Basic Math Examples

$(\frac{3}{7} + \frac{7}{3}) \cdot \frac{5}{6}$

Step 1

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

$(\frac{3}{7} \cdot \frac{3}{3} + \frac{7}{3}) \cdot \frac{5}{6}$

Step 2

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

$(\frac{3}{7} \cdot \frac{3}{3} + \frac{7}{3} \cdot \frac{7}{7}) \cdot \frac{5}{6}$

Step 3

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$(\frac{3 \cdot 3}{7 \cdot 3} + \frac{7}{3} \cdot \frac{7}{7}) \cdot \frac{5}{6}$

Step 3.2

Multiply $7$ by $3$ .

$(\frac{3 \cdot 3}{21} + \frac{7}{3} \cdot \frac{7}{7}) \cdot \frac{5}{6}$

Step 3.3

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

$(\frac{3 \cdot 3}{21} + \frac{7 \cdot 7}{3 \cdot 7}) \cdot \frac{5}{6}$

Step 3.4

Multiply $3$ by $7$ .

$(\frac{3 \cdot 3}{21} + \frac{7 \cdot 7}{21}) \cdot \frac{5}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 7 \cdot 7}{21} \cdot \frac{5}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 + 7 \cdot 7}{21} \cdot \frac{5}{6}$

Step 5.2

Multiply $7$ by $7$ .

$\frac{9 + 49}{21} \cdot \frac{5}{6}$

Step 5.3

Add $9$ and $49$ .

$\frac{58}{21} \cdot \frac{5}{6}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $58$ .

$\frac{2 (29)}{21} \cdot \frac{5}{6}$

Step 6.2

Factor $2$ out of $6$ .

$\frac{2 \cdot 29}{21} \cdot \frac{5}{2 \cdot 3}$

Step 6.3

Cancel the common factor.

$\frac{2 \cdot 29}{21} \cdot \frac{5}{2 \cdot 3}$

Step 6.4

Rewrite the expression.

$\frac{29}{21} \cdot \frac{5}{3}$

Step 7

Multiply $\frac{29}{21}$ by $\frac{5}{3}$ .

$\frac{29 \cdot 5}{21 \cdot 3}$

Step 8

Multiply.

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Step 8.1

Multiply $29$ by $5$ .

$\frac{145}{21 \cdot 3}$

Step 8.2

Multiply $21$ by $3$ .

$\frac{145}{63}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{145}{63}$

Decimal Form:

$2.30158730 \dots$

Mixed Number Form:

$2 \frac{19}{63}$