Question

use the number line to find the sum.
$1\frac{3}{4} + 2\frac{3}{4}$
options: $3\frac{2}{4}$, 4, $4\frac{2}{4}$, 5

Explanation:

Step1: Convert mixed numbers to improper fractions

$1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}$, $2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}$

Step2: Add the improper fractions

$\frac{7}{4}+\frac{11}{4}=\frac{7 + 11}{4}=\frac{18}{4}$

Step3: Simplify the result

$\frac{18}{4}=\frac{9}{2}=4\frac{1}{2}$? Wait, no, wait. Wait, maybe using the number line. Wait, the first number is $1\frac{3}{4}$, then we add $2\frac{3}{4}$. Let's do it as mixed numbers: add the whole numbers and the fractions. Whole numbers: $1 + 2 = 3$. Fractions: $\frac{3}{4}+\frac{3}{4}=\frac{6}{4}=\frac{3}{2}=1\frac{1}{2}$. Then total is $3+1\frac{1}{2}=4\frac{1}{2}$? Wait, but the options have $4\frac{2}{4}$ which is equal to $4\frac{1}{2}$. Wait, let's check the number line. Starting at $1\frac{3}{4}$, moving $2\frac{3}{4}$ units. Let's count the intervals. Each unit is divided into 4 parts. $1\frac{3}{4}$ is at 7/4. Adding $2\frac{3}{4}$ (11/4) gives 18/4 = 9/2 = 4.5, which is $4\frac{2}{4}$ (since 2/4 = 1/2). So the correct option is the one with $4\frac{2}{4}$.

Answer:

The correct option is the one labeled with $4\frac{2}{4}$ (the second option from the left among the choices, assuming the choices are $3\frac{2}{4}$, 4, $4\frac{2}{4}$, 5; so the answer is the option with $4\frac{2}{4}$).