{7}{960} - \frac{11}{12} \cdot \frac{80}{80}$

Step 3

Write each expression with a common denominator of $960$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{12}$ by $\frac{80}{80}$ .

$\frac{7}{960} - \frac{11 \cdot 80}{12 \cdot 80}$

Multiply $12$ by $80$ .

$\frac{7}{960} - \frac{11 \cdot 80}{960}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 - 11 \cdot 80}{960}$

Step 5

Simplify the numerator.

Multiply $- 11$ by $80$ .

$\frac{7 - 880}{960}$

Subtract $880$ from $7$ .

$\frac{- 873}{960}$

Step 6

Cancel the common factor of $- 873$ and $960$ .

Factor $3$ out of $- 873$ .

$\frac{3 (- 291)}{960}$

Cancel the common factors.

Factor $3$ out of $960$ .

$\frac{3 \cdot - 291}{3 \cdot 320}$

Cancel the common factor.

$\frac{3 \cdot - 291}{3 \cdot 320}$

Rewrite the expression.

$\frac{- 291}{320}$

Step 7

Move the negative in front of the fraction.

$- \frac{291}{320}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{291}{320}$

Decimal Form:

$- 0.909375$

Evaluate (((7/4)^2-7/4*3/2)/5)/12-(11/24)/(1/2)

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