Basic Math Examples

$\frac{1}{4} \div \frac{4}{7} + 20 \cdot \frac{1}{16}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{4} \cdot \frac{7}{4} + 20 \cdot \frac{1}{16}$

Step 1.2

Multiply $\frac{1}{4} \cdot \frac{7}{4}$ .

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Step 1.2.1

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

$\frac{7}{4 \cdot 4} + 20 \cdot \frac{1}{16}$

Step 1.2.2

Multiply $4$ by $4$ .

$\frac{7}{16} + 20 \cdot \frac{1}{16}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $20$ .

$\frac{7}{16} + 4 (5) \cdot \frac{1}{16}$

Step 1.3.2

Factor $4$ out of $16$ .

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

Step 1.3.3

Cancel the common factor.

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

Step 1.3.4

Rewrite the expression.

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

Step 1.4

Combine $5$ and $\frac{1}{4}$ .

$\frac{7}{16} + \frac{5}{4}$

Step 2

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{16} + \frac{5}{4} \cdot \frac{4}{4}$

Step 3

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

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Step 3.1

Multiply $\frac{5}{4}$ by $\frac{4}{4}$ .

$\frac{7}{16} + \frac{5 \cdot 4}{4 \cdot 4}$

Step 3.2

Multiply $4$ by $4$ .

$\frac{7}{16} + \frac{5 \cdot 4}{16}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 + 5 \cdot 4}{16}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $4$ .

$\frac{7 + 20}{16}$

Step 5.2

Add $7$ and $20$ .

$\frac{27}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{16}$

Decimal Form:

$1.6875$

Mixed Number Form:

$1 \frac{11}{16}$