Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $1$ .

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

Step 2

Convert $4 \frac{3}{2}$ to an improper fraction.

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Step 2.1

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

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

Step 2.2

Add $4$ and $\frac{3}{2}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$(\frac{4}{3} - \frac{8 + 3}{2}) \cdot ((\frac{1}{3}) - 2 \frac{1}{3})$

Step 2.2.4.2

Add $8$ and $3$ .

$(\frac{4}{3} - \frac{11}{2}) \cdot ((\frac{1}{3}) - 2 \frac{1}{3})$

Step 3

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

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Step 3.1

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

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - (2 + \frac{1}{3}))$

Step 3.2

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

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Step 3.2.1

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

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - (2 \cdot \frac{3}{3} + \frac{1}{3}))$

Step 3.2.2

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

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - (\frac{2 \cdot 3}{3} + \frac{1}{3}))$

Step 3.2.3

Combine the numerators over the common denominator.

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - \frac{2 \cdot 3 + 1}{3})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $3$ .

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - \frac{6 + 1}{3})$

Step 3.2.4.2

Add $6$ and $1$ .

$(\frac{4}{3} - \frac{11}{2}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 4

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{4}{3} \cdot \frac{2}{2} - \frac{11}{2}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 5

To write $- \frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{4}{3} \cdot \frac{2}{2} - \frac{11}{2} \cdot \frac{3}{3}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$(\frac{4 \cdot 2}{3 \cdot 2} - \frac{11}{2} \cdot \frac{3}{3}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 6.2

Multiply $3$ by $2$ .

$(\frac{4 \cdot 2}{6} - \frac{11}{2} \cdot \frac{3}{3}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 6.3

Multiply $\frac{11}{2}$ by $\frac{3}{3}$ .

$(\frac{4 \cdot 2}{6} - \frac{11 \cdot 3}{2 \cdot 3}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 6.4

Multiply $2$ by $3$ .

$(\frac{4 \cdot 2}{6} - \frac{11 \cdot 3}{6}) \cdot (\frac{1}{3} - \frac{7}{3})$

Step 7

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 - 11 \cdot 3}{6} \cdot (\frac{1}{3} - \frac{7}{3})$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $4$ by $2$ .

$\frac{8 - 11 \cdot 3}{6} \cdot (\frac{1}{3} - \frac{7}{3})$

Step 8.2

Multiply $- 11$ by $3$ .

$\frac{8 - 33}{6} \cdot (\frac{1}{3} - \frac{7}{3})$

Step 8.3

Subtract $33$ from $8$ .

$\frac{- 25}{6} \cdot (\frac{1}{3} - \frac{7}{3})$

Step 9

Move the negative in front of the fraction.

$- \frac{25}{6} \cdot (\frac{1}{3} - \frac{7}{3})$

Step 10

Combine the numerators over the common denominator.

$- \frac{25}{6} \cdot \frac{1 - 7}{3}$

Step 11

Subtract $7$ from $1$ .

$- \frac{25}{6} \cdot \frac{- 6}{3}$

Step 12

Cancel the common factor of $6$ .

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Step 12.1

Move the leading negative in $- \frac{25}{6}$ into the numerator.

$\frac{- 25}{6} \cdot \frac{- 6}{3}$

Step 12.2

Factor $6$ out of $- 6$ .

$\frac{- 25}{6} \cdot \frac{6 (- 1)}{3}$

Step 12.3

Cancel the common factor.

$\frac{- 25}{6} \cdot \frac{6 \cdot - 1}{3}$

Step 12.4

Rewrite the expression.

$- 25 \cdot \frac{- 1}{3}$

Step 13

Combine $- 25$ and $\frac{- 1}{3}$ .

$\frac{- 25 \cdot - 1}{3}$

Step 14

Multiply $- 25$ by $- 1$ .

$\frac{25}{3}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{3}$

Decimal Form:

$8.\overline{3}$

Mixed Number Form:

$8 \frac{1}{3}$