Basic Math Examples

$16 \frac{1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1

Convert $16 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$16 + \frac{1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1.2

Add $16$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$16 \cdot \frac{2}{2} + \frac{1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1.2.2

Combine $16$ and $\frac{2}{2}$ .

$\frac{16 \cdot 2}{2} + \frac{1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 + 1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $16$ by $2$ .

$\frac{32 + 1}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 1.2.4.2

Add $32$ and $1$ .

$\frac{33}{2} - (1 \frac{1}{4} + 4 \frac{1}{8})$

Step 2

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{33}{2} - (1 + \frac{1}{4} + 4 \frac{1}{8})$

Step 2.2

Add $1$ and $\frac{1}{4}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{33}{2} - (\frac{4}{4} + \frac{1}{4} + 4 \frac{1}{8})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{33}{2} - (\frac{4 + 1}{4} + 4 \frac{1}{8})$

Step 2.2.3

Add $4$ and $1$ .

$\frac{33}{2} - (\frac{5}{4} + 4 \frac{1}{8})$

Step 3

Convert $4 \frac{1}{8}$ to an improper fraction.

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Step 3.1

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

$\frac{33}{2} - (\frac{5}{4} + 4 + \frac{1}{8})$

Step 3.2

Add $4$ and $\frac{1}{8}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{33}{2} - (\frac{5}{4} + 4 \cdot \frac{8}{8} + \frac{1}{8})$

Step 3.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{33}{2} - (\frac{5}{4} + \frac{4 \cdot 8}{8} + \frac{1}{8})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{33}{2} - (\frac{5}{4} + \frac{4 \cdot 8 + 1}{8})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $8$ .

$\frac{33}{2} - (\frac{5}{4} + \frac{32 + 1}{8})$

Step 3.2.4.2

Add $32$ and $1$ .

$\frac{33}{2} - (\frac{5}{4} + \frac{33}{8})$

Step 4

Simplify each term.

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Step 4.1

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{33}{2} - (\frac{5}{4} \cdot \frac{2}{2} + \frac{33}{8})$

Step 4.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1

Multiply $\frac{5}{4}$ by $\frac{2}{2}$ .

$\frac{33}{2} - (\frac{5 \cdot 2}{4 \cdot 2} + \frac{33}{8})$

Step 4.2.2

Multiply $4$ by $2$ .

$\frac{33}{2} - (\frac{5 \cdot 2}{8} + \frac{33}{8})$

Step 4.3

Combine the numerators over the common denominator.

$\frac{33}{2} - \frac{5 \cdot 2 + 33}{8}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $5$ by $2$ .

$\frac{33}{2} - \frac{10 + 33}{8}$

Step 4.4.2

Add $10$ and $33$ .

$\frac{33}{2} - \frac{43}{8}$

Step 5

To write $\frac{33}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{33}{2} \cdot \frac{4}{4} - \frac{43}{8}$

Step 6

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{33}{2}$ by $\frac{4}{4}$ .

$\frac{33 \cdot 4}{2 \cdot 4} - \frac{43}{8}$

Step 6.2

Multiply $2$ by $4$ .

$\frac{33 \cdot 4}{8} - \frac{43}{8}$

Step 7

Combine the numerators over the common denominator.

$\frac{33 \cdot 4 - 43}{8}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $33$ by $4$ .

$\frac{132 - 43}{8}$

Step 8.2

Subtract $43$ from $132$ .

$\frac{89}{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{89}{8}$

Decimal Form:

$11.125$

Mixed Number Form:

$11 \frac{1}{8}$