We are asked to solve two math problems. First, $1 \frac{1}{4} - \frac{1}{3} = ?$ Second, $60 - 42 \div 6 = ?$

1. Problem Description

We are asked to solve two math problems.

First, $1 \frac{1}{4} - \frac{1}{3} = ?$

Second, $60 - 42 \div 6 = ?$

2. Solution Steps

For the first problem, $1 \frac{1}{4} - \frac{1}{3}$:

First, we convert the mixed number $1 \frac{1}{4}$ to an improper fraction.

$1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}$

So, the problem becomes $\frac{5}{4} - \frac{1}{3}$.

Next, we find a common denominator for the fractions. The least common multiple of 4 and 3 is

1

2. $\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$

$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Now we can subtract the fractions.

$\frac{15}{12} - \frac{4}{12} = \frac{15-4}{12} = \frac{11}{12}$

For the second problem, $60 - 42 \div 6$:

According to the order of operations (PEMDAS/BODMAS), we must perform division before subtraction.

$42 \div 6 = 7$

So, the problem becomes $60 - 7$.

$60 - 7 = 53$

3. Final Answer

The answer to the first problem is $\frac{11}{12}$.

The answer to the second problem is $53$.