Basic Math Examples

$(2.6 \div 1.2 - 4 \frac{1}{2}) \div (0.75 - \frac{1}{3})$

Step 1

Convert

$4 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$(2.6 \div 1.2 - (4 + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

Step 1.2

Add

$4$ and

$\frac{1}{2}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$(2.6 \div 1.2 - (4 \cdot \frac{2}{2} + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

Step 1.2.2

Combine

$4$ and

$\frac{2}{2}$ .

$(2.6 \div 1.2 - (\frac{4 \cdot 2}{2} + \frac{1}{2})) \div (0.75 - \frac{1}{3})$

Step 1.2.3

Combine the numerators over the common denominator.

$(2.6 \div 1.2 - \frac{4 \cdot 2 + 1}{2}) \div (0.75 - \frac{1}{3})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$2$ .

$(2.6 \div 1.2 - \frac{8 + 1}{2}) \div (0.75 - \frac{1}{3})$

Step 1.2.4.2

Add

$8$ and

$1$ .

$(2.6 \div 1.2 - \frac{9}{2}) \div (0.75 - \frac{1}{3})$

Step 2

Rewrite the division as a fraction.

$\frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$

Step 3

Multiply the numerator and denominator of the fraction by

$6$ .

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Step 3.1

Multiply

$\frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$ by

$\frac{6}{6}$ .

$\frac{6}{6} \cdot \frac{2.6 \div 1.2 - \frac{9}{2}}{0.75 - \frac{1}{3}}$

Step 3.2

Combine.

$\frac{6 (2.6 \div 1.2 - \frac{9}{2})}{6 (0.75 - \frac{1}{3})}$

Step 4

Apply the distributive property.

$\frac{6 (2.6 \div 1.2) + 6 (- \frac{9}{2})}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5

Simplify by cancelling.

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Step 5.1

Cancel the common factor of

$2$ .

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Step 5.1.1

Move the leading negative in

$- \frac{9}{2}$ into the numerator.

$\frac{6 (2.6 \div 1.2) + 6 (\frac{- 9}{2})}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5.1.2

Factor

$2$ out of

$6$ .

$\frac{6 (2.6 \div 1.2) + 2 (3) \frac{- 9}{2}}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5.1.3

Cancel the common factor.

$\frac{6 (2.6 \div 1.2) + 2 \cdot 3 \frac{- 9}{2}}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5.1.4

Rewrite the expression.

$\frac{6 (2.6 \div 1.2) + 3 \cdot - 9}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5.2

Multiply

$3$ by

$- 9$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 6 (- \frac{1}{3})}$

Step 5.3

Cancel the common factor of

$3$ .

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Step 5.3.1

Move the leading negative in

$- \frac{1}{3}$ into the numerator.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 6 (\frac{- 1}{3})}$

Step 5.3.2

Factor

$3$ out of

$6$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 3 (2) \frac{- 1}{3}}$

Step 5.3.3

Cancel the common factor.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 3 \cdot 2 \frac{- 1}{3}}$

Step 5.3.4

Rewrite the expression.

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 + 2 \cdot - 1}$

Step 5.4

Multiply

$2$ by

$- 1$ .

$\frac{6 (2.6 \div 1.2) - 27}{6 \cdot 0.75 - 2}$

Step 6

Simplify the numerator.

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Step 6.1

Divide

$2.6$ by

$1.2$ .

$\frac{6 \cdot 2.1\overline{6} - 27}{6 \cdot 0.75 - 2}$

Step 6.2

Multiply

$6$ by

$2.1\overline{6}$ .

$\frac{13 - 27}{6 \cdot 0.75 - 2}$

Step 6.3

Subtract

$27$ from

$13$ .

$\frac{- 14}{6 \cdot 0.75 - 2}$

Step 7

Simplify the denominator.

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Step 7.1

Multiply

$6$ by

$0.75$ .

$\frac{- 14}{4.5 - 2}$

Step 7.2

Subtract

$2$ from

$4.5$ .

$\frac{- 14}{2.5}$

Step 8

Divide

$- 14$ by

$2.5$ .

$- 5.6$