Basic Math Examples

$3 \frac{8}{7} + 1 \frac{3}{6}$

Step 1

Convert $3 \frac{8}{7}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{8}{7} + 1 \frac{3}{6}$

Step 1.2

Add $3$ and $\frac{8}{7}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$3 \cdot \frac{7}{7} + \frac{8}{7} + 1 \frac{3}{6}$

Step 1.2.2

Combine $3$ and $\frac{7}{7}$ .

$\frac{3 \cdot 7}{7} + \frac{8}{7} + 1 \frac{3}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 + 8}{7} + 1 \frac{3}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $7$ .

$\frac{21 + 8}{7} + 1 \frac{3}{6}$

Step 1.2.4.2

Add $21$ and $8$ .

$\frac{29}{7} + 1 \frac{3}{6}$

Step 2

Convert $1 \frac{3}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{29}{7} + 1 + \frac{3}{6}$

Step 2.2

Add $1$ and $\frac{3}{6}$ .

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Step 2.2.1

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

$\frac{29}{7} + \frac{6}{6} + \frac{3}{6}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{29}{7} + \frac{6 + 3}{6}$

Step 2.2.3

Add $6$ and $3$ .

$\frac{29}{7} + \frac{9}{6}$

Step 3

Cancel the common factor of $9$ and $6$ .

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Step 3.1

Factor $3$ out of $9$ .

$\frac{29}{7} + \frac{3 (3)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6$ .

$\frac{29}{7} + \frac{3 \cdot 3}{3 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\frac{29}{7} + \frac{3 \cdot 3}{3 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\frac{29}{7} + \frac{3}{2}$

Step 4

To write $\frac{29}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{29}{7} \cdot \frac{2}{2} + \frac{3}{2}$

Step 5

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{29}{7} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{7}{7}$

Step 6

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{29}{7}$ by $\frac{2}{2}$ .

$\frac{29 \cdot 2}{7 \cdot 2} + \frac{3}{2} \cdot \frac{7}{7}$

Step 6.2

Multiply $7$ by $2$ .

$\frac{29 \cdot 2}{14} + \frac{3}{2} \cdot \frac{7}{7}$

Step 6.3

Multiply $\frac{3}{2}$ by $\frac{7}{7}$ .

$\frac{29 \cdot 2}{14} + \frac{3 \cdot 7}{2 \cdot 7}$

Step 6.4

Multiply $2$ by $7$ .

$\frac{29 \cdot 2}{14} + \frac{3 \cdot 7}{14}$

Step 7

Combine the numerators over the common denominator.

$\frac{29 \cdot 2 + 3 \cdot 7}{14}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $29$ by $2$ .

$\frac{58 + 3 \cdot 7}{14}$

Step 8.2

Multiply $3$ by $7$ .

$\frac{58 + 21}{14}$

Step 8.3

Add $58$ and $21$ .

$\frac{79}{14}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{79}{14}$

Decimal Form:

$5.64285714 \dots$

Mixed Number Form:

$5 \frac{9}{14}$