Basic Math Examples

$6 \frac{5}{6} + 3 \frac{1}{4}$

Step 1

Convert $6 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$6 + \frac{5}{6} + 3 \frac{1}{4}$

Step 1.2

Add $6$ and $\frac{5}{6}$ .

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Step 1.2.1

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

$6 \cdot \frac{6}{6} + \frac{5}{6} + 3 \frac{1}{4}$

Step 1.2.2

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

$\frac{6 \cdot 6}{6} + \frac{5}{6} + 3 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 6 + 5}{6} + 3 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $6$ .

$\frac{36 + 5}{6} + 3 \frac{1}{4}$

Step 1.2.4.2

Add $36$ and $5$ .

$\frac{41}{6} + 3 \frac{1}{4}$

Step 2

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{41}{6} + 3 + \frac{1}{4}$

Step 2.2

Add $3$ and $\frac{1}{4}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{41}{6} + 3 \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{41}{6} + \frac{3 \cdot 4}{4} + \frac{1}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{41}{6} + \frac{3 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $4$ .

$\frac{41}{6} + \frac{12 + 1}{4}$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{41}{6} + \frac{13}{4}$

Step 3

To write $\frac{41}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{41}{6} \cdot \frac{2}{2} + \frac{13}{4}$

Step 4

To write $\frac{13}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{41}{6} \cdot \frac{2}{2} + \frac{13}{4} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{41}{6}$ by $\frac{2}{2}$ .

$\frac{41 \cdot 2}{6 \cdot 2} + \frac{13}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply $6$ by $2$ .

$\frac{41 \cdot 2}{12} + \frac{13}{4} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{13}{4}$ by $\frac{3}{3}$ .

$\frac{41 \cdot 2}{12} + \frac{13 \cdot 3}{4 \cdot 3}$

Step 5.4

Multiply $4$ by $3$ .

$\frac{41 \cdot 2}{12} + \frac{13 \cdot 3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{41 \cdot 2 + 13 \cdot 3}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $41$ by $2$ .

$\frac{82 + 13 \cdot 3}{12}$

Step 7.2

Multiply $13$ by $3$ .

$\frac{82 + 39}{12}$

Step 7.3

Add $82$ and $39$ .

$\frac{121}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{121}{12}$

Decimal Form:

$10.08\overline{3}$

Mixed Number Form:

$10 \frac{1}{12}$