Addition and Subtraction of Mixed Numbers - Examples, Exercises and Solutions

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 $\frac{2}{3}$.

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 $7\frac{3}{5}$.

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 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 $2\frac{2}{5} + 2\frac{2}{5}$, 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.

To solve the subtraction of the mixed numbers $7\frac{1}{4} - 3\frac{2}{4}$, we follow these steps:

• Step 1: Subtract the whole numbers:
  $7 - 3 = 4$.
• Step 2: Subtract the fractions:
  $\frac{1}{4} - \frac{2}{4}$ results in $\frac{-1}{4}$, because the numerators give $1 - 2 = -1$.
• Step 3: Combine these results, we initially have $4\frac{-1}{4}$. Since we can't leave a negative fraction in this form, we adjust by borrowing 1 from the whole number:
• Convert $1$ (borrowed from 4) into $\frac{4}{4}$ which combines with the fraction: $\frac{4}{4} - \frac{1}{4} = \frac{3}{4}$.
• Step 4: Adjusting the whole number:
  Remove 1 from 4 to account for the adjustment: $4 - 1 = 3$.

Therefore, combining these parts, the mixed number resulting from the subtraction is $3\frac{3}{4}$.

Thus, the final result is $3\frac{3}{4}$.

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

• Step 1: Decompose each mixed number into its whole and fractional parts.
• Step 2: Subtract the whole numbers.
• Step 3: Subtract the fractional parts having the same denominator.
• Step 4: Combine the results to find the final answer.

Now, let's work through each step:

Step 1: Decompose the mixed numbers.
- The first mixed number is $1\frac{2}{3}$, which can be expressed as the whole number 1 and the fraction $\frac{2}{3}$.
- The second mixed number is $1\frac{1}{3}$, which can be expressed as the whole number 1 and the fraction $\frac{1}{3}$.

Step 2: Subtract the whole numbers.
- Subtract the whole numbers: $1 - 1 = 0$.

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

Step 4: Combine the results.
- Since the whole number result is 0, the result of the fractional subtraction $\frac{1}{3}$ is the final answer.

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

To solve $13\frac{2}{3} - 3\frac{1}{3}$, we'll follow these steps:

• Step 1: Subtract the whole numbers: $13 - 3 = 10$.
• Step 2: Subtract the fractions: $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$.
• Step 3: Combine the results: Combine the whole number and the fraction to get $10\frac{1}{3}$.

Therefore, the solution to the problem is $10\frac{1}{3}$.

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

• Step 1: Extract the whole number and fraction parts from each mixed number.
• Step 2: Add the whole numbers together.
• Step 3: Add the fractions together using their common denominator.
• Step 4: Combine the results, checking if any simplification is needed.

Now, let's work through each step:
Step 1: From $3\frac{1}{4}$, the whole number is $3$ and the fraction is $\frac{1}{4}$. From $1\frac{2}{4}$, the whole number is $1$ and the fraction is $\frac{2}{4}$.
Step 2: Add the whole numbers: $3 + 1 = 4$.
Step 3: Add the fractions $\frac{1}{4} + \frac{2}{4}$. Since the denominators are the same, we add the numerators: $\frac{1+2}{4} = \frac{3}{4}$.
Step 4: Combine the results from Steps 2 and 3 to get $4 + \frac{3}{4} = 4\frac{3}{4}$.

Therefore, the solution to the problem is $4\frac{3}{4}$, which matches choice 3.

To solve the problem $4\frac{1}{2} - 2\frac{1}{2}$, we need to follow these steps:

• Step 1: Identify the components of each mixed number.
  $4\frac{1}{2}$ consists of a whole number $4$ and a fraction $\frac{1}{2}$.
  $2\frac{1}{2}$ consists of a whole number $2$ and a fraction $\frac{1}{2}$.
• Step 2: Subtract the whole numbers.
  Subtract the whole number of the second from the first: $4 - 2 = 2$.
• Step 3: Subtract the fractions.
  Since both fractions are $\frac{1}{2}$, subtract them: $\frac{1}{2} - \frac{1}{2} = 0$.
• Step 4: Combine the results.
  The result from the whole numbers is $2$, and the result from the fractions is $0$. So, $2 + 0 = 2$.

Therefore, the answer to the problem $4\frac{1}{2} - 2\frac{1}{2}$ is $2$.

To solve the problem $6 + 5\frac{2}{3}$, we will follow these steps:

• Step 1: Identify the whole numbers: $6$ and $5$.
• Step 2: Add the whole numbers: $6 + 5 = 11$.
• Step 3: Recognize the fractional part: $\frac{2}{3}$.
• Step 4: Combine the whole number result with the fractional part: $11 + \frac{2}{3}$.

Resultantly, when adding these components, the complete sum is $11\frac{2}{3}$.

Therefore, the solution to the problem is $11\frac{2}{3}$.

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

• Step 1: Separate the mixed number into whole and fractional parts.
• Step 2: Add the whole numbers separately from the fractional part.
• Step 3: Combine the results for the final sum.

Now, let's work through each step:

Step 1: The mixed number $2\frac{1}{3}$ consists of the whole number 2 and the fraction $\frac{1}{3}$.

Step 2: Add the whole numbers: $7 + 2 = 9$.

Step 3: Since the fraction $\frac{1}{3}$ has no other fractional parts to add, we simply keep it as is and attach it to the 9.

Therefore, the overall sum is $9\frac{1}{3}$.

After comparing our solution to the possible answer choices, the correct choice is $9\frac{1}{3}$.

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

• Step 1: Identify the whole and fractional parts of the mixed number.
• Step 2: Add the whole numbers together.
• Step 3: Combine the result with the fractional part.

Now, let's work through each step:
Step 1: The mixed number $3\frac{3}{7}$ consists of the whole number 3 and the fraction $\frac{3}{7}$.
Step 2: Add the whole numbers: $3 + 2 = 5$.
Step 3: The final result combines the sum of the whole numbers with the original fraction: $5 + \frac{3}{7} = 5\frac{3}{7}$.

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

To solve the problem $1 + 2\frac{1}{2}$, follow these steps:

• Step 1: Identify the numbers to add: $1$ is a whole number, and $2\frac{1}{2}$ is a mixed number consisting of the whole part $2$ and the fractional part $\frac{1}{2}$.
• Step 2: Add the whole numbers: $1 + 2 = 3$.
• Step 3: Keep the fractional part from the mixed number unchanged: $\frac{1}{2}$.
• Step 4: Combine the result of the whole numbers' addition with the fractional part: $3 + \frac{1}{2} = 3\frac{1}{2}$.

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

To solve the problem of $1 - \frac{3}{4}$, we need to follow these steps:

• Step 1: Express the whole number 1 as a fraction with the same denominator as $\frac{3}{4}$.
• Step 2: Perform the subtraction with the common denominators.
• Step 3: Simplify the resulting fraction, if necessary.

Let's work through each step:
Step 1: Convert the whole number 1 into a fraction with a denominator of 4. Therefore, $1$ can be written as $\frac{4}{4}$.
Step 2: Now subtract $\frac{3}{4}$ from $\frac{4}{4}$. The formula for subtracting fractions is:

Using the numbers we have:

Step 3: The resulting fraction $\frac{1}{4}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{1}{4}$.