Simplify (7a)/(12b)-(2a)/(15b)

$\frac{7 a}{12 b} - \frac{2 a}{15 b}$

Step 1

To write $\frac{7 a}{12 b}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7 a}{12 b} \cdot \frac{5}{5} - \frac{2 a}{15 b}$

Step 2

To write $- \frac{2 a}{15 b}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 a}{12 b} \cdot \frac{5}{5} - \frac{2 a}{15 b} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $60 b$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7 a}{12 b}$ by $\frac{5}{5}$ .

$\frac{7 a \cdot 5}{12 b \cdot 5} - \frac{2 a}{15 b} \cdot \frac{4}{4}$

Multiply $5$ by $12$ .

$\frac{7 a \cdot 5}{60 b} - \frac{2 a}{15 b} \cdot \frac{4}{4}$

Multiply $\frac{2 a}{15 b}$ by $\frac{4}{4}$ .

$\frac{7 a \cdot 5}{60 b} - \frac{2 a \cdot 4}{15 b \cdot 4}$

Multiply $4$ by $15$ .

$\frac{7 a \cdot 5}{60 b} - \frac{2 a \cdot 4}{60 b}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 a \cdot 5 - 2 a \cdot 4}{60 b}$

Step 5

Simplify the numerator.

Factor $a$ out of $7 a \cdot 5 - 2 a \cdot 4$ .

Factor $a$ out of $7 a \cdot 5$ .

$\frac{a (7 \cdot 5) - 2 a \cdot 4}{60 b}$

Factor $a$ out of $- 2 a \cdot 4$ .

$\frac{a (7 \cdot 5) + a (- 2 \cdot 4)}{60 b}$

Factor $a$ out of $a (7 \cdot 5) + a (- 2 \cdot 4)$ .

$\frac{a (7 \cdot 5 - 2 \cdot 4)}{60 b}$

Multiply $7$ by $5$ .

$\frac{a (35 - 2 \cdot 4)}{60 b}$

Multiply $- 2$ by $4$ .

$\frac{a (35 - 8)}{60 b}$

Subtract $8$ from $35$ .

$\frac{a \cdot 27}{60 b}$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $27$ and $60$ .

Factor $3$ out of $a \cdot 27$ .

$\frac{3 (a \cdot 9)}{60 b}$

Cancel the common factors.

Factor $3$ out of $60 b$ .

$\frac{3 (a \cdot 9)}{3 (20 b)}$

Cancel the common factor.

$\frac{3 (a \cdot 9)}{3 (20 b)}$

Rewrite the expression.

$\frac{a \cdot 9}{20 b}$

Move $9$ to the left of $a$ .

$\frac{9 a}{20 b}$

Simplify (7a)/(12b)-(2a)/(15b)

Related Questions

Support LCMGCF.com by disabling your adblocker.