Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $2$ .

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

Step 1.3.3

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

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

Step 1.3.4

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

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

Step 1.5.2

Add $4$ and $3$ .

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

Step 1.6

Apply the product rule to $\frac{7}{6}$ .

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

Step 1.7

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

$\frac{7}{3} - \frac{1}{4} \cdot \frac{49}{6^{2}}$

Step 1.8

Raise $6$ to the power of $2$ .

$\frac{7}{3} - \frac{1}{4} \cdot \frac{49}{36}$

Step 1.9

Multiply $- \frac{1}{4} \cdot \frac{49}{36}$ .

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Step 1.9.1

Multiply $\frac{49}{36}$ by $\frac{1}{4}$ .

$\frac{7}{3} - \frac{49}{36 \cdot 4}$

Step 1.9.2

Multiply $36$ by $4$ .

$\frac{7}{3} - \frac{49}{144}$

Step 2

To write $\frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{48}{48}$ .

$\frac{7}{3} \cdot \frac{48}{48} - \frac{49}{144}$

Step 3

Write each expression with a common denominator of $144$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{3}$ by $\frac{48}{48}$ .

$\frac{7 \cdot 48}{3 \cdot 48} - \frac{49}{144}$

Step 3.2

Multiply $3$ by $48$ .

$\frac{7 \cdot 48}{144} - \frac{49}{144}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 48 - 49}{144}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $48$ .

$\frac{336 - 49}{144}$

Step 5.2

Subtract $49$ from $336$ .

$\frac{287}{144}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{287}{144}$

Decimal Form:

$1.9930\overline{5}$

Mixed Number Form:

$1 \frac{143}{144}$