Basic Math Examples

2 + \frac{5}{9} - \frac{3}{a^{2}} \div 2 - \frac{5}{9} + \frac{2}{9^{2}}

$2 + \frac{5}{9} - \frac{3}{a^{2}} \div 2 - \frac{5}{9} + \frac{2}{9^{2}}$

Step 1

Combine the opposite terms in

2 + \frac{5}{9} - \frac{3}{a^{2}} \div 2 - \frac{5}{9} + \frac{2}{9^{2}}

$2 + \frac{5}{9} - \frac{3}{a^{2}} \div 2 - \frac{5}{9} + \frac{2}{9^{2}}$ .

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Step 1.1

Combine the numerators over the common denominator.

2 - \frac{3}{a^{2}} \div 2 + \frac{5 - 5}{9} + \frac{2}{9^{2}}

$2 - \frac{3}{a^{2}} \div 2 + \frac{5 - 5}{9} + \frac{2}{9^{2}}$

Step 1.2

Subtract

5

$5$ from

5

$5$ .

2 - \frac{3}{a^{2}} \div 2 + \frac{0}{9} + \frac{2}{9^{2}}

$2 - \frac{3}{a^{2}} \div 2 + \frac{0}{9} + \frac{2}{9^{2}}$

Step 1.3

Divide

0

$0$ by

9

$9$ .

2 - \frac{3}{a^{2}} \div 2 + 0 + \frac{2}{9^{2}}

$2 - \frac{3}{a^{2}} \div 2 + 0 + \frac{2}{9^{2}}$

Step 1.4

Add

2 - \frac{3}{a^{2}} \div 2

$2 - \frac{3}{a^{2}} \div 2$ and

0

$0$ .

2 - \frac{3}{a^{2}} \div 2 + \frac{2}{9^{2}}

$2 - \frac{3}{a^{2}} \div 2 + \frac{2}{9^{2}}$

2 - \frac{3}{a^{2}} \div 2 + \frac{2}{9^{2}}

$2 - \frac{3}{a^{2}} \div 2 + \frac{2}{9^{2}}$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$2 - \frac{\frac{3}{a^{2}}}{2} + \frac{2}{9^{2}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$2 - (\frac{3}{a^{2}} \cdot \frac{1}{2}) + \frac{2}{9^{2}}$

Step 2.3

Combine.

$2 - \frac{3 \cdot 1}{a^{2} \cdot 2} + \frac{2}{9^{2}}$

Step 2.4

Multiply

$3$ by

$1$ .

$2 - \frac{3}{a^{2} \cdot 2} + \frac{2}{9^{2}}$

Step 2.5

Move

$2$ to the left of

$a^{2}$ .

$2 - \frac{3}{2 \cdot a^{2}} + \frac{2}{9^{2}}$

Step 2.6

Raise

$9$ to the power of

$2$ .

$2 - \frac{3}{2 a^{2}} + \frac{2}{81}$

Step 3

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{81}{81}$ .

$- \frac{3}{2 a^{2}} + 2 \cdot \frac{81}{81} + \frac{2}{81}$

Step 4

Combine

$2$ and

$\frac{81}{81}$ .

$- \frac{3}{2 a^{2}} + \frac{2 \cdot 81}{81} + \frac{2}{81}$

Step 5

Combine the numerators over the common denominator.

$- \frac{3}{2 a^{2}} + \frac{2 \cdot 81 + 2}{81}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$2$ by

$81$ .

$- \frac{3}{2 a^{2}} + \frac{162 + 2}{81}$

Step 6.2

Add

$162$ and

$2$ .

$- \frac{3}{2 a^{2}} + \frac{164}{81}$