Mixed Numbers and Fractions Greater Than 1

To solve the problem of converting the improper fraction $\frac{10}{6}$ to a mixed number, follow these steps:

• Step 1: Divide the numerator (10) by the denominator (6). The result is $10 \div 6 = 1$ with a remainder of 4.
• Step 2: The quotient (1) becomes the whole number part of the mixed number.
• Step 3: The remainder (4) forms the numerator of the fraction, while the original denominator (6) remains the same, giving us $\frac{4}{6}$.
• Step 4: Simplify the fraction $\frac{4}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2, resulting in $\frac{2}{3}$.

Thus, the improper fraction $\frac{10}{6}$ can be expressed as the mixed number $1\frac{2}{3}$.

Comparing this with the answer choices, we see that choice "1$\frac{4}{6}$" before simplification aligns with our calculations, and simplification details the fraction.

Therefore, the solution to the problem is $1\frac{2}{3}$ or as above in the original fraction form before simplification.

To solve the problem, we will convert the given improper fraction $\frac{10}{7}$ to a mixed number by dividing the numerator by the denominator.

• Step 1: Divide the numerator (10) by the denominator (7). This gives a quotient and a remainder.

• Step 2: Calculating $10 \div 7$ gives a quotient of 1 because 7 goes into 10 once.

• Step 3: Multiply the quotient by the divisor ($1 \times 7 = 7$).

• Step 4: Subtract the product obtained in step 3 from the original numerator to find the remainder: $10 - 7 = 3$.

• Step 5: Compose the mixed number using the quotient as the whole number and the remainder over the divisor as the fraction part: $\frac{3}{7}$.

Thus, the mixed number representation of $\frac{10}{7}$ is $\mathbf{1\frac{3}{7}}$.

To solve this problem, we'll convert the improper fraction $\frac{12}{10}$ into a mixed number.

The steps are as follows:

• Step 1: Divide the numerator (12) by the denominator (10) to determine the integer part.
  Performing the division, $12 \div 10 = 1$ with a remainder of 2. So, the integer part is 1.
• Step 2: Compute the fractional part using the remainder. The remainder from the division is 2, so the fractional part is $\frac{2}{10}$.
• Step 3: Combine the integer part and the fractional part.
  Thus, $\frac{12}{10}$ as a mixed number is $1\frac{2}{10}$. Write it as $1\frac{1}{5}$ since $\frac{2}{10} = \frac{1}{5}$ when simplified.

Upon checking with the choices provided, $1\frac{2}{10}$ matches choice 2. However, it should be noted $1\frac{2}{10} = 1\frac{1}{5}$ when simplified.

Therefore, the solution is the correct interpretation of the fraction as a mixed number $1\frac{2}{10}$ but can also be seen as $1\frac{1}{5}$.

To solve this problem, we need to convert the improper fraction $\frac{12}{8}$ into a mixed number.

Here's how we'll do it:

• The first step is to divide the numerator by the denominator: $12 \div 8$.
• This division gives us a quotient of 1 and a remainder of 4.
• The quotient, 1, becomes the whole number part of our mixed number.
• The remainder is used as the new numerator over the original denominator to form the fractional part: $\frac{4}{8}$.
• The mixed number is thus $1\frac{4}{8}$.
• Finally, since $\frac{4}{8}$ can be simplified, we reduce it to $\frac{1}{2}$.

Thus, the mixed number representation is correctly simplified as $1\frac{1}{2}$.

However, when selecting from the given choices, the correct choice based on the options provided is $1\frac{4}{8}$ (Choice 4), which matches the unsimplified form.

Therefore, the solution to the problem is $1\frac{4}{8}$.

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 $1\frac{2}{11}$.