Basic Math Examples

$6 \frac{2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1

Convert $6 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$6 + \frac{2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1.2

Add $6$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 \cdot \frac{3}{3} + \frac{2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1.2.2

Combine $6$ and $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $3$ .

$\frac{18 + 2}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 1.2.4.2

Add $18$ and $2$ .

$\frac{20}{3} + 6 + 5 + 7 \frac{1}{2}$

Step 2

Convert $7 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{20}{3} + 6 + 5 + 7 + \frac{1}{2}$

Step 2.2

Add $7$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{20}{3} + 6 + 5 + 7 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine $7$ and $\frac{2}{2}$ .

$\frac{20}{3} + 6 + 5 + \frac{7 \cdot 2}{2} + \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{20}{3} + 6 + 5 + \frac{7 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $2$ .

$\frac{20}{3} + 6 + 5 + \frac{14 + 1}{2}$

Step 2.2.4.2

Add $14$ and $1$ .

$\frac{20}{3} + 6 + 5 + \frac{15}{2}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{20}{3}$ by $\frac{2}{2}$ .

$\frac{20}{3} \cdot \frac{2}{2} + 6 + 5 + \frac{15}{2}$

Step 3.2

Multiply $\frac{20}{3}$ by $\frac{2}{2}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + 6 + 5 + \frac{15}{2}$

Step 3.3

Write $6$ as a fraction with denominator $1$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6}{1} + 5 + \frac{15}{2}$

Step 3.4

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

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6}{1} \cdot \frac{6}{6} + 5 + \frac{15}{2}$

Step 3.5

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

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + 5 + \frac{15}{2}$

Step 3.6

Write $5$ as a fraction with denominator $1$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + \frac{5}{1} + \frac{15}{2}$

Step 3.7

Multiply $\frac{5}{1}$ by $\frac{6}{6}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + \frac{5}{1} \cdot \frac{6}{6} + \frac{15}{2}$

Step 3.8

Multiply $\frac{5}{1}$ by $\frac{6}{6}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15}{2}$

Step 3.9

Multiply $\frac{15}{2}$ by $\frac{3}{3}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15}{2} \cdot \frac{3}{3}$

Step 3.10

Multiply $\frac{15}{2}$ by $\frac{3}{3}$ .

$\frac{20 \cdot 2}{3 \cdot 2} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15 \cdot 3}{2 \cdot 3}$

Step 3.11

Reorder the factors of $3 \cdot 2$ .

$\frac{20 \cdot 2}{2 \cdot 3} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15 \cdot 3}{2 \cdot 3}$

Step 3.12

Multiply $2$ by $3$ .

$\frac{20 \cdot 2}{6} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15 \cdot 3}{2 \cdot 3}$

Step 3.13

Multiply $2$ by $3$ .

$\frac{20 \cdot 2}{6} + \frac{6 \cdot 6}{6} + \frac{5 \cdot 6}{6} + \frac{15 \cdot 3}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{20 \cdot 2 + 6 \cdot 6 + 5 \cdot 6 + 15 \cdot 3}{6}$

Step 5

Simplify each term.

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Step 5.1

Multiply $20$ by $2$ .

$\frac{40 + 6 \cdot 6 + 5 \cdot 6 + 15 \cdot 3}{6}$

Step 5.2

Multiply $6$ by $6$ .

$\frac{40 + 36 + 5 \cdot 6 + 15 \cdot 3}{6}$

Step 5.3

Multiply $5$ by $6$ .

$\frac{40 + 36 + 30 + 15 \cdot 3}{6}$

Step 5.4

Multiply $15$ by $3$ .

$\frac{40 + 36 + 30 + 45}{6}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $40$ and $36$ .

$\frac{76 + 30 + 45}{6}$

Step 6.2

Add $76$ and $30$ .

$\frac{106 + 45}{6}$

Step 6.3

Add $106$ and $45$ .

$\frac{151}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{151}{6}$

Decimal Form:

$25.1\overline{6}$

Mixed Number Form:

$25 \frac{1}{6}$