7 1/2 - 1 5/6 = [__] [__]/[__]

Answer 1

To calculate $7\frac{1}{2}-1\frac{5}{6}$, we first convert both mixed numbers into improper fractions.

1. Convert $7\frac{1}{2}$: $$7\frac{1}{2}=\frac{(7\times 2)+1}{2}=\frac{14+1}{2}=\frac{15}{2}$$

2. Convert $1\frac{5}{6}$: $$1\frac{5}{6}=\frac{(1\times 6)+5}{6}=\frac{6+5}{6}=\frac{11}{6}$$

Now we can subtract the two improper fractions: $$\frac{15}{2}-\frac{11}{6}$$

To subtract these fractions, we need a common denominator. The least common multiple of 2 and 6 is 6.

3. Convert $\frac{15}{2}$ to a fraction with a denominator of 6: $$\frac{15}{2}=\frac{15\times 3}{2\times 3}=\frac{45}{6}$$

Now we can perform the subtraction: $$\frac{45}{6}-\frac{11}{6}=\frac{45-11}{6}=\frac{34}{6}$$

4. Simplify $\frac{34}{6}$: $$\frac{34}{6}=\frac{17}{3}$$

Next, we convert $\frac{17}{3}$ back into a mixed number.

5. Divide 17 by 3:
   • 3 goes into 17 five times (5 x 3 = 15)
   • Remainder is 2.

So, $\frac{17}{3}=5\frac{2}{3}$.

Thus, $7\frac{1}{2}-1\frac{5}{6}=5\frac{2}{3}$.

The answer in the required format is: $$5\frac{2}{3}$$