To solve the given expression $1 \frac{3}{4} + 2 \frac{1}{3}$, we will break it down into steps:

Step 1: Convert mixed numbers to improper fractions

1. For $1 \frac{3}{4}$: $1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$

2. For $2 \frac{1}{3}$: $2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3}$

So, the expression becomes: $\frac{7}{4} + \frac{7}{3}$

Step 2: Find a common denominator

The denominators are 4 and 3. The least common denominator (LCD) is 12. Rewrite each fraction with a denominator of 12:

1. $\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}$
2. $\frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}$

Now the expression becomes: $\frac{21}{12} + \frac{28}{12}$

Step 3: Add the fractions

$\frac{21}{12} + \frac{28}{12} = \frac{21 + 28}{12} = \frac{49}{12}$

Step 4: Convert back to a mixed number (if needed)

Divide $49$ by $12$:

• $49 \div 12 = 4$ remainder $1$.

So, $\frac{49}{12} = 4 \frac{1}{12}$.

Final Answer:

The value of the expression is: $4 \frac{1}{12}$

Let me know if you'd like a detailed breakdown of any step or further examples.

Related Questions:

1. How do you find the least common denominator for fractions?
2. What are the steps to convert mixed numbers to improper fractions?
3. How can improper fractions be converted back to mixed numbers?
4. What are practical uses of adding mixed numbers in real life?
5. How do you simplify improper fractions to their simplest form?

Tip:

Always simplify fractions when possible to make the calculations and final results more straightforward!