Trigonometry Examples

$\frac{5}{3} + 3 \cdot 5 = 4 \frac{1}{6}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{5}{3} + 3 \cdot 5$ .

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Step 1.1.1

Multiply $3$ by $5$ .

$\frac{5}{3} + 15 = 4 \frac{1}{6}$

Step 1.1.2

To write $15$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3} + 15 \cdot \frac{3}{3} = 4 \frac{1}{6}$

Step 1.1.3

Combine $15$ and $\frac{3}{3}$ .

$\frac{5}{3} + \frac{15 \cdot 3}{3} = 4 \frac{1}{6}$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{5 + 15 \cdot 3}{3} = 4 \frac{1}{6}$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $15$ by $3$ .

$\frac{5 + 45}{3} = 4 \frac{1}{6}$

Step 1.1.5.2

Add $5$ and $45$ .

$\frac{50}{3} = 4 \frac{1}{6}$

Step 2

Simplify the right side.

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Step 2.1

Convert $4 \frac{1}{6}$ to an improper fraction.

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Step 2.1.1

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

$\frac{50}{3} = 4 + \frac{1}{6}$

Step 2.1.2

Add $4$ and $\frac{1}{6}$ .

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Step 2.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{50}{3} = 4 \cdot \frac{6}{6} + \frac{1}{6}$

Step 2.1.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{50}{3} = \frac{4 \cdot 6}{6} + \frac{1}{6}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{50}{3} = \frac{4 \cdot 6 + 1}{6}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $4$ by $6$ .

$\frac{50}{3} = \frac{24 + 1}{6}$

Step 2.1.2.4.2

Add $24$ and $1$ .

$\frac{50}{3} = \frac{25}{6}$

Step 3

Since $\frac{50}{3} \neq \frac{25}{6}$ , there are no solutions.

No solution