Basic Math Examples

$\frac{2}{9} \cdot (\frac{17}{10} - 1 \frac{1}{4})$

Step 1

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

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Step 1.1

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

$\frac{2}{9} \cdot (\frac{17}{10} - (1 + \frac{1}{4}))$

Step 1.2

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

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Step 1.2.1

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

$\frac{2}{9} \cdot (\frac{17}{10} - (\frac{4}{4} + \frac{1}{4}))$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2}{9} \cdot (\frac{17}{10} - \frac{4 + 1}{4})$

Step 1.2.3

Add $4$ and $1$ .

$\frac{2}{9} \cdot (\frac{17}{10} - \frac{5}{4})$

Step 2

To write $\frac{17}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{9} \cdot (\frac{17}{10} \cdot \frac{2}{2} - \frac{5}{4})$

Step 3

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

$\frac{2}{9} \cdot (\frac{17}{10} \cdot \frac{2}{2} - \frac{5}{4} \cdot \frac{5}{5})$

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{17}{10}$ by $\frac{2}{2}$ .

$\frac{2}{9} \cdot (\frac{17 \cdot 2}{10 \cdot 2} - \frac{5}{4} \cdot \frac{5}{5})$

Step 4.2

Multiply $10$ by $2$ .

$\frac{2}{9} \cdot (\frac{17 \cdot 2}{20} - \frac{5}{4} \cdot \frac{5}{5})$

Step 4.3

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

$\frac{2}{9} \cdot (\frac{17 \cdot 2}{20} - \frac{5 \cdot 5}{4 \cdot 5})$

Step 4.4

Multiply $4$ by $5$ .

$\frac{2}{9} \cdot (\frac{17 \cdot 2}{20} - \frac{5 \cdot 5}{20})$

Step 5

Combine the numerators over the common denominator.

$\frac{2}{9} \cdot \frac{17 \cdot 2 - 5 \cdot 5}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $17$ by $2$ .

$\frac{2}{9} \cdot \frac{34 - 5 \cdot 5}{20}$

Step 6.2

Multiply $- 5$ by $5$ .

$\frac{2}{9} \cdot \frac{34 - 25}{20}$

Step 6.3

Subtract $25$ from $34$ .

$\frac{2}{9} \cdot \frac{9}{20}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $20$ .

$\frac{2}{9} \cdot \frac{9}{2 (10)}$

Step 7.2

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9}{2 \cdot 10}$

Step 7.3

Rewrite the expression.

$\frac{1}{9} \cdot \frac{9}{10}$

Step 8

Cancel the common factor of $9$ .

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Step 8.1

Cancel the common factor.

$\frac{1}{9} \cdot \frac{9}{10}$

Step 8.2

Rewrite the expression.

$\frac{1}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$