Basic Math Examples

$(\frac{9}{5} - \frac{9}{10}) (\frac{9}{5} + \frac{9}{10})$

Step 1

To write $\frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{9}{5}$ by $\frac{2}{2}$ .

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

Step 2.2

Multiply $5$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $9$ by $2$ .

$\frac{18 - 9}{10} (\frac{9}{5} + \frac{9}{10})$

Step 4.2

Subtract $9$ from $18$ .

$\frac{9}{10} (\frac{9}{5} + \frac{9}{10})$

Step 5

To write $\frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{10} (\frac{9}{5} \cdot \frac{2}{2} + \frac{9}{10})$

Step 6

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{9}{5}$ by $\frac{2}{2}$ .

$\frac{9}{10} (\frac{9 \cdot 2}{5 \cdot 2} + \frac{9}{10})$

Step 6.2

Multiply $5$ by $2$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

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Step 8.1

Multiply $9$ by $2$ .

$\frac{9}{10} \cdot \frac{18 + 9}{10}$

Step 8.2

Add $18$ and $9$ .

$\frac{9}{10} \cdot \frac{27}{10}$

Step 9

Multiply $\frac{9}{10} \cdot \frac{27}{10}$ .

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Step 9.1

Multiply $\frac{9}{10}$ by $\frac{27}{10}$ .

$\frac{9 \cdot 27}{10 \cdot 10}$

Step 9.2

Multiply $9$ by $27$ .

$\frac{243}{10 \cdot 10}$

Step 9.3

Multiply $10$ by $10$ .

$\frac{243}{100}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{243}{100}$

Decimal Form:

$2.43$

Mixed Number Form:

$2 \frac{43}{100}$