3 1/12-1 5/6=1 17/24

Let's solve the equation \( 3 \frac{1}{12} - 1 \frac{5}{6} \) step by step.

1. First, convert the mixed numbers into improper fractions.

   For \( 3 \frac{1}{12} \): \[ 3 \frac{1}{12} = \frac{3 \times 12 + 1}{12} = \frac{36 + 1}{12} = \frac{37}{12} \]

   For \( 1 \frac{5}{6} \): \[ 1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \]

2. Now we need to subtract the two fractions: \[ \frac{37}{12} - \frac{11}{6} \]

   To subtract these fractions, we need a common denominator. The least common multiple of 12 and 6 is 12. We can convert \( \frac{11}{6} \) to have a denominator of 12: \[ \frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12} \]

3. Now we can perform the subtraction: \[ \frac{37}{12} - \frac{22}{12} = \frac{37 - 22}{12} = \frac{15}{12} \]

4. Simplify \( \frac{15}{12} \): \[ \frac{15}{12} = \frac{5}{4} = 1 \frac{1}{4} \]

So, \[ 3 \frac{1}{12} - 1 \frac{5}{6} = 1 \frac{1}{4} \]

Now we can compare this result with \( 1 \frac{17}{24} \).

Converting \( 1 \frac{1}{4} \) to an improper fraction to see if it equals \( 1 \frac{17}{24} \): \[ 1 \frac{1}{4} = \frac{5}{4} \] And converting \( 1 \frac{17}{24} \): \[ 1 \frac{17}{24} = \frac{24 + 17}{24} = \frac{41}{24} \]

Now let's compare \( \frac{5}{4} \) to \( \frac{41}{24} \): Converting \( \frac{5}{4} \) to a fraction with a denominator of 24: \[ \frac{5}{4} = \frac{5 \times 6}{4 \times 6} = \frac{30}{24} \]

Since \( \frac{30}{24} \) does not equal \( \frac{41}{24} \), we can conclude: \[ 3 \frac{1}{12} - 1 \frac{5}{6} \text{ does not equal } 1 \frac{17}{24}. \]