Basic Math Examples

$\frac{7}{10} + 1 \frac{7}{15}$

Step 1

Convert $1 \frac{7}{15}$ to an improper fraction.

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Step 1.1

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

$\frac{7}{10} + 1 + \frac{7}{15}$

Step 1.2

Add $1$ and $\frac{7}{15}$ .

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Step 1.2.1

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

$\frac{7}{10} + \frac{15}{15} + \frac{7}{15}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{7}{10} + \frac{15 + 7}{15}$

Step 1.2.3

Add $15$ and $7$ .

$\frac{7}{10} + \frac{22}{15}$

Step 2

To write $\frac{7}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{10} \cdot \frac{3}{3} + \frac{22}{15}$

Step 3

To write $\frac{22}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7}{10} \cdot \frac{3}{3} + \frac{22}{15} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{10}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 3}{10 \cdot 3} + \frac{22}{15} \cdot \frac{2}{2}$

Step 4.2

Multiply $10$ by $3$ .

$\frac{7 \cdot 3}{30} + \frac{22}{15} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{22}{15}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 3}{30} + \frac{22 \cdot 2}{15 \cdot 2}$

Step 4.4

Multiply $15$ by $2$ .

$\frac{7 \cdot 3}{30} + \frac{22 \cdot 2}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 3 + 22 \cdot 2}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $3$ .

$\frac{21 + 22 \cdot 2}{30}$

Step 6.2

Multiply $22$ by $2$ .

$\frac{21 + 44}{30}$

Step 6.3

Add $21$ and $44$ .

$\frac{65}{30}$

Step 7

Cancel the common factor of $65$ and $30$ .

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Step 7.1

Factor $5$ out of $65$ .

$\frac{5 (13)}{30}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $5$ out of $30$ .

$\frac{5 \cdot 13}{5 \cdot 6}$

Step 7.2.2

Cancel the common factor.

$\frac{5 \cdot 13}{5 \cdot 6}$

Step 7.2.3

Rewrite the expression.

$\frac{13}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{6}$

Decimal Form:

$2.1\overline{6}$

Mixed Number Form:

$2 \frac{1}{6}$