Basic Math Examples

$\frac{5}{9} + \frac{3}{4 j d \cdot d y g y}$

Step 1

Simplify each term.

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Step 1.1

Multiply $d$ by $d$ by adding the exponents.

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Step 1.1.1

Move $d$ .

$\frac{5}{9} + \frac{3}{4 j (d \cdot d) y g y}$

Step 1.1.2

Multiply $d$ by $d$ .

$\frac{5}{9} + \frac{3}{4 j d^{2} y g y}$

Step 1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 1.2.1

Move $y$ .

$\frac{5}{9} + \frac{3}{4 j d^{2} (y \cdot y) g}$

Step 1.2.2

Multiply $y$ by $y$ .

$\frac{5}{9} + \frac{3}{4 j d^{2} y^{2} g}$

Step 2

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{4 j g d^{2} y^{2}}{4 j g d^{2} y^{2}}$ .

$\frac{5}{9} \cdot \frac{4 j g d^{2} y^{2}}{4 j g d^{2} y^{2}} + \frac{3}{4 j d^{2} y^{2} g}$

Step 3

To write $\frac{3}{4 j d^{2} y^{2} g}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{9} \cdot \frac{4 j g d^{2} y^{2}}{4 j g d^{2} y^{2}} + \frac{3}{4 j d^{2} y^{2} g} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $36 j g d^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{9}$ by $\frac{4 j g d^{2} y^{2}}{4 j g d^{2} y^{2}}$ .

$\frac{5 (4 j g d^{2} y^{2})}{9 (4 j g d^{2} y^{2})} + \frac{3}{4 j d^{2} y^{2} g} \cdot \frac{9}{9}$

Step 4.2

Multiply $4$ by $9$ .

$\frac{5 (4 j g d^{2} y^{2})}{36 (j g d^{2} y^{2})} + \frac{3}{4 j d^{2} y^{2} g} \cdot \frac{9}{9}$

Step 4.3

Multiply $\frac{3}{4 j d^{2} y^{2} g}$ by $\frac{9}{9}$ .

$\frac{5 (4 j g d^{2} y^{2})}{36 (j g d^{2} y^{2})} + \frac{3 \cdot 9}{4 j d^{2} y^{2} g \cdot 9}$

Step 4.4

Multiply $9$ by $4$ .

$\frac{5 (4 j g d^{2} y^{2})}{36 (j g d^{2} y^{2})} + \frac{3 \cdot 9}{36 j d^{2} y^{2} g}$

Step 4.5

Reorder the factors of $36 (j g d^{2} y^{2})$ .

$\frac{5 (4 j g d^{2} y^{2})}{36 d^{2} y^{2} g j} + \frac{3 \cdot 9}{36 j d^{2} y^{2} g}$

Step 4.6

Reorder the factors of $36 j d^{2} y^{2} g$ .

$\frac{5 (4 j g d^{2} y^{2})}{36 d^{2} y^{2} g j} + \frac{3 \cdot 9}{36 d^{2} y^{2} g j}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 (4 j g d^{2} y^{2}) + 3 \cdot 9}{36 d^{2} y^{2} g j}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $4$ .

$\frac{20 j g d^{2} y^{2} + 3 \cdot 9}{36 d^{2} y^{2} g j}$

Step 6.2

Multiply $3$ by $9$ .

$\frac{20 j g d^{2} y^{2} + 27}{36 d^{2} y^{2} g j}$