Mixed Numbers and Remainders Practice Problems

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 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 this problem, we'll convert the improper fraction into a mixed number. Here's how:

• Step 1: Perform division. Divide the numerator (7) by the denominator (4).
• Step 2: Determine the whole number part. The division $7 \div 4$ equals 1 with a remainder of 3.
• Step 3: Form the fractional part. Use the remainder (3) over the original denominator (4) to form the fractional part of the mixed number.

Now, let's work through each step:
Step 1: Calculate $7 \div 4$ which gives us a quotient of 1 and a remainder of 3.
Step 2: The whole number is 1.
Step 3: The fractional part is $\frac{3}{4}$, which comes from the remainder over the original denominator.

Therefore, the mixed number is $1\frac{3}{4}$.

To convert the improper fraction $\frac{8}{5}$ into a mixed number, follow these steps:

• First, divide the numerator (8) by the denominator (5).
• The division $8 \div 5 = 1$ gives us the whole number part of the mixed number, because 5 fits into 8 a maximum of once.
• Next, calculate the remainder of the division. The remainder is $8 - 5 \times 1 = 3$.
• Thus, our remainder of 3 becomes the numerator of the fractional part of our mixed number.
• The denominator of the fraction remains the same, which is 5.

Combining these parts, the mixed number from the fraction $\frac{8}{5}$ is $1\frac{3}{5}$.

Therefore, the correct answer is $1\frac{3}{5}$.