Addition and Subtraction of Mixed Numbers: Addition and subtraction from a whole

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 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 subtracting $\frac{1}{2}$ from the whole number $2$, we proceed as follows:

First, understand that the whole number $2$ can be considered as a fraction with a denominator of 2. This means that $2$ is equivalent to $\frac{4}{2}$. This step is crucial to ensure both numbers have a common denominator, facilitating the subtraction of fractions.

Now, subtract the fraction $\frac{1}{2}$ from $\frac{4}{2}$:

$\frac{4}{2} - \frac{1}{2} = \frac{4-1}{2} = \frac{3}{2}$

The fraction $\frac{3}{2}$ is improper because the numerator is larger than the denominator. Thus, we convert this into a mixed number, which is a combination of a whole number and a proper fraction. The mixed number form of $\frac{3}{2}$ is $1\frac{1}{2}$ because $2$ fits into $3$ once with a remainder of $1$.

Therefore, the result of $2-\frac{1}{2}$ is $\mathbf{1\frac{1}{2}}$.

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 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:

$\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$

Using the numbers we have:

$\frac{4}{4} - \frac{3}{4} = \frac{4-3}{4} = \frac{1}{4}$

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

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

To solve this problem, we will follow these steps:

• Step 1: Convert the whole number 4 into a fraction with a denominator of 7.
• Step 2: Subtract the fraction $\frac{3}{7}$ from the converted fraction.
• Step 3: Simplify the resulting fraction and convert it to a mixed number if possible.

Now, let's work through each step:
Step 1: Convert the whole number 4 to a fraction with denominator 7. We multiply the numerator and denominator by 7 to get $\frac{28}{7}$.
Step 2: Subtract the fraction $\frac{3}{7}$ from $\frac{28}{7}$:

$\frac{28}{7} - \frac{3}{7} = \frac{28-3}{7} = \frac{25}{7}$

Step 3: Convert the fraction $\frac{25}{7}$ into a mixed number:

Divide 25 by 7, which gives us a quotient of 3 and a remainder of 4. Thus, the fraction $\frac{25}{7}$ is equivalent to the mixed number $3\frac{4}{7}$.

Therefore, the solution to the problem is $3\frac{4}{7}$.

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

• Step 1: Convert 4 to a fraction that shares a common denominator with $\frac{5}{7}$.
• Step 2: Perform the subtraction.
• Step 3: Simplify the result into a mixed fraction.

Now, let's work through each step:
Step 1: Convert 4 to the fraction form $\frac{28}{7}$, because $\frac{28}{7}$ is equivalent to 4.

Step 2: Subtract the fractions:
$\frac{28}{7} - \frac{5}{7} = \frac{28 - 5}{7} = \frac{23}{7}$.

Step 3: Convert $\frac{23}{7}$ to a mixed fraction.
Divide 23 by 7, which goes 3 times with a remainder of 2. Hence, $\frac{23}{7} = 3\frac{2}{7}$.

Therefore, the solution to the problem is $3\frac{2}{7}$.

To solve the problem, we need to subtract the mixed number $2\frac{2}{5}$ from 6. We will handle the subtraction in steps:

• Step 1: Break the mixed fraction $2\frac{2}{5}$ into its whole and fractional parts: the whole number is 2, and the fractional part is $\frac{2}{5}$.
• Step 2: Subtract the whole numbers: $6 - 2 = 4$.
• Step 3: Now, we need to subtract the fractional part from 4: $4 - \frac{2}{5}$.
• Step 4: Convert 4 to a fraction with the same denominator as $\frac{2}{5}$.
  This means writing 4 as $\frac{20}{5}$ (since $4 = \frac{20}{5}$).
• Step 5: Perform the subtraction: $\frac{20}{5} - \frac{2}{5} = \frac{18}{5}$.
• Step 6: Convert $\frac{18}{5}$ back to a mixed number.
  Divide 18 by 5: 18 divided by 5 is 3 with a remainder of 3. This gives the mixed number $3\frac{3}{5}$.

Therefore, the final result of $6 - 2\frac{2}{5}$ is $\mathbf{3\frac{3}{5}}$.

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

• Step 1: Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
• Step 2: Subtract the improper fraction from the whole number 5.
• Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed number to an improper fraction. For $2\frac{1}{3}$, multiply the whole number 2 by the denominator 3 and add the numerator 1: $(2 \times 3) + 1 = 7$. Thus, $2\frac{1}{3}$ is $\frac{7}{3}$.

Step 2: Subtract $\frac{7}{3}$ from 5. First, convert 5 to a fraction with the same denominator: $5 = \frac{15}{3}$. Subtract: $\frac{15}{3} - \frac{7}{3} = \frac{8}{3}$.

Step 3: Convert $\frac{8}{3}$ back to a mixed number. Divide 8 by 3: 8 divided by 3 is 2 with a remainder of 2, so $\frac{8}{3} = 2\frac{2}{3}$.

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