Basic Math Examples

$\frac{7}{4 z} - \frac{5}{3 z}$

Step 1

To write $\frac{7}{4 z}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{4 z} \cdot \frac{3}{3} - \frac{5}{3 z}$

Step 2

To write $- \frac{5}{3 z}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{4 z} \cdot \frac{3}{3} - \frac{5}{3 z} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $12 z$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7}{4 z}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 3}{4 z \cdot 3} - \frac{5}{3 z} \cdot \frac{4}{4}$

Step 3.2

Multiply $3$ by $4$ .

$\frac{7 \cdot 3}{12 z} - \frac{5}{3 z} \cdot \frac{4}{4}$

Step 3.3

Multiply $\frac{5}{3 z}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 3}{12 z} - \frac{5 \cdot 4}{3 z \cdot 4}$

Step 3.4

Multiply $4$ by $3$ .

$\frac{7 \cdot 3}{12 z} - \frac{5 \cdot 4}{12 z}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 3 - 5 \cdot 4}{12 z}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $7$ by $3$ .

$\frac{21 - 5 \cdot 4}{12 z}$

Step 5.2

Multiply $- 5$ by $4$ .

$\frac{21 - 20}{12 z}$

Step 5.3

Subtract $20$ from $21$ .

$\frac{1}{12 z}$