simplify -3/4r + 3 - -5/6r - 6

Answer 1

To simplify the expression $-\frac{3}{4}r+3--\frac{5}{6}r-6$, follow these steps:

1. Eliminate the negative sign in front of -5/6r: $-\frac{3}{4}r+3+\frac{5}{6}r-6$

2. Combine like terms:

   • For the constant terms: $3-6=-3$
   • For the variable terms: Combine $-\frac{3}{4}r$ and $\frac{5}{6}r$.

   To combine $-\frac{3}{4}r$ and $\frac{5}{6}r$, we need a common denominator. The least common multiple of 4 and 6 is 12.

   • Convert $-\frac{3}{4}r$ to twelfths: $$-\frac{3}{4}r=-\frac{3\times 3}{4\times 3}r=-\frac{9}{12}r$$

   • Convert $\frac{5}{6}r$ to twelfths: $$\frac{5}{6}r=\frac{5\times 2}{6\times 2}r=\frac{10}{12}r$$

3. Now combine the variable terms: $-\frac{9}{12}r+\frac{10}{12}r=\frac{10-9}{12}r=\frac{1}{12}r$

4. Putting it all together: $$\frac{1}{12}r-3$$

Therefore, the simplified expression is: $$\frac{1}{12}r-3$$