Fractions as Divisors - Examples, Exercises and Solutions

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 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 $\frac{13}{9}$ 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 solve the problem of converting the fraction $\frac{16}{10}$ to a mixed number, we proceed with the following steps:

• Step 1: Identify the numerator (16) and the denominator (10).
• Step 2: Divide the numerator by the denominator to find the whole number part.
  Dividing 16 by 10 gives us a quotient of 1 (whole number) and a remainder of 6.
• Step 3: Express the result as a mixed number.
  The whole number part is 1, and the remainder is the numerator of the fractional part over the original denominator. This is $\frac{6}{10}$.
• Step 4: Write the final mixed number as: $1\frac{6}{10}$.

Therefore, the mixed number form of the fraction $\frac{16}{10}$ is $1\frac{6}{10}$.

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 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 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 $1\frac{3}{5}$.

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'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 $\frac{6}{2}$ 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 $3$.

To determine the fraction illustrated in the drawing, we must follow these procedures:

• Step 1: Count the Total Number of Parts
  Examine the drawing to determine how many equal parts the entire shape is divided into. According to the drawing, the shape is divided into a total of 6 parts.
• Step 2: Count the Shaded Parts
  Next, count the number of parts that are shaded. From the drawing, we can identify that 3 of these parts are shaded.
• Step 3: Write the Fraction
  The fraction is represented by placing the number of shaded parts as the numerator and the total number of parts as the denominator. Therefore, we write the fraction as $\frac{3}{6}$.

Thus, the solution to the problem is $\frac{3}{6}$.

To solve this problem, observe the visual representation as follows:

First, we need to count the total number of equal parts shown in the drawing. By examining the entire diagram, we can see that there are a total of six rectangles.

Second, we need to count how many of these boxes are shaded. Upon reviewing, we see that four boxes are shaded.

Therefore, the fraction of the shaded boxes compared to the entire group is given by the ratio of shaded boxes over the total number of boxes.

Thus, the fraction represented by the drawing is:

$\frac{4}{6}$

This corresponds to the first answer choice. Therefore, the correct answer is $\frac{4}{6}$.

To find the fraction represented by the shaded areas, follow these steps:

• Step 1: Count the total number of rectangles. There are 7 rectangles in the drawing.
• Step 2: Count the number of shaded rectangles. There are 3 shaded rectangles.
• Step 3: Form the fraction, using the number of shaded rectangles as the numerator and the total number of rectangles as the denominator.

Therefore, the fraction of the drawing that is shaded is $\frac{3}{7}$.

This value corresponds to option 4 in the provided choices, confirming $\frac{3}{7}$ is the correct answer.

To solve the problem, we will follow these steps:

• Step 1: Count the total number of equal parts shown in the drawing.
• Step 2: Count the number of shaded parts in the drawing.
• Step 3: Form the fraction using the number of shaded parts over the total number of parts.

Now, let's address these steps in detail:

Step 1: Count the total equal parts.
From the drawing, it appears there are 7 equal parts.

Step 2: Count the shaded parts.
There are 5 shaded parts highlighted in the drawing.

Step 3: Write the fraction.
Now, we write the fraction as:
$\frac{5}{7}$

This fraction represents the shaded area of the total, therefore the solution to the problem is $\frac{5}{7}$.

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 $\frac{7}{7}$.