Verified Answer :

  • Identify the expression components: \(1 \frac{3}{4}\) and \(2 \frac{2}{2}\).
  • Simplify \(2 \frac{2}{2}\) to \(3\) since \(\frac{2}{2} = 1\).
  • Add the whole number parts: \(1 + 3 = 4\).
  • Combine the results to get the final sum: \(4 \frac{3}{4}\) or \(\frac{19}{4}\).
  • The final answer is \(\boxed{4 \frac{3}{4}}\).

Explanation

  1. Analysis of the Expression

The objective is to simplify the expression \(1 \frac{3}{4} + 2 \frac{2}{2}\). A mixed number of the form \(A \frac{B}{C}\) is defined as the sum of the integer part \(A\) and the fractional part \(\frac{B}{C}\). Therefore, our expression can be broken down into individual parts for easier calculation.

  1. Simplifying the First Term

First, we address the mixed number \(1 \frac{3}{4}\). By definition, this is equal to \(1 + \frac{3}{4}\). This part is already in its simplest fractional form relative to the whole number.

  1. Simplifying the Second Term

Next, we look at the mixed number \(2 \frac{2}{2}\). This is equivalent to \(2 + \frac{2}{2}\). Since any non-zero number divided by itself is 1, the fraction \(\frac{2}{2}\) simplifies to \(1\). Therefore, \(2 \frac{2}{2} = 2 + 1 = 3\).

  1. Final Addition and Simplification

Finally, we add the results from the previous steps. We have \(1 + \frac{3}{4}\) from the first term and \(3\) from the second term. Combining these, we get:
\[ (1 + \frac{3}{4}) + 3 = (1 + 3) + \frac{3}{4} = 4 + \frac{3}{4} = 4 \frac{3}{4} \]
Expressed as an improper fraction, this is \(4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}\). Thus, the simplified result is \(4 \frac{3}{4}\).

Examples

Imagine you are baking a cake. You need \(1 \frac{3}{4}\) cups of flour for the batter and your recipe calls for another \(2 \frac{2}{2}\) cups of flour for the frosting. To know the total amount of flour required, you add these quantities together. Calculating \(1 \frac{3}{4} + 3\) ensures you have exactly \(4 \frac{3}{4}\) cups of flour ready to use for your baking.

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