Evaluate 3/4-6/7(1/2)^2

$\frac{3}{4} - \frac{6}{7} {(\frac{1}{2})}^{2}$

Step 1

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

$\frac{3}{4} - \frac{6}{7} \cdot \frac{1^{2}}{2^{2}}$

One to any power is one.

$\frac{3}{4} - \frac{6}{7} \cdot \frac{1}{2^{2}}$

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

$\frac{3}{4} - \frac{6}{7} \cdot \frac{1}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{6}{7}$ into the numerator.

$\frac{3}{4} + \frac{- 6}{7} \cdot \frac{1}{4}$

Factor $2$ out of $- 6$ .

$\frac{3}{4} + \frac{2 (- 3)}{7} \cdot \frac{1}{4}$

Factor $2$ out of $4$ .

$\frac{3}{4} + \frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 2}$

Cancel the common factor.

$\frac{3}{4} + \frac{2 \cdot - 3}{7} \cdot \frac{1}{2 \cdot 2}$

Rewrite the expression.

$\frac{3}{4} + \frac{- 3}{7} \cdot \frac{1}{2}$

Multiply $\frac{- 3}{7}$ by $\frac{1}{2}$ .

$\frac{3}{4} + \frac{- 3}{7 \cdot 2}$

Multiply $7$ by $2$ .

$\frac{3}{4} + \frac{- 3}{14}$

Move the negative in front of the fraction.

$\frac{3}{4} - \frac{3}{14}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3}{4} \cdot \frac{7}{7} - \frac{3}{14}$

Step 3

To write $- \frac{3}{14}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{4} \cdot \frac{7}{7} - \frac{3}{14} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 \cdot 7}{4 \cdot 7} - \frac{3}{14} \cdot \frac{2}{2}$

Multiply $4$ by $7$ .

$\frac{3 \cdot 7}{28} - \frac{3}{14} \cdot \frac{2}{2}$

Multiply $\frac{3}{14}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 7}{28} - \frac{3 \cdot 2}{14 \cdot 2}$

Multiply $14$ by $2$ .

$\frac{3 \cdot 7}{28} - \frac{3 \cdot 2}{28}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 - 3 \cdot 2}{28}$

Step 6

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{21 - 3 \cdot 2}{28}$

Multiply $- 3$ by $2$ .

$\frac{21 - 6}{28}$

Subtract $6$ from $21$ .

$\frac{15}{28}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{28}$

Decimal Form:

$0.53571428 \dots$

Evaluate 3/4-6/7(1/2)^2

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