Mixed Numbers and Remainders Practice Problems

The problem involves finding the fraction represented by shaded parts in a drawing. Here's a step-by-step guide to solve it:

• Step 1: Count the total number of sections in the drawing. There are 7 blocks arranged linearly.
• Step 2: Since each block appears to be fully shaded, count those shaded. Each of the 7 blocks is shaded.
• Step 3: The fraction is formed by placing the number of shaded sections over the total sections. Thus, the fraction is $\frac{7}{7}$.

The fraction for the shaded portion of the drawing is $\frac{7}{7}$, which is a complete whole, as every block is shaded.

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

To convert the improper fraction $\frac{13}{11}$ into a mixed number, we need to perform division to separate the whole number from the fractional part.

• Step 1: Divide the numerator by the denominator. - Perform the division: $13 \div 11 = 1$. Since 13 is not a multiple of 11, we obtain a quotient and a remainder. - The division gives a quotient of 1 and a remainder of 2 (since $13 - 11 \times 1 = 2$).
• Step 2: Express the remainder as part of the fraction. - The remainder is 2, and this will be the numerator of the fractional part. - The denominator remains the same, 11.
• Step 3: Write the mixed number. - Combine the whole number and the fraction. - The mixed number is $1\frac{2}{11}$.

Now, let's verify our solution with the given choices. The correct option matches Choice 2, which is $1\frac{2}{11}$.

Therefore, the fraction $\frac{13}{11}$ as a mixed number is $1\frac{2}{11}$.

To convert the improper fraction $\frac{13}{9}$ into a mixed number, we follow these steps:

• Step 1: Perform the division of the numerator by the denominator. Divide 13 by 9.
• Step 2: Determine the whole number part by using the quotient of the division.
• Step 3: Find the remainder to establish the fractional part.
• Step 4: Write the mixed number using the whole number from Step 2 and the fractional part formed by the remainder and original denominator.

Let's carry out these steps in detail:

Divide 13 by 9:

$13 \div 9 = 1$ with a remainder of $4$.

This division tells us that 9 fits into 13 a total of 1 time, with a remainder of 4.

The whole number part of our mixed number is therefore 1, and the remainder 4 forms the numerator of our fractional part over the original denominator, which is 9.

So, the fractional part is $\frac{4}{9}$.

Therefore, the improper fraction $\frac{13}{9}$ as a mixed number is $\mathbf{1\frac{4}{9}}$.

To convert the improper fraction $\frac{17}{11}$ to a mixed number, we proceed as follows:

• Step 1: Perform the division $17 \div 11$. We find: - The quotient (whole number) is 1 since 11 goes into 17 once.
  - The remainder is 6 because $17 - (11 \times 1) = 6$.

• Step 2: Express the remainder as a fraction over the original denominator. Hence, the fractional part is $\frac{6}{11}$.

• Step 3: Combine the quotient and the remainder fraction to form the mixed number: $1\frac{6}{11}$.

Therefore, the mixed number equivalent of the fraction $\frac{17}{11}$ is $1\frac{6}{11}$.

To convert the improper fraction $\frac{6}{2}$ into a mixed number, we need to divide the numerator by the denominator:

Step 1: Evaluate the division $6 \div 2$.
By performing this division, we find that $6 \div 2 = 3$.

Since the division results in a whole number, the mixed number equivalent of $\frac{6}{2}$ is simply $3$. Therefore, there is no fractional part remaining.

Thus, the fraction $\frac{6}{2}$ expressed as a mixed number is $3$.