Basic Math Examples

$- 3 \cdot (- 1 \frac{7}{12}) - (\frac{- 3}{2})$

Step 1

Convert $1 \frac{7}{12}$ to an improper fraction.

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Step 1.1

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

$- 3 \cdot (- (1 + \frac{7}{12})) - (\frac{- 3}{2})$

Step 1.2

Add $1$ and $\frac{7}{12}$ .

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Step 1.2.1

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

$- 3 \cdot (- (\frac{12}{12} + \frac{7}{12})) - (\frac{- 3}{2})$

Step 1.2.2

Combine the numerators over the common denominator.

$- 3 \cdot (- \frac{12 + 7}{12}) - (\frac{- 3}{2})$

Step 1.2.3

Add $12$ and $7$ .

$- 3 \cdot (- \frac{19}{12}) - (\frac{- 3}{2})$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Move the leading negative in $- \frac{19}{12}$ into the numerator.

$- 3 \cdot \frac{- 19}{12} - (\frac{- 3}{2})$

Step 2.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \cdot \frac{- 19}{12} - (\frac{- 3}{2})$

Step 2.1.3

Factor $3$ out of $12$ .

$3 \cdot - 1 \cdot \frac{- 19}{3 \cdot 4} - (\frac{- 3}{2})$

Step 2.1.4

Cancel the common factor.

$3 \cdot - 1 \cdot \frac{- 19}{3 \cdot 4} - (\frac{- 3}{2})$

Step 2.1.5

Rewrite the expression.

$- 1 \cdot \frac{- 19}{4} - (\frac{- 3}{2})$

Step 2.2

Move the negative in front of the fraction.

$- 1 \cdot (- \frac{19}{4}) - (\frac{- 3}{2})$

Step 2.3

Multiply $- 1 (- \frac{19}{4})$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{19}{4}) - (\frac{- 3}{2})$

Step 2.3.2

Multiply $\frac{19}{4}$ by $1$ .

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

Step 2.4

Move the negative in front of the fraction.

$\frac{19}{4} - - \frac{3}{2}$

Step 2.5

Multiply $- - \frac{3}{2}$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$\frac{19}{4} + 1 (\frac{3}{2})$

Step 2.5.2

Multiply $\frac{3}{2}$ by $1$ .

$\frac{19}{4} + \frac{3}{2}$

Step 3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{19}{4} + \frac{3}{2} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{19}{4} + \frac{3 \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{19}{4} + \frac{3 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 + 3 \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $2$ .

$\frac{19 + 6}{4}$

Step 6.2

Add $19$ and $6$ .

$\frac{25}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{4}$

Decimal Form:

$6.25$

Mixed Number Form:

$6 \frac{1}{4}$