Basic Math Examples

$8$ , $8 \frac{1}{2}$ , $9$ , $9 \frac{1}{2}$ , $10$ , $10 \frac{1}{2}$ , $11$

Step 1

Convert $8 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$8, 8 + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 1.2

Add $8$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8, 8 \cdot \frac{2}{2} + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 1.2.2

Combine $8$ and $\frac{2}{2}$ .

$8, \frac{8 \cdot 2}{2} + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 1.2.3

Combine the numerators over the common denominator.

$8, \frac{8 \cdot 2 + 1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $2$ .

$8, \frac{16 + 1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 1.2.4.2

Add $16$ and $1$ .

$8, \frac{17}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2

Convert $9 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$8, \frac{17}{2}, 9, 9 + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2.2

Add $9$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8, \frac{17}{2}, 9, 9 \cdot \frac{2}{2} + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2.2.2

Combine $9$ and $\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{9 \cdot 2}{2} + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2.2.3

Combine the numerators over the common denominator.

$8, \frac{17}{2}, 9, \frac{9 \cdot 2 + 1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $9$ by $2$ .

$8, \frac{17}{2}, 9, \frac{18 + 1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2.2.4.2

Add $18$ and $1$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 \frac{1}{2}, 11$

Step 3

Convert $10 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 + \frac{1}{2}, 11$

Step 3.2

Add $10$ and $\frac{1}{2}$ .

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Step 3.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 \cdot \frac{2}{2} + \frac{1}{2}, 11$

Step 3.2.2

Combine $10$ and $\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{10 \cdot 2}{2} + \frac{1}{2}, 11$

Step 3.2.3

Combine the numerators over the common denominator.

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{10 \cdot 2 + 1}{2}, 11$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $10$ by $2$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{20 + 1}{2}, 11$

Step 3.2.4.2

Add $20$ and $1$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{21}{2}, 11$

Step 4

The mode is the element that occurs most in the data set. In this case, all elements occur only once, so there is no mode.

No mode