Basic Math Examples

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

Step 1

Convert $3 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $3$ and $\frac{3}{8}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 1.2.2

Combine $3$ and $\frac{8}{8}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $8$ .

$(\frac{24 + 3}{8} - 2 \frac{1}{4}) \cdot 1 \frac{1}{3}$

Step 1.2.4.2

Add $24$ and $3$ .

$(\frac{27}{8} - 2 \frac{1}{4}) \cdot 1 \frac{1}{3}$

Step 2

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$(\frac{27}{8} - (2 + \frac{1}{4})) \cdot 1 \frac{1}{3}$

Step 2.2

Add $2$ and $\frac{1}{4}$ .

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Step 2.2.1

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

$(\frac{27}{8} - (2 \cdot \frac{4}{4} + \frac{1}{4})) \cdot 1 \frac{1}{3}$

Step 2.2.2

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

$(\frac{27}{8} - (\frac{2 \cdot 4}{4} + \frac{1}{4})) \cdot 1 \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{27}{8} - \frac{2 \cdot 4 + 1}{4}) \cdot 1 \frac{1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$(\frac{27}{8} - \frac{8 + 1}{4}) \cdot 1 \frac{1}{3}$

Step 2.2.4.2

Add $8$ and $1$ .

$(\frac{27}{8} - \frac{9}{4}) \cdot 1 \frac{1}{3}$

Step 3

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

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Step 3.1

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

$(\frac{27}{8} - \frac{9}{4}) \cdot (1 + \frac{1}{3})$

Step 3.2

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

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Step 3.2.1

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

$(\frac{27}{8} - \frac{9}{4}) \cdot (\frac{3}{3} + \frac{1}{3})$

Step 3.2.2

Combine the numerators over the common denominator.

$(\frac{27}{8} - \frac{9}{4}) \cdot \frac{3 + 1}{3}$

Step 3.2.3

Add $3$ and $1$ .

$(\frac{27}{8} - \frac{9}{4}) \cdot \frac{4}{3}$

Step 4

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{27}{8} - \frac{9}{4} \cdot \frac{2}{2}) \cdot \frac{4}{3}$

Step 5

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$(\frac{27}{8} - \frac{9 \cdot 2}{4 \cdot 2}) \cdot \frac{4}{3}$

Step 5.2

Multiply $4$ by $2$ .

$(\frac{27}{8} - \frac{9 \cdot 2}{8}) \cdot \frac{4}{3}$

Step 6

Combine the numerators over the common denominator.

$\frac{27 - 9 \cdot 2}{8} \cdot \frac{4}{3}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 9$ by $2$ .

$\frac{27 - 18}{8} \cdot \frac{4}{3}$

Step 7.2

Subtract $18$ from $27$ .

$\frac{9}{8} \cdot \frac{4}{3}$

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Factor $3$ out of $9$ .

$\frac{3 (3)}{8} \cdot \frac{4}{3}$

Step 8.2

Cancel the common factor.

$\frac{3 \cdot 3}{8} \cdot \frac{4}{3}$

Step 8.3

Rewrite the expression.

$\frac{3}{8} \cdot 4$

Step 9

Cancel the common factor of $4$ .

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Step 9.1

Factor $4$ out of $8$ .

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

Step 9.2

Cancel the common factor.

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

Step 9.3

Rewrite the expression.

$\frac{3}{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$