Basic Math Examples

$\frac{119}{25}$ , $4.49$ , $4 \frac{3}{4}$ , $4.752$

Step 1

Convert $4 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$\frac{119}{25}, 4.49, 4 + \frac{3}{4}, 4.752$

Step 1.2

Add $4$ and $\frac{3}{4}$ .

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Step 1.2.1

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

$\frac{119}{25}, 4.49, 4 \cdot \frac{4}{4} + \frac{3}{4}, 4.752$

Step 1.2.2

Combine $4$ and $\frac{4}{4}$ .

$\frac{119}{25}, 4.49, \frac{4 \cdot 4}{4} + \frac{3}{4}, 4.752$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{119}{25}, 4.49, \frac{4 \cdot 4 + 3}{4}, 4.752$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $4$ .

$\frac{119}{25}, 4.49, \frac{16 + 3}{4}, 4.752$

Step 1.2.4.2

Add $16$ and $3$ .

$\frac{119}{25}, 4.49, \frac{19}{4}, 4.752$

Step 2

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

$\frac{\frac{119}{25} + 4.49 + \frac{19}{4} + 4.752}{4}$

Step 3

Simplify the numerator.

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Step 3.1

To write $4.49$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{\frac{119}{25} + 4.49 \cdot \frac{25}{25} + \frac{19}{4} + 4.752}{4}$

Step 3.2

Combine $4.49$ and $\frac{25}{25}$ .

$\frac{\frac{119}{25} + \frac{4.49 \cdot 25}{25} + \frac{19}{4} + 4.752}{4}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{119 + 4.49 \cdot 25}{25} + \frac{19}{4} + 4.752}{4}$

Step 3.4

To write $\frac{119 + 4.49 \cdot 25}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{119 + 4.49 \cdot 25}{25} \cdot \frac{4}{4} + \frac{19}{4} + 4.752}{4}$

Step 3.5

To write $\frac{19}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{\frac{119 + 4.49 \cdot 25}{25} \cdot \frac{4}{4} + \frac{19}{4} \cdot \frac{25}{25} + 4.752}{4}$

Step 3.6

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.6.1

Multiply $\frac{119 + 4.49 \cdot 25}{25}$ by $\frac{4}{4}$ .

$\frac{\frac{(119 + 4.49 \cdot 25) \cdot 4}{25 \cdot 4} + \frac{19}{4} \cdot \frac{25}{25} + 4.752}{4}$

Step 3.6.2

Multiply $25$ by $4$ .

$\frac{\frac{(119 + 4.49 \cdot 25) \cdot 4}{100} + \frac{19}{4} \cdot \frac{25}{25} + 4.752}{4}$

Step 3.6.3

Multiply $\frac{19}{4}$ by $\frac{25}{25}$ .

$\frac{\frac{(119 + 4.49 \cdot 25) \cdot 4}{100} + \frac{19 \cdot 25}{4 \cdot 25} + 4.752}{4}$

Step 3.6.4

Multiply $4$ by $25$ .

$\frac{\frac{(119 + 4.49 \cdot 25) \cdot 4}{100} + \frac{19 \cdot 25}{100} + 4.752}{4}$

Step 3.7

Combine the numerators over the common denominator.

$\frac{\frac{(119 + 4.49 \cdot 25) \cdot 4 + 19 \cdot 25}{100} + 4.752}{4}$

Step 3.8

Simplify the numerator.

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Step 3.8.1

Multiply $4.49$ by $25$ .

$\frac{\frac{(119 + 112.25) \cdot 4 + 19 \cdot 25}{100} + 4.752}{4}$

Step 3.8.2

Add $119$ and $112.25$ .

$\frac{\frac{231.25 \cdot 4 + 19 \cdot 25}{100} + 4.752}{4}$

Step 3.8.3

Multiply $231.25$ by $4$ .

$\frac{\frac{925 + 19 \cdot 25}{100} + 4.752}{4}$

Step 3.8.4

Multiply $19$ by $25$ .

$\frac{\frac{925 + 475}{100} + 4.752}{4}$

Step 3.8.5

Add $925$ and $475$ .

$\frac{\frac{1400}{100} + 4.752}{4}$

Step 3.9

To write $4.752$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$\frac{\frac{1400}{100} + 4.752 \cdot \frac{100}{100}}{4}$

Step 3.10

Combine $4.752$ and $\frac{100}{100}$ .

$\frac{\frac{1400}{100} + \frac{4.752 \cdot 100}{100}}{4}$

Step 3.11

Combine the numerators over the common denominator.

$\frac{\frac{1400 + 4.752 \cdot 100}{100}}{4}$

Step 3.12

Rewrite $\frac{1400 + 4.752 \cdot 100}{100}$ in a factored form.

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Step 3.12.1

Multiply $4.752$ by $100$ .

$\frac{\frac{1400 + 475.2}{100}}{4}$

Step 3.12.2

Add $1400$ and $475.2$ .

$\frac{\frac{1875.2}{100}}{4}$

Step 3.12.3

Divide $1875.2$ by $100$ .

$\frac{18.752}{4}$

Step 4

Divide $18.752$ by $4$ .

$4.688$

Step 5

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.

$4.7$