Verified Answer :

  • Understand that a mixed number \(A \frac{B}{C}\) is \(A + \frac{B}{C}\).
  • Simplify the second term: \(2 \frac{2}{2} = 2 + 1 = 3\).
  • Add the result to the first term: \(1 \frac{3}{4} + 3 = 4 \frac{3}{4}\).
  • Express as a final value: \(\boxed{4 \frac{3}{4}}\).

Explanation

  1. Analyzing the Expression

The goal is to simplify the expression \(1 \frac{3}{4} + 2 \frac{2}{2}\). A mixed number of the form \(A \frac{B}{C}\) is equivalent to the sum \(A + \frac{B}{C}\). Therefore, our expression is equivalent to \(\left(1 + \frac{3}{4}\right) + \left(2 + \frac{2}{2}\right)\). We can simplify these components independently before adding them together.

  1. Simplifying the Second Mixed Number

We first examine the second mixed number, \(2 \frac{2}{2}\). The fractional part is \(\frac{2}{2}\), which simplifies to \(1\). Substituting this back into the mixed number, we get:
\[2 \frac{2}{2} = 2 + \frac{2}{2} = 2 + 1 = 3.\]
This simplifies the second part of our expression significantly to the integer 3.

  1. Combining the Parts and Final Result

Now we add the first mixed number, \(1 \frac{3}{4}\), to the result of the second part, 3.
\[1 \frac{3}{4} + 3 = \left(1 + \frac{3}{4}\right) + 3\]
We can group the integer parts together:
\[(1 + 3) + \frac{3}{4} = 4 + \frac{3}{4} = 4 \frac{3}{4}\]
Alternatively, as an improper fraction:
\[4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}\]
Thus, the final simplified result is \(4 \frac{3}{4}\).

Examples

Imagine you are baking cookies and the recipe requires \(1 \frac{3}{4}\) cups of flour for the first batch and \(2 \frac{2}{2}\) (which is 3) cups of flour for the second batch. To know the total flour needed for both, you add these amounts: \(1 \frac{3}{4} + 3 = 4 \frac{3}{4}\) cups. This simple addition helps you manage your supplies efficiently while following your recipe perfectly.

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