Basic Math Examples

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

Step 1

Convert $1 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{2}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $5$ and $2$ .

$- \frac{2}{3} \cdot (\frac{7}{5} - 3 \frac{1}{2})$

Step 2

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$- \frac{2}{3} \cdot (\frac{7}{5} - (3 + \frac{1}{2}))$

Step 2.2

Add $3$ and $\frac{1}{2}$ .

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Step 2.2.1

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

$- \frac{2}{3} \cdot (\frac{7}{5} - (3 \cdot \frac{2}{2} + \frac{1}{2}))$

Step 2.2.2

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

$- \frac{2}{3} \cdot (\frac{7}{5} - (\frac{3 \cdot 2}{2} + \frac{1}{2}))$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{2}{3} \cdot (\frac{7}{5} - \frac{3 \cdot 2 + 1}{2})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $2$ .

$- \frac{2}{3} \cdot (\frac{7}{5} - \frac{6 + 1}{2})$

Step 2.2.4.2

Add $6$ and $1$ .

$- \frac{2}{3} \cdot (\frac{7}{5} - \frac{7}{2})$

Step 3

To write $\frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2}{3} \cdot (\frac{7}{5} \cdot \frac{2}{2} - \frac{7}{2})$

Step 4

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{2}{3} \cdot (\frac{7}{5} \cdot \frac{2}{2} - \frac{7}{2} \cdot \frac{5}{5})$

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 $\frac{7}{5}$ by $\frac{2}{2}$ .

$- \frac{2}{3} \cdot (\frac{7 \cdot 2}{5 \cdot 2} - \frac{7}{2} \cdot \frac{5}{5})$

Step 5.2

Multiply $5$ by $2$ .

$- \frac{2}{3} \cdot (\frac{7 \cdot 2}{10} - \frac{7}{2} \cdot \frac{5}{5})$

Step 5.3

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$- \frac{2}{3} \cdot (\frac{7 \cdot 2}{10} - \frac{7 \cdot 5}{2 \cdot 5})$

Step 5.4

Multiply $2$ by $5$ .

$- \frac{2}{3} \cdot (\frac{7 \cdot 2}{10} - \frac{7 \cdot 5}{10})$

Step 6

Combine the numerators over the common denominator.

$- \frac{2}{3} \cdot \frac{7 \cdot 2 - 7 \cdot 5}{10}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $7$ by $2$ .

$- \frac{2}{3} \cdot \frac{14 - 7 \cdot 5}{10}$

Step 7.2

Multiply $- 7$ by $5$ .

$- \frac{2}{3} \cdot \frac{14 - 35}{10}$

Step 7.3

Subtract $35$ from $14$ .

$- \frac{2}{3} \cdot \frac{- 21}{10}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 21}{10}$

Step 8.2

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 21}{10}$

Step 8.3

Factor $2$ out of $10$ .

$\frac{2 \cdot - 1}{3} \cdot \frac{- 21}{2 \cdot 5}$

Step 8.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 21}{2 \cdot 5}$

Step 8.5

Rewrite the expression.

$\frac{- 1}{3} \cdot \frac{- 21}{5}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Factor $3$ out of $- 21$ .

$\frac{- 1}{3} \cdot \frac{3 (- 7)}{5}$

Step 9.2

Cancel the common factor.

$\frac{- 1}{3} \cdot \frac{3 \cdot - 7}{5}$

Step 9.3

Rewrite the expression.

$- 1 \cdot \frac{- 7}{5}$

Step 10

Move the negative in front of the fraction.

$- 1 \cdot (- \frac{7}{5})$

Step 11

Multiply $- 1 (- \frac{7}{5})$ .

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Step 11.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{7}{5})$

Step 11.2

Multiply $\frac{7}{5}$ by $1$ .

$\frac{7}{5}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{5}$

Decimal Form:

$1.4$

Mixed Number Form:

$1 \frac{2}{5}$