Basic Math Examples

$(2 \frac{4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1

Convert $2 \frac{4}{9}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1.2

Add $2$ and $\frac{4}{9}$ .

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Step 1.2.1

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

$(2 \cdot \frac{9}{9} + \frac{4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1.2.2

Combine $2$ and $\frac{9}{9}$ .

$(\frac{2 \cdot 9}{9} + \frac{4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{2 \cdot 9 + 4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $9$ .

$(\frac{18 + 4}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 1.2.4.2

Add $18$ and $4$ .

$(\frac{22}{9} + \frac{1}{3}) \cdot (1 \frac{1}{4} - \frac{1}{8})$

Step 2

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

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Step 2.1

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

$(\frac{22}{9} + \frac{1}{3}) \cdot (1 + \frac{1}{4} - \frac{1}{8})$

Step 2.2

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

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Step 2.2.1

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

$(\frac{22}{9} + \frac{1}{3}) \cdot (\frac{4}{4} + \frac{1}{4} - \frac{1}{8})$

Step 2.2.2

Combine the numerators over the common denominator.

$(\frac{22}{9} + \frac{1}{3}) \cdot (\frac{4 + 1}{4} - \frac{1}{8})$

Step 2.2.3

Add $4$ and $1$ .

$(\frac{22}{9} + \frac{1}{3}) \cdot (\frac{5}{4} - \frac{1}{8})$

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{22}{9} + \frac{1}{3} \cdot \frac{3}{3}) \cdot (\frac{5}{4} - \frac{1}{8})$

Step 4

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$(\frac{22}{9} + \frac{3}{3 \cdot 3}) \cdot (\frac{5}{4} - \frac{1}{8})$

Step 4.2

Multiply $3$ by $3$ .

$(\frac{22}{9} + \frac{3}{9}) \cdot (\frac{5}{4} - \frac{1}{8})$

Step 5

Combine the numerators over the common denominator.

$\frac{22 + 3}{9} \cdot (\frac{5}{4} - \frac{1}{8})$

Step 6

Add $22$ and $3$ .

$\frac{25}{9} \cdot (\frac{5}{4} - \frac{1}{8})$

Step 7

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{9} \cdot (\frac{5}{4} \cdot \frac{2}{2} - \frac{1}{8})$

Step 8

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

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Step 8.1

Multiply $\frac{5}{4}$ by $\frac{2}{2}$ .

$\frac{25}{9} \cdot (\frac{5 \cdot 2}{4 \cdot 2} - \frac{1}{8})$

Step 8.2

Multiply $4$ by $2$ .

$\frac{25}{9} \cdot (\frac{5 \cdot 2}{8} - \frac{1}{8})$

Step 9

Combine the numerators over the common denominator.

$\frac{25}{9} \cdot \frac{5 \cdot 2 - 1}{8}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $5$ by $2$ .

$\frac{25}{9} \cdot \frac{10 - 1}{8}$

Step 10.2

Subtract $1$ from $10$ .

$\frac{25}{9} \cdot \frac{9}{8}$

Step 11

Cancel the common factor of $9$ .

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Step 11.1

Cancel the common factor.

$\frac{25}{9} \cdot \frac{9}{8}$

Step 11.2

Rewrite the expression.

$25 \cdot \frac{1}{8}$

Step 12

Combine $25$ and $\frac{1}{8}$ .

$\frac{25}{8}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{8}$

Decimal Form:

$3.125$

Mixed Number Form:

$3 \frac{1}{8}$