Basic Math Examples

$14 \frac{1}{3} + 16 + 6 \frac{1}{2}$

Step 1

Convert $14 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$14 + \frac{1}{3} + 16 + 6 \frac{1}{2}$

Step 1.2

Add $14$ and $\frac{1}{3}$ .

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Step 1.2.1

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

$14 \cdot \frac{3}{3} + \frac{1}{3} + 16 + 6 \frac{1}{2}$

Step 1.2.2

Combine $14$ and $\frac{3}{3}$ .

$\frac{14 \cdot 3}{3} + \frac{1}{3} + 16 + 6 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{14 \cdot 3 + 1}{3} + 16 + 6 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $14$ by $3$ .

$\frac{42 + 1}{3} + 16 + 6 \frac{1}{2}$

Step 1.2.4.2

Add $42$ and $1$ .

$\frac{43}{3} + 16 + 6 \frac{1}{2}$

Step 2

Convert $6 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{43}{3} + 16 + 6 + \frac{1}{2}$

Step 2.2

Add $6$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{43}{3} + 16 + 6 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{43}{3} + 16 + \frac{6 \cdot 2}{2} + \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{43}{3} + 16 + \frac{6 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $6$ by $2$ .

$\frac{43}{3} + 16 + \frac{12 + 1}{2}$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{43}{3} + 16 + \frac{13}{2}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{43}{3}$ by $\frac{2}{2}$ .

$\frac{43}{3} \cdot \frac{2}{2} + 16 + \frac{13}{2}$

Step 3.2

Multiply $\frac{43}{3}$ by $\frac{2}{2}$ .

$\frac{43 \cdot 2}{3 \cdot 2} + 16 + \frac{13}{2}$

Step 3.3

Write $16$ as a fraction with denominator $1$ .

$\frac{43 \cdot 2}{3 \cdot 2} + \frac{16}{1} + \frac{13}{2}$

Step 3.4

Multiply $\frac{16}{1}$ by $\frac{6}{6}$ .

$\frac{43 \cdot 2}{3 \cdot 2} + \frac{16}{1} \cdot \frac{6}{6} + \frac{13}{2}$

Step 3.5

Multiply $\frac{16}{1}$ by $\frac{6}{6}$ .

$\frac{43 \cdot 2}{3 \cdot 2} + \frac{16 \cdot 6}{6} + \frac{13}{2}$

Step 3.6

Multiply $\frac{13}{2}$ by $\frac{3}{3}$ .

$\frac{43 \cdot 2}{3 \cdot 2} + \frac{16 \cdot 6}{6} + \frac{13}{2} \cdot \frac{3}{3}$

Step 3.7

Multiply $\frac{13}{2}$ by $\frac{3}{3}$ .

$\frac{43 \cdot 2}{3 \cdot 2} + \frac{16 \cdot 6}{6} + \frac{13 \cdot 3}{2 \cdot 3}$

Step 3.8

Reorder the factors of $3 \cdot 2$ .

$\frac{43 \cdot 2}{2 \cdot 3} + \frac{16 \cdot 6}{6} + \frac{13 \cdot 3}{2 \cdot 3}$

Step 3.9

Multiply $2$ by $3$ .

$\frac{43 \cdot 2}{6} + \frac{16 \cdot 6}{6} + \frac{13 \cdot 3}{2 \cdot 3}$

Step 3.10

Multiply $2$ by $3$ .

$\frac{43 \cdot 2}{6} + \frac{16 \cdot 6}{6} + \frac{13 \cdot 3}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{43 \cdot 2 + 16 \cdot 6 + 13 \cdot 3}{6}$

Step 5

Simplify each term.

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Step 5.1

Multiply $43$ by $2$ .

$\frac{86 + 16 \cdot 6 + 13 \cdot 3}{6}$

Step 5.2

Multiply $16$ by $6$ .

$\frac{86 + 96 + 13 \cdot 3}{6}$

Step 5.3

Multiply $13$ by $3$ .

$\frac{86 + 96 + 39}{6}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $86$ and $96$ .

$\frac{182 + 39}{6}$

Step 6.2

Add $182$ and $39$ .

$\frac{221}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{221}{6}$

Decimal Form:

$36.8\overline{3}$

Mixed Number Form:

$36 \frac{5}{6}$