Algebra Examples

$\frac{5}{8}$ , $\frac{3}{4}$ , $1 \frac{1}{8}$ , $1 \frac{1}{4}$

Step 1

Convert $1 \frac{1}{8}$ to an improper fraction.

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Step 1.1

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

$\frac{5}{8}, \frac{3}{4}, 1 + \frac{1}{8}, 1 \frac{1}{4}$

Step 1.2

Add $1$ and $\frac{1}{8}$ .

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Step 1.2.1

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

$\frac{5}{8}, \frac{3}{4}, \frac{8}{8} + \frac{1}{8}, 1 \frac{1}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{5}{8}, \frac{3}{4}, \frac{8 + 1}{8}, 1 \frac{1}{4}$

Step 1.2.3

Add $8$ and $1$ .

$\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, 1 \frac{1}{4}$

Step 2

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, 1 + \frac{1}{4}$

Step 2.2

Add $1$ and $\frac{1}{4}$ .

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Step 2.2.1

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

$\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, \frac{4}{4} + \frac{1}{4}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, \frac{4 + 1}{4}$

Step 2.2.3

Add $4$ and $1$ .

$\frac{5}{8}, \frac{3}{4}, \frac{9}{8}, \frac{5}{4}$

Step 3

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

$\frac{\frac{5}{8} + \frac{3}{4} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4

Simplify the numerator.

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Step 4.1

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{5}{8} + \frac{3}{4} \cdot \frac{2}{2} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$\frac{\frac{5}{8} + \frac{3 \cdot 2}{4 \cdot 2} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.2.2

Multiply $4$ by $2$ .

$\frac{\frac{5}{8} + \frac{3 \cdot 2}{8} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{\frac{5 + 3 \cdot 2}{8} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $3$ by $2$ .

$\frac{\frac{5 + 6}{8} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.4.2

Add $5$ and $6$ .

$\frac{\frac{11}{8} + \frac{9}{8} + \frac{5}{4}}{4}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{\frac{11 + 9}{8} + \frac{5}{4}}{4}$

Step 4.6

Add $11$ and $9$ .

$\frac{\frac{20}{8} + \frac{5}{4}}{4}$

Step 4.7

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{20}{8} + \frac{5}{4} \cdot \frac{2}{2}}{4}$

Step 4.8

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.8.1

Multiply $\frac{5}{4}$ by $\frac{2}{2}$ .

$\frac{\frac{20}{8} + \frac{5 \cdot 2}{4 \cdot 2}}{4}$

Step 4.8.2

Multiply $4$ by $2$ .

$\frac{\frac{20}{8} + \frac{5 \cdot 2}{8}}{4}$

Step 4.9

Combine the numerators over the common denominator.

$\frac{\frac{20 + 5 \cdot 2}{8}}{4}$

Step 4.10

Simplify the numerator.

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Step 4.10.1

Multiply $5$ by $2$ .

$\frac{\frac{20 + 10}{8}}{4}$

Step 4.10.2

Add $20$ and $10$ .

$\frac{\frac{30}{8}}{4}$

Step 4.11

Cancel the common factor of $30$ and $8$ .

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Step 4.11.1

Factor $2$ out of $30$ .

$\frac{\frac{2 (15)}{8}}{4}$

Step 4.11.2

Cancel the common factors.

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Step 4.11.2.1

Factor $2$ out of $8$ .

$\frac{\frac{2 \cdot 15}{2 \cdot 4}}{4}$

Step 4.11.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 15}{2 \cdot 4}}{4}$

Step 4.11.2.3

Rewrite the expression.

$\frac{\frac{15}{4}}{4}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{4} \cdot \frac{1}{4}$

Step 6

Multiply $\frac{15}{4} \cdot \frac{1}{4}$ .

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Step 6.1

Multiply $\frac{15}{4}$ by $\frac{1}{4}$ .

$\frac{15}{4 \cdot 4}$

Step 6.2

Multiply $4$ by $4$ .

$\frac{15}{16}$

Step 7

Divide.

$0.9375$

Step 8

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.

$0.9$