Basic Math Examples

$\frac{3}{5} + \frac{7 (\sqrt{53})}{53} \div 1 + (\frac{3}{5}) (- \frac{7 (\sqrt{53})}{53})$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{3}{5} + \frac{\frac{7 (\sqrt{53})}{53}}{1} + (\frac{3}{5}) (- \frac{7 (\sqrt{53})}{53})$

Step 1.2

Divide $\frac{7 (\sqrt{53})}{53}$ by $1$ .

$\frac{3}{5} + \frac{7 (\sqrt{53})}{53} + (\frac{3}{5}) (- \frac{7 (\sqrt{53})}{53})$

Step 1.3

Multiply $\frac{3}{5} (- \frac{7 \sqrt{53}}{53})$ .

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Step 1.3.1

Multiply $\frac{3}{5}$ by $\frac{7 \sqrt{53}}{53}$ .

$\frac{3}{5} + \frac{7 \sqrt{53}}{53} - \frac{3 (7 \sqrt{53})}{5 \cdot 53}$

Step 1.3.2

Multiply $7$ by $3$ .

$\frac{3}{5} + \frac{7 \sqrt{53}}{53} - \frac{21 \sqrt{53}}{5 \cdot 53}$

Step 1.3.3

Multiply $5$ by $53$ .

$\frac{3}{5} + \frac{7 \sqrt{53}}{53} - \frac{21 \sqrt{53}}{265}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{3}{5}$ by $\frac{53}{53}$ .

$\frac{3}{5} \cdot \frac{53}{53} + \frac{7 \sqrt{53}}{53} - \frac{21 \sqrt{53}}{265}$

Step 2.2

Multiply $\frac{3}{5}$ by $\frac{53}{53}$ .

$\frac{3 \cdot 53}{5 \cdot 53} + \frac{7 \sqrt{53}}{53} - \frac{21 \sqrt{53}}{265}$

Step 2.3

Multiply $\frac{7 \sqrt{53}}{53}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 53}{5 \cdot 53} + \frac{7 \sqrt{53}}{53} \cdot \frac{5}{5} - \frac{21 \sqrt{53}}{265}$

Step 2.4

Multiply $\frac{7 \sqrt{53}}{53}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 53}{5 \cdot 53} + \frac{7 \sqrt{53} \cdot 5}{53 \cdot 5} - \frac{21 \sqrt{53}}{265}$

Step 2.5

Multiply $5$ by $53$ .

$\frac{3 \cdot 53}{265} + \frac{7 \sqrt{53} \cdot 5}{53 \cdot 5} - \frac{21 \sqrt{53}}{265}$

Step 2.6

Reorder the factors of $53 \cdot 5$ .

$\frac{3 \cdot 53}{265} + \frac{7 \sqrt{53} \cdot 5}{5 \cdot 53} - \frac{21 \sqrt{53}}{265}$

Step 2.7

Multiply $5$ by $53$ .

$\frac{3 \cdot 53}{265} + \frac{7 \sqrt{53} \cdot 5}{265} - \frac{21 \sqrt{53}}{265}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \cdot 53 + 7 \sqrt{53} \cdot 5 - 21 \sqrt{53}}{265}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $53$ .

$\frac{159 + 7 \sqrt{53} \cdot 5 - 21 \sqrt{53}}{265}$

Step 4.2

Multiply $5$ by $7$ .

$\frac{159 + 35 \sqrt{53} - 21 \sqrt{53}}{265}$

Step 5

Subtract $21 \sqrt{53}$ from $35 \sqrt{53}$ .

$\frac{159 + 14 \sqrt{53}}{265}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{159 + 14 \sqrt{53}}{265}$

Decimal Form:

$0.98460957 \dots$