Basic Math Examples

$\frac{3}{5}$ , $\frac{7}{8}$ , $\frac{1}{40}$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{\frac{3}{5} + \frac{7}{8} + \frac{1}{40}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{3}{5} \cdot \frac{8}{8} + \frac{7}{8} + \frac{1}{40}}{3}$

Step 2.2

To write $\frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{3}{5} \cdot \frac{8}{8} + \frac{7}{8} \cdot \frac{5}{5} + \frac{1}{40}}{3}$

Step 2.3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{3}{5}$ by $\frac{8}{8}$ .

$\frac{\frac{3 \cdot 8}{5 \cdot 8} + \frac{7}{8} \cdot \frac{5}{5} + \frac{1}{40}}{3}$

Step 2.3.2

Multiply $5$ by $8$ .

$\frac{\frac{3 \cdot 8}{40} + \frac{7}{8} \cdot \frac{5}{5} + \frac{1}{40}}{3}$

Step 2.3.3

Multiply $\frac{7}{8}$ by $\frac{5}{5}$ .

$\frac{\frac{3 \cdot 8}{40} + \frac{7 \cdot 5}{8 \cdot 5} + \frac{1}{40}}{3}$

Step 2.3.4

Multiply $8$ by $5$ .

$\frac{\frac{3 \cdot 8}{40} + \frac{7 \cdot 5}{40} + \frac{1}{40}}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{3 \cdot 8 + 7 \cdot 5}{40} + \frac{1}{40}}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $8$ .

$\frac{\frac{24 + 7 \cdot 5}{40} + \frac{1}{40}}{3}$

Step 2.5.2

Multiply $7$ by $5$ .

$\frac{\frac{24 + 35}{40} + \frac{1}{40}}{3}$

Step 2.5.3

Add $24$ and $35$ .

$\frac{\frac{59}{40} + \frac{1}{40}}{3}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{\frac{59 + 1}{40}}{3}$

Step 2.7

Add $59$ and $1$ .

$\frac{\frac{60}{40}}{3}$

Step 2.8

Cancel the common factor of $60$ and $40$ .

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Step 2.8.1

Factor $20$ out of $60$ .

$\frac{\frac{20 (3)}{40}}{3}$

Step 2.8.2

Cancel the common factors.

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Step 2.8.2.1

Factor $20$ out of $40$ .

$\frac{\frac{20 \cdot 3}{20 \cdot 2}}{3}$

Step 2.8.2.2

Cancel the common factor.

$\frac{\frac{20 \cdot 3}{20 \cdot 2}}{3}$

Step 2.8.2.3

Rewrite the expression.

$\frac{\frac{3}{2}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{2} \cdot \frac{1}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{1}{3}$

Step 4.2

Rewrite the expression.

$\frac{1}{2}$

Step 5

Divide.

$0.5$