To solve the expression $\frac{29}{60} \pm \frac{3}{4}$, let's break it down step by step.

Step 1: Find a common denominator

The common denominator between 60 and 4 is 60.

• Convert $\frac{3}{4}$ to have a denominator of 60: $\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}$

Step 2: Perform the operations

Now, substitute the fractions: $\frac{29}{60} \pm \frac{45}{60}$

For Addition:

$\frac{29}{60} + \frac{45}{60} = \frac{29 + 45}{60} = \frac{74}{60} = \frac{37}{30}$

For Subtraction:

$\frac{29}{60} - \frac{45}{60} = \frac{29 - 45}{60} = \frac{-16}{60} = \frac{-4}{15}$

Final Answers:

• Addition: $\frac{37}{30}$
• Subtraction: $\frac{-4}{15}$

Would you like any further details or explanations?

Here are five related questions:

1. How do you add fractions with different denominators?
2. How can you simplify fractions after addition or subtraction?
3. What is the least common denominator and how is it used?
4. How do you convert an improper fraction to a mixed number?
5. What are the properties of fractions when dealing with negative numbers?

Tip: Always simplify fractions whenever possible to make the final answer easier to interpret.