Basic Math Examples

$\frac{5}{9} - \frac{1}{4} \div \frac{25}{a^{2}} - \frac{1}{16}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{9} - (\frac{1}{4} \cdot \frac{a^{2}}{25}) - \frac{1}{16}$

Step 1.2

Combine.

$\frac{5}{9} - \frac{1 a^{2}}{4 \cdot 25} - \frac{1}{16}$

Step 1.3

Multiply $a^{2}$ by $1$ .

$\frac{5}{9} - \frac{a^{2}}{4 \cdot 25} - \frac{1}{16}$

Step 1.4

Multiply $4$ by $25$ .

$\frac{5}{9} - \frac{a^{2}}{100} - \frac{1}{16}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{5}{9}$ by $\frac{400}{400}$ .

$\frac{5}{9} \cdot \frac{400}{400} - \frac{a^{2}}{100} - \frac{1}{16}$

Step 2.2

Multiply $\frac{5}{9}$ by $\frac{400}{400}$ .

$\frac{5 \cdot 400}{9 \cdot 400} - \frac{a^{2}}{100} - \frac{1}{16}$

Step 2.3

Multiply $\frac{a^{2}}{100}$ by $\frac{36}{36}$ .

$\frac{5 \cdot 400}{9 \cdot 400} - (\frac{a^{2}}{100} \cdot \frac{36}{36}) - \frac{1}{16}$

Step 2.4

Multiply $\frac{a^{2}}{100}$ by $\frac{36}{36}$ .

$\frac{5 \cdot 400}{9 \cdot 400} - \frac{a^{2} \cdot 36}{100 \cdot 36} - \frac{1}{16}$

Step 2.5

Multiply $\frac{1}{16}$ by $\frac{225}{225}$ .

$\frac{5 \cdot 400}{9 \cdot 400} - \frac{a^{2} \cdot 36}{100 \cdot 36} - (\frac{1}{16} \cdot \frac{225}{225})$

Step 2.6

Multiply $\frac{1}{16}$ by $\frac{225}{225}$ .

$\frac{5 \cdot 400}{9 \cdot 400} - \frac{a^{2} \cdot 36}{100 \cdot 36} - \frac{225}{16 \cdot 225}$

Step 2.7

Multiply $9$ by $400$ .

$\frac{5 \cdot 400}{3600} - \frac{a^{2} \cdot 36}{100 \cdot 36} - \frac{225}{16 \cdot 225}$

Step 2.8

Reorder the factors of $100 \cdot 36$ .

$\frac{5 \cdot 400}{3600} - \frac{a^{2} \cdot 36}{36 \cdot 100} - \frac{225}{16 \cdot 225}$

Step 2.9

Multiply $36$ by $100$ .

$\frac{5 \cdot 400}{3600} - \frac{a^{2} \cdot 36}{3600} - \frac{225}{16 \cdot 225}$

Step 2.10

Multiply $16$ by $225$ .

$\frac{5 \cdot 400}{3600} - \frac{a^{2} \cdot 36}{3600} - \frac{225}{3600}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 \cdot 400 - a^{2} \cdot 36 - 225}{3600}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $400$ .

$\frac{2000 - a^{2} \cdot 36 - 225}{3600}$

Step 4.2

Multiply $36$ by $- 1$ .

$\frac{2000 - 36 a^{2} - 225}{3600}$

Step 5

Simplify with factoring out.

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Step 5.1

Subtract $225$ from $2000$ .

$\frac{- 36 a^{2} + 1775}{3600}$

Step 5.2

Factor $- 1$ out of $- 36 a^{2}$ .

$\frac{- (36 a^{2}) + 1775}{3600}$

Step 5.3

Rewrite $1775$ as $- 1 (- 1775)$ .

$\frac{- (36 a^{2}) - 1 (- 1775)}{3600}$

Step 5.4

Factor $- 1$ out of $- (36 a^{2}) - 1 (- 1775)$ .

$\frac{- (36 a^{2} - 1775)}{3600}$

Step 5.5

Simplify the expression.

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Step 5.5.1

Rewrite $- (36 a^{2} - 1775)$ as $- 1 (36 a^{2} - 1775)$ .

$\frac{- 1 (36 a^{2} - 1775)}{3600}$

Step 5.5.2

Move the negative in front of the fraction.

$- \frac{36 a^{2} - 1775}{3600}$