Basic Math Examples

$45 \div 3 \frac{6}{13} - 13$ , $6 + 1 \frac{3}{8}$

Step 1

Arrange the terms in ascending order.

$45 \div 3 \frac{6}{13} - 13, 6 + 1 \frac{3}{8}$

Step 2

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{45 \div 3 \frac{6}{13} - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 3

Remove parentheses.

$\frac{45 \div 3 \frac{6}{13} - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4

Convert $3 \frac{6}{13}$ to an improper fraction.

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Step 4.1

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

$\frac{45 \div (3 + \frac{6}{13}) - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4.2

Add $3$ and $\frac{6}{13}$ .

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Step 4.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{45 \div (3 \cdot \frac{13}{13} + \frac{6}{13}) - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4.2.2

Combine $3$ and $\frac{13}{13}$ .

$\frac{45 \div (\frac{3 \cdot 13}{13} + \frac{6}{13}) - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{45 \div \frac{3 \cdot 13 + 6}{13} - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $3$ by $13$ .

$\frac{45 \div \frac{39 + 6}{13} - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 4.2.4.2

Add $39$ and $6$ .

$\frac{45 \div \frac{45}{13} - 13 + 6 + 1 \frac{3}{8}}{2}$

Step 5

Convert $1 \frac{3}{8}$ to an improper fraction.

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Step 5.1

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

$\frac{45 \div \frac{45}{13} - 13 + 6 + 1 + \frac{3}{8}}{2}$

Step 5.2

Add $1$ and $\frac{3}{8}$ .

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Step 5.2.1

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

$\frac{45 \div \frac{45}{13} - 13 + 6 + \frac{8}{8} + \frac{3}{8}}{2}$

Step 5.2.2

Combine the numerators over the common denominator.

$\frac{45 \div \frac{45}{13} - 13 + 6 + \frac{8 + 3}{8}}{2}$

Step 5.2.3

Add $8$ and $3$ .

$\frac{45 \div \frac{45}{13} - 13 + 6 + \frac{11}{8}}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Add $- 13$ and $6$ .

$\frac{45 \div \frac{45}{13} - 7 + \frac{11}{8}}{2}$

Step 6.2

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

$\frac{45 \div \frac{45}{13} - 7 \cdot \frac{8}{8} + \frac{11}{8}}{2}$

Step 6.3

Combine $- 7$ and $\frac{8}{8}$ .

$\frac{45 \div \frac{45}{13} + \frac{- 7 \cdot 8}{8} + \frac{11}{8}}{2}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{45 \div \frac{45}{13} + \frac{- 7 \cdot 8 + 11}{8}}{2}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 7$ by $8$ .

$\frac{45 \div \frac{45}{13} + \frac{- 56 + 11}{8}}{2}$

Step 6.5.2

Add $- 56$ and $11$ .

$\frac{45 \div \frac{45}{13} + \frac{- 45}{8}}{2}$

Step 6.6

Simplify each term.

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Step 6.6.1

To divide by a fraction, multiply by its reciprocal.

$\frac{45 (\frac{13}{45}) + \frac{- 45}{8}}{2}$

Step 6.6.2

Cancel the common factor of $45$ .

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Step 6.6.2.1

Cancel the common factor.

$\frac{45 (\frac{13}{45}) + \frac{- 45}{8}}{2}$

Step 6.6.2.2

Rewrite the expression.

$\frac{13 + \frac{- 45}{8}}{2}$

Step 6.6.3

Move the negative in front of the fraction.

$\frac{13 - \frac{45}{8}}{2}$

Step 6.7

To write $13$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{13 \cdot \frac{8}{8} - \frac{45}{8}}{2}$

Step 6.8

Combine $13$ and $\frac{8}{8}$ .

$\frac{\frac{13 \cdot 8}{8} - \frac{45}{8}}{2}$

Step 6.9

Combine the numerators over the common denominator.

$\frac{\frac{13 \cdot 8 - 45}{8}}{2}$

Step 6.10

Simplify the numerator.

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Step 6.10.1

Multiply $13$ by $8$ .

$\frac{\frac{104 - 45}{8}}{2}$

Step 6.10.2

Subtract $45$ from $104$ .

$\frac{\frac{59}{8}}{2}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{59}{8} \cdot \frac{1}{2}$

Step 8

Multiply $\frac{59}{8} \cdot \frac{1}{2}$ .

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Step 8.1

Multiply $\frac{59}{8}$ by $\frac{1}{2}$ .

$\frac{59}{8 \cdot 2}$

Step 8.2

Multiply $8$ by $2$ .

$\frac{59}{16}$

Step 9

Convert the median $\frac{59}{16}$ to decimal.

$3.6875$