Basic Math Examples

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

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine $2$ and $\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.2.4.2

Add $4$ and $1$ .

$\frac{{(\frac{1}{4})}^{2}}{\frac{5}{2} - \frac{3}{4} + \frac{3}{7}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $\frac{1}{4}$ .

$\frac{\frac{1^{2}}{4^{2}}}{\frac{5}{2} - \frac{3}{4} + \frac{3}{7}}$

Step 2.2

One to any power is one.

$\frac{\frac{1}{4^{2}}}{\frac{5}{2} - \frac{3}{4} + \frac{3}{7}}$

Step 2.3

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

$\frac{\frac{1}{16}}{\frac{5}{2} - \frac{3}{4} + \frac{3}{7}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{16}}{\frac{5}{2} \cdot \frac{2}{2} - \frac{3}{4} + \frac{3}{7}}$

Step 3.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$\frac{\frac{1}{16}}{\frac{5 \cdot 2}{2 \cdot 2} - \frac{3}{4} + \frac{3}{7}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{\frac{1}{16}}{\frac{5 \cdot 2}{4} - \frac{3}{4} + \frac{3}{7}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{1}{16}}{\frac{5 \cdot 2 - 3}{4} + \frac{3}{7}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $5$ by $2$ .

$\frac{\frac{1}{16}}{\frac{10 - 3}{4} + \frac{3}{7}}$

Step 3.4.2

Subtract $3$ from $10$ .

$\frac{\frac{1}{16}}{\frac{7}{4} + \frac{3}{7}}$

Step 3.5

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

$\frac{\frac{1}{16}}{\frac{7}{4} \cdot \frac{7}{7} + \frac{3}{7}}$

Step 3.6

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

$\frac{\frac{1}{16}}{\frac{7}{4} \cdot \frac{7}{7} + \frac{3}{7} \cdot \frac{4}{4}}$

Step 3.7

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

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Step 3.7.1

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

$\frac{\frac{1}{16}}{\frac{7 \cdot 7}{4 \cdot 7} + \frac{3}{7} \cdot \frac{4}{4}}$

Step 3.7.2

Multiply $4$ by $7$ .

$\frac{\frac{1}{16}}{\frac{7 \cdot 7}{28} + \frac{3}{7} \cdot \frac{4}{4}}$

Step 3.7.3

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

$\frac{\frac{1}{16}}{\frac{7 \cdot 7}{28} + \frac{3 \cdot 4}{7 \cdot 4}}$

Step 3.7.4

Multiply $7$ by $4$ .

$\frac{\frac{1}{16}}{\frac{7 \cdot 7}{28} + \frac{3 \cdot 4}{28}}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{\frac{1}{16}}{\frac{7 \cdot 7 + 3 \cdot 4}{28}}$

Step 3.9

Simplify the numerator.

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Step 3.9.1

Multiply $7$ by $7$ .

$\frac{\frac{1}{16}}{\frac{49 + 3 \cdot 4}{28}}$

Step 3.9.2

Multiply $3$ by $4$ .

$\frac{\frac{1}{16}}{\frac{49 + 12}{28}}$

Step 3.9.3

Add $49$ and $12$ .

$\frac{\frac{1}{16}}{\frac{61}{28}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{16} \cdot \frac{28}{61}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $16$ .

$\frac{1}{4 (4)} \cdot \frac{28}{61}$

Step 5.2

Factor $4$ out of $28$ .

$\frac{1}{4 \cdot 4} \cdot \frac{4 \cdot 7}{61}$

Step 5.3

Cancel the common factor.

$\frac{1}{4 \cdot 4} \cdot \frac{4 \cdot 7}{61}$

Step 5.4

Rewrite the expression.

$\frac{1}{4} \cdot \frac{7}{61}$

Step 6

Multiply $\frac{1}{4}$ by $\frac{7}{61}$ .

$\frac{7}{4 \cdot 61}$

Step 7

Multiply $4$ by $61$ .

$\frac{7}{244}$