Basic Math Examples

$(6 \frac{1}{4} - 8) \div 0.5$

Step 1

Convert $6 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(6 + \frac{1}{4} - 8) \div 0.5$

Step 1.2

Add $6$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(6 \cdot \frac{4}{4} + \frac{1}{4} - 8) \div 0.5$

Step 1.2.2

Combine $6$ and $\frac{4}{4}$ .

$(\frac{6 \cdot 4}{4} + \frac{1}{4} - 8) \div 0.5$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{6 \cdot 4 + 1}{4} - 8) \div 0.5$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $4$ .

$(\frac{24 + 1}{4} - 8) \div 0.5$

Step 1.2.4.2

Add $24$ and $1$ .

$(\frac{25}{4} - 8) \div 0.5$

Step 2

Rewrite the division as a fraction.

$\frac{\frac{25}{4} - 8}{0.5}$

Step 3

Simplify the numerator.

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Step 3.1

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{25}{4} - 8 \cdot \frac{4}{4}}{0.5}$

Step 3.2

Combine $- 8$ and $\frac{4}{4}$ .

$\frac{\frac{25}{4} + \frac{- 8 \cdot 4}{4}}{0.5}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{25 - 8 \cdot 4}{4}}{0.5}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $- 8$ by $4$ .

$\frac{\frac{25 - 32}{4}}{0.5}$

Step 3.4.2

Subtract $32$ from $25$ .

$\frac{\frac{- 7}{4}}{0.5}$

Step 3.5

Move the negative in front of the fraction.

$\frac{- \frac{7}{4}}{0.5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{7}{4} \cdot \frac{1}{0.5}$

Step 5

Cancel the common factor of $0.5$ .

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Step 5.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} \cdot \frac{1}{0.5}$

Step 5.2

Factor $0.5$ out of $- 7$ .

$\frac{0.5 (- 14)}{4} \cdot \frac{1}{0.5}$

Step 5.3

Cancel the common factor.

$\frac{0.5 \cdot - 14}{4} \cdot \frac{1}{0.5}$

Step 5.4

Rewrite the expression.

$\frac{- 14}{4}$

Step 6

Cancel the common factor of $- 14$ and $4$ .

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Step 6.1

Factor $2$ out of $- 14$ .

$\frac{2 (- 7)}{4}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot - 7}{2 \cdot 2}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot - 7}{2 \cdot 2}$

Step 6.2.3

Rewrite the expression.

$\frac{- 7}{2}$

Step 7

Move the negative in front of the fraction.

$- \frac{7}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{2}$

Decimal Form:

$- 3.5$

Mixed Number Form:

$- 3 \frac{1}{2}$