Basic Math Examples

find the decimal expansion of $\frac{10}{3}$ , $\frac{7}{8}$ and $\frac{1}{7}$

Step 1

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

$\frac{\frac{10}{3} + \frac{7}{8} + \frac{1}{7}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{10}{3} \cdot \frac{8}{8} + \frac{7}{8} + \frac{1}{7}}{3}$

Step 2.2

To write $\frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{10}{3} \cdot \frac{8}{8} + \frac{7}{8} \cdot \frac{3}{3} + \frac{1}{7}}{3}$

Step 2.3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{10}{3}$ by $\frac{8}{8}$ .

$\frac{\frac{10 \cdot 8}{3 \cdot 8} + \frac{7}{8} \cdot \frac{3}{3} + \frac{1}{7}}{3}$

Step 2.3.2

Multiply $3$ by $8$ .

$\frac{\frac{10 \cdot 8}{24} + \frac{7}{8} \cdot \frac{3}{3} + \frac{1}{7}}{3}$

Step 2.3.3

Multiply $\frac{7}{8}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 8}{24} + \frac{7 \cdot 3}{8 \cdot 3} + \frac{1}{7}}{3}$

Step 2.3.4

Multiply $8$ by $3$ .

$\frac{\frac{10 \cdot 8}{24} + \frac{7 \cdot 3}{24} + \frac{1}{7}}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{\frac{10 \cdot 8 + 7 \cdot 3}{24} + \frac{1}{7}}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $10$ by $8$ .

$\frac{\frac{80 + 7 \cdot 3}{24} + \frac{1}{7}}{3}$

Step 2.5.2

Multiply $7$ by $3$ .

$\frac{\frac{80 + 21}{24} + \frac{1}{7}}{3}$

Step 2.5.3

Add $80$ and $21$ .

$\frac{\frac{101}{24} + \frac{1}{7}}{3}$

Step 2.6

To write $\frac{101}{24}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{101}{24} \cdot \frac{7}{7} + \frac{1}{7}}{3}$

Step 2.7

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{\frac{101}{24} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{24}{24}}{3}$

Step 2.8

Write each expression with a common denominator of $168$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.8.1

Multiply $\frac{101}{24}$ by $\frac{7}{7}$ .

$\frac{\frac{101 \cdot 7}{24 \cdot 7} + \frac{1}{7} \cdot \frac{24}{24}}{3}$

Step 2.8.2

Multiply $24$ by $7$ .

$\frac{\frac{101 \cdot 7}{168} + \frac{1}{7} \cdot \frac{24}{24}}{3}$

Step 2.8.3

Multiply $\frac{1}{7}$ by $\frac{24}{24}$ .

$\frac{\frac{101 \cdot 7}{168} + \frac{24}{7 \cdot 24}}{3}$

Step 2.8.4

Multiply $7$ by $24$ .

$\frac{\frac{101 \cdot 7}{168} + \frac{24}{168}}{3}$

Step 2.9

Combine the numerators over the common denominator.

$\frac{\frac{101 \cdot 7 + 24}{168}}{3}$

Step 2.10

Simplify the numerator.

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Step 2.10.1

Multiply $101$ by $7$ .

$\frac{\frac{707 + 24}{168}}{3}$

Step 2.10.2

Add $707$ and $24$ .

$\frac{\frac{731}{168}}{3}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{731}{168} \cdot \frac{1}{3}$

Step 4

Multiply $\frac{731}{168} \cdot \frac{1}{3}$ .

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Step 4.1

Multiply $\frac{731}{168}$ by $\frac{1}{3}$ .

$\frac{731}{168 \cdot 3}$

Step 4.2

Multiply $168$ by $3$ .

$\frac{731}{504}$

Step 5

Divide.

$1.45039682$

Step 6

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$1.5$