Basic Math Examples

$- 6 (4 \frac{3}{4}) + 2 (4 \frac{3}{4} + 2) - 5$

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.

$- 6 (4 + \frac{3}{4}) + 2 (4 \frac{3}{4} + 2) - 5$

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 $\frac{4}{4}$ .

$- 6 (4 \cdot \frac{4}{4} + \frac{3}{4}) + 2 (4 \frac{3}{4} + 2) - 5$

Step 1.2.2

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

$- 6 (\frac{4 \cdot 4}{4} + \frac{3}{4}) + 2 (4 \frac{3}{4} + 2) - 5$

Step 1.2.3

Combine the numerators over the common denominator.

$- 6 \frac{4 \cdot 4 + 3}{4} + 2 (4 \frac{3}{4} + 2) - 5$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $4$ .

$- 6 \frac{16 + 3}{4} + 2 (4 \frac{3}{4} + 2) - 5$

Step 1.2.4.2

Add $16$ and $3$ .

$- 6 (\frac{19}{4}) + 2 (4 \frac{3}{4} + 2) - 5$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $- 6$ .

$2 (- 3) \frac{19}{4} + 2 (4 \frac{3}{4} + 2) - 5$

Step 2.2

Factor $2$ out of $4$ .

$2 \cdot - 3 \frac{19}{2 \cdot 2} + 2 (4 \frac{3}{4} + 2) - 5$

Step 2.3

Cancel the common factor.

$2 \cdot - 3 \frac{19}{2 \cdot 2} + 2 (4 \frac{3}{4} + 2) - 5$

Step 2.4

Rewrite the expression.

$- 3 (\frac{19}{2}) + 2 (4 \frac{3}{4} + 2) - 5$

Step 3

Combine $- 3$ and $\frac{19}{2}$ .

$\frac{- 3 \cdot 19}{2} + 2 (4 \frac{3}{4} + 2) - 5$

Step 4

Multiply $- 3$ by $19$ .

$\frac{- 57}{2} + 2 (4 \frac{3}{4} + 2) - 5$

Step 5

Move the negative in front of the fraction.

$- \frac{57}{2} + 2 (4 \frac{3}{4} + 2) - 5$

Step 6

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

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Step 6.1

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

$- \frac{57}{2} + 2 (4 + \frac{3}{4} + 2) - 5$

Step 6.2

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

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Step 6.2.1

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

$- \frac{57}{2} + 2 (4 \cdot \frac{4}{4} + \frac{3}{4} + 2) - 5$

Step 6.2.2

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

$- \frac{57}{2} + 2 (\frac{4 \cdot 4}{4} + \frac{3}{4} + 2) - 5$

Step 6.2.3

Combine the numerators over the common denominator.

$- \frac{57}{2} + 2 (\frac{4 \cdot 4 + 3}{4} + 2) - 5$

Step 6.2.4

Simplify the numerator.

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Step 6.2.4.1

Multiply $4$ by $4$ .

$- \frac{57}{2} + 2 (\frac{16 + 3}{4} + 2) - 5$

Step 6.2.4.2

Add $16$ and $3$ .

$- \frac{57}{2} + 2 (\frac{19}{4} + 2) - 5$

Step 7

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{57}{2} + 2 (\frac{19}{4} + 2 \cdot \frac{4}{4}) - 5$

Step 8

Combine $2$ and $\frac{4}{4}$ .

$- \frac{57}{2} + 2 (\frac{19}{4} + \frac{2 \cdot 4}{4}) - 5$

Step 9

Combine the numerators over the common denominator.

$- \frac{57}{2} + 2 \frac{19 + 2 \cdot 4}{4} - 5$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $2$ by $4$ .

$- \frac{57}{2} + 2 \frac{19 + 8}{4} - 5$

Step 10.2

Add $19$ and $8$ .

$- \frac{57}{2} + 2 (\frac{27}{4}) - 5$

Step 11

Cancel the common factor of $2$ .

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Step 11.1

Factor $2$ out of $4$ .

$- \frac{57}{2} + 2 \frac{27}{2 (2)} - 5$

Step 11.2

Cancel the common factor.

$- \frac{57}{2} + 2 \frac{27}{2 \cdot 2} - 5$

Step 11.3

Rewrite the expression.

$- \frac{57}{2} + \frac{27}{2} - 5$

Step 12

Combine the numerators over the common denominator.

$\frac{- 57 + 27}{2} - 5$

Step 13

Add $- 57$ and $27$ .

$\frac{- 30}{2} - 5$

Step 14

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 30}{2} - 5 \cdot \frac{2}{2}$

Step 15

Combine $- 5$ and $\frac{2}{2}$ .

$\frac{- 30}{2} + \frac{- 5 \cdot 2}{2}$

Step 16

Combine the numerators over the common denominator.

$\frac{- 30 - 5 \cdot 2}{2}$

Step 17

Simplify the numerator.

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Step 17.1

Multiply $- 5$ by $2$ .

$\frac{- 30 - 10}{2}$

Step 17.2

Subtract $10$ from $- 30$ .

$\frac{- 40}{2}$

Step 18

Divide $- 40$ by $2$ .

$- 20$