Basic Math Examples

$20 \frac{3}{6} - 13 \frac{6}{8}$

Step 1

Convert $20 \frac{3}{6}$ to an improper fraction.

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Step 1.1

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

$20 + \frac{3}{6} - 13 \frac{6}{8}$

Step 1.2

Add $20$ and $\frac{3}{6}$ .

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Step 1.2.1

To write $20$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$20 \cdot \frac{6}{6} + \frac{3}{6} - 13 \frac{6}{8}$

Step 1.2.2

Combine $20$ and $\frac{6}{6}$ .

$\frac{20 \cdot 6}{6} + \frac{3}{6} - 13 \frac{6}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{20 \cdot 6 + 3}{6} - 13 \frac{6}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $20$ by $6$ .

$\frac{120 + 3}{6} - 13 \frac{6}{8}$

Step 1.2.4.2

Add $120$ and $3$ .

$\frac{123}{6} - 13 \frac{6}{8}$

Step 2

Convert $13 \frac{6}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{123}{6} - (13 + \frac{6}{8})$

Step 2.2

Add $13$ and $\frac{6}{8}$ .

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Step 2.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{123}{6} - (13 \cdot \frac{8}{8} + \frac{6}{8})$

Step 2.2.2

Combine $13$ and $\frac{8}{8}$ .

$\frac{123}{6} - (\frac{13 \cdot 8}{8} + \frac{6}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{123}{6} - \frac{13 \cdot 8 + 6}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $13$ by $8$ .

$\frac{123}{6} - \frac{104 + 6}{8}$

Step 2.2.4.2

Add $104$ and $6$ .

$\frac{123}{6} - \frac{110}{8}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $123$ and $6$ .

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Step 3.1.1

Factor $3$ out of $123$ .

$\frac{3 (41)}{6} - \frac{110}{8}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 41}{3 \cdot 2} - \frac{110}{8}$

Step 3.1.2.2

Cancel the common factor.

$\frac{3 \cdot 41}{3 \cdot 2} - \frac{110}{8}$

Step 3.1.2.3

Rewrite the expression.

$\frac{41}{2} - \frac{110}{8}$

Step 3.2

Cancel the common factor of $110$ and $8$ .

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Step 3.2.1

Factor $2$ out of $110$ .

$\frac{41}{2} - \frac{2 (55)}{8}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $8$ .

$\frac{41}{2} - \frac{2 \cdot 55}{2 \cdot 4}$

Step 3.2.2.2

Cancel the common factor.

$\frac{41}{2} - \frac{2 \cdot 55}{2 \cdot 4}$

Step 3.2.2.3

Rewrite the expression.

$\frac{41}{2} - \frac{55}{4}$

Step 4

To write $\frac{41}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{41}{2} \cdot \frac{2}{2} - \frac{55}{4}$

Step 5

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

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Step 5.1

Multiply $\frac{41}{2}$ by $\frac{2}{2}$ .

$\frac{41 \cdot 2}{2 \cdot 2} - \frac{55}{4}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{41 \cdot 2}{4} - \frac{55}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{41 \cdot 2 - 55}{4}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $41$ by $2$ .

$\frac{82 - 55}{4}$

Step 7.2

Subtract $55$ from $82$ .

$\frac{27}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{4}$

Decimal Form:

$6.75$

Mixed Number Form:

$6 \frac{3}{4}$