−3 1/6+5 3/4

Question

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Answer 1

To add the mixed numbers $-3\frac{1}{6}$ and $5\frac{3}{4}$, follow these steps:

1. Convert the mixed numbers to improper fractions.

   • For $-3\frac{1}{6}$: $$-3\frac{1}{6}=-(3\times 6+1)/6=-\frac{19}{6}$$
   • For $5\frac{3}{4}$: $$5\frac{3}{4}=(5\times 4+3)/4=\frac{23}{4}$$

2. Find a common denominator.

   • The denominators are $6$ and $4$. The least common multiple (LCM) of $6$ and $4$ is $12$.

3. Convert both fractions to have the common denominator of $12$.

   • For $-\frac{19}{6}$: $$-\frac{19}{6}=-\frac{19\times 2}{6\times 2}=-\frac{38}{12}$$
   • For $\frac{23}{4}$: $$\frac{23}{4}=\frac{23\times 3}{4\times 3}=\frac{69}{12}$$

4. Add the fractions. $$-\frac{38}{12}+\frac{69}{12}=\frac{-38+69}{12}=\frac{31}{12}$$

5. Convert the improper fraction back to a mixed number. $\frac{31}{12}$ is equal to $2\frac{7}{12}$ because:

   • $31÷12=2$ with a remainder of $7$.

Thus, the final result is: $$\boxed{{\displaystyle 2\frac{7}{12}}}$$