Basic Math Examples

$\frac{1}{2} \cdot (- \frac{3}{\frac{5}{4}}) + \frac{3}{5} - \frac{1}{10}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot (- (3 (\frac{4}{5}))) + \frac{3}{5} - \frac{1}{10}$

Step 1.2

Multiply $3 (\frac{4}{5})$ .

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Step 1.2.1

Combine $3$ and $\frac{4}{5}$ .

$\frac{1}{2} \cdot (- \frac{3 \cdot 4}{5}) + \frac{3}{5} - \frac{1}{10}$

Step 1.2.2

Multiply $3$ by $4$ .

$\frac{1}{2} \cdot (- \frac{12}{5}) + \frac{3}{5} - \frac{1}{10}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Move the leading negative in $- \frac{12}{5}$ into the numerator.

$\frac{1}{2} \cdot \frac{- 12}{5} + \frac{3}{5} - \frac{1}{10}$

Step 1.3.2

Factor $2$ out of $- 12$ .

$\frac{1}{2} \cdot \frac{2 (- 6)}{5} + \frac{3}{5} - \frac{1}{10}$

Step 1.3.3

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 \cdot - 6}{5} + \frac{3}{5} - \frac{1}{10}$

Step 1.3.4

Rewrite the expression.

$\frac{- 6}{5} + \frac{3}{5} - \frac{1}{10}$

Step 1.4

Move the negative in front of the fraction.

$- \frac{6}{5} + \frac{3}{5} - \frac{1}{10}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 6 + 3}{5} + \frac{- 1}{10}$

Step 2.2

Add $- 6$ and $3$ .

$\frac{- 3}{5} + \frac{- 1}{10}$

Step 3

Simplify each term.

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Step 3.1

Move the negative in front of the fraction.

$- \frac{3}{5} + \frac{- 1}{10}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{3}{5} - \frac{1}{10}$

Step 4

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{5} \cdot \frac{2}{2} - \frac{1}{10}$

Step 5

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$- \frac{3 \cdot 2}{5 \cdot 2} - \frac{1}{10}$

Step 5.2

Multiply $5$ by $2$ .

$- \frac{3 \cdot 2}{10} - \frac{1}{10}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 3 \cdot 2 - 1}{10}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 3$ by $2$ .

$\frac{- 6 - 1}{10}$

Step 7.2

Subtract $1$ from $- 6$ .

$\frac{- 7}{10}$

Step 8

Move the negative in front of the fraction.

$- \frac{7}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{10}$

Decimal Form:

$- 0.7$