Addition and Subtraction of Mixed Numbers

To solve this problem, we'll follow these steps:

• Step 1: Add the whole number parts.
• Step 2: Add the fractional parts.
• Step 3: Combine results and simplify if necessary.

Now, let's work through each step:
Step 1: The mixed numbers are $5\frac{2}{5}$ and $2\frac{1}{5}$. First, add the whole number parts: $5 + 2 = 7$.
Step 2: Next, add the fractional parts: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$. Since the denominators are the same, just add the numerators.
Step 3: Combine these sums to form the mixed number: $7 + \frac{3}{5} = 7\frac{3}{5}$.

Therefore, the solution to the problem is $7\frac{3}{5}$.

To solve this problem, we will add the mixed numbers $6\frac{2}{6}$ and $1\frac{2}{6}$ by following these steps:

• Step 1: Add the integer parts: $6 + 1 = 7$.
• Step 2: Add the fractional parts: $\frac{2}{6} + \frac{2}{6} = \frac{4}{6}$.
• Step 3: Combine the results to express the sum: $7 + \frac{4}{6}$.

Now, let's work through each step:
Step 1: Adding the whole numbers, we get $7$.
Step 2: Since both fractions have a common denominator of 6, we add the numerators: $2 + 2 = 4$, thus giving us the fraction $\frac{4}{6}$.
Step 3: The combined sum of the whole number and the fraction is $7\frac{4}{6}$.

Hence, the solution to the problem is $7\frac{4}{6}$.

To solve the problem $2\frac{1}{3} - 1\frac{2}{3}$, we'll perform the following steps:

• Step 1: Subtract the integer parts: $2 - 1 = 1$.
• Step 2: Subtract the fractional parts: $\frac{1}{3} - \frac{2}{3}$.

To calculate $\frac{1}{3} - \frac{2}{3}$:

Since the fractions have a common denominator, subtract only the numerators:
$1 - 2 = -1$.
Therefore, $\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$.

Now combine the results:

The subtraction results in $1 - \frac{1}{3}$.

To simplify, note $1 = \frac{3}{3}$.

Thus, $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$.

Therefore, the solution to $2\frac{1}{3} - 1\frac{2}{3}$ is $\frac{2}{3}$.

Let's solve the problem step-by-step:

• Step 1: Identify the parts of the mixed number $10\frac{1}{2}$. It consists of the whole number $10$ and the fraction $\frac{1}{2}$.

• Step 2: We'll subtract $\frac{1}{2}$ (the fraction we are given to subtract) from the fraction part of the mixed number:

$\frac{1}{2} - \frac{1}{2} = 0$

Step 3: After performing the subtraction, the fractional part becomes $0$.

Step 4: This leaves us with the whole part of the mixed number on its own, which is $10$.

Therefore, the solution to the problem is $10$.

To solve the problem $2\frac{2}{5} + 2\frac{2}{5}$, follow these steps:

• Step 1: Add the whole numbers together. We have $2 + 2 = 4$.
• Step 2: Add the fractional parts together. Since both fractions have the same denominator, simply add the numerators: $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$.
• Step 3: Combine the results from Step 1 and Step 2. The sum of the whole numbers and fraction parts is $4 + \frac{4}{5} = 4\frac{4}{5}$.

Thus, the sum of $2\frac{2}{5}$ and $2\frac{2}{5}$ is $\mathbf{4\frac{4}{5}}$.

The answer corresponds to choice 4.