Mixed Numbers and Fractions Greater than 1: Writing fractions in their simplest form

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

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 $\frac{13}{9}$ 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 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 $\frac{17}{11}$ 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 $\frac{13}{11}$ 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 $\frac{6}{2}$ 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 solve the problem of converting $\frac{14}{6}$ into a mixed number, we will perform the following steps:

• Step 1: Divide the Numerator by the Denominator
  Divide 14 by 6. The division gives us a quotient (whole number) and a remainder.

• Step 2: Determine the Whole Number
  The whole number from the division of 14 by 6 is 2, because $6 \times 2 = 12$ with a remainder.

• Step 3: Find the Remainder
  Subtract $12$ from $14$ to find the remainder: $14 - 12 = 2$.

• Step 4: Construct the Mixed Number
  The remainder 2 becomes the numerator of the fractional part, keeping the original denominator 6. Therefore, the mixed number is $2\frac{2}{6}$.

Thus, the improper fraction$\frac{14}{6}$ can be expressed as the mixed number $2\frac{2}{6}$.

The solution to the problem is $2\frac{2}{6}$.

To convert the improper fraction $\frac{8}{3}$ into a mixed number, we begin by performing long division on 8 by 3.

• Step 1: Divide 8 by 3. The division gives us 2 as the whole number because 3 fits into 8 two times.
• Step 2: Calculate the remainder: $8 - (3 \times 2) = 2$.
• Step 3: Construct the fractional part with the remainder. The remainder over the original denominator gives us $\frac{2}{3}$.

Therefore, putting it together, $\frac{8}{3}$ as a mixed number is $2\frac{2}{3}$.

The correct answer is choice 3: $2\frac{2}{3}$.

To convert the improper fraction $\frac{12}{5}$ into a mixed number, we need to understand how to express the fraction as a combination of a whole number and a proper fraction.

• Step 1: Divide the numerator by the denominator. We have $12 \div 5$.
• Step 2: Perform the division.
  When dividing 12 by 5, the quotient is 2, since $5 \times 2 = 10$. This gives us the whole number part of the mixed number.
• Step 3: Determine the remainder.
  The remainder is $12 - 10 = 2$. This remainder becomes the numerator of the fractional part.
• Step 4: Write the mixed number.
  Using the quotient and remainder, we express the fraction as a mixed number: $2\frac{2}{5}$.

Therefore, the fraction $\frac{12}{5}$ as a mixed number is $2\frac{2}{5}$.

To convert the fraction $\frac{7}{2}$ into a mixed number, follow these steps:

• Step 1: Divide the numerator by the denominator. Perform the division $7 \div 2$.
• Step 2: Determine the quotient and remainder. The division $7 \div 2$ gives a quotient of 3 and a remainder of 1.
• Step 3: The quotient becomes the whole number part of the mixed number.
• Step 4: Write the remainder over the original denominator to form the fractional part. So, the remainder 1 over 2 gives the fraction $\frac{1}{2}$.

Therefore, the mixed number is $3\frac{1}{2}$.

This corresponds to choice 2.

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

• Step 1: Divide the numerator by the denominator.
• Step 2: Determine if the result is a whole number or a mixed number.

Now, let's proceed with these steps:
Step 1: We have the fraction $\frac{16}{4}$. To convert this into a mixed number, we need to perform the division of 16 by 4.
Step 2: Performing the division, $\frac{16}{4} = 4$. Since there is no remainder, the result is a whole number, not a mixed number.

Therefore, the fraction $\frac{16}{4}$ as a mixed number is $4$.

To convert $\frac{19}{2}$ into a mixed number, let's follow these steps:

• Step 1: Divide the numerator by the denominator.
  Perform $19 \div 2$. The quotient is 9 and the remainder is 1.
• Step 2: Express the result as a mixed number.
  The quotient 9 will be the whole number part, and the remainder 1 will be the numerator of the fractional part, over the original denominator 2. Therefore, we express the result as $9\frac{1}{2}$.

Hence, the fraction $\frac{19}{2}$ as a mixed number is $9\frac{1}{2}$.

To solve the problem of converting the improper fraction $\frac{15}{4}$ into a mixed number, we follow these steps:

• Step 1: Perform division $15 \div 4$.
• Step 2: Identify the quotient and the remainder.
• Step 3: Construct the mixed number using whole number from quotient and remainder for fractional part.

Let's work through these steps:

Step 1: Divide the numerator by the denominator. Here, $15 \div 4 = 3$ with a remainder of 3. This means 4 goes into 15 a total of 3 times, and there are 3 remainder.

Step 2: The quotient from the division is the whole number part of the mixed number. Hence, the whole number part is 3.

Step 3: The remainder becomes the numerator of the fractional part. The denominator remains the same as the original fraction. Therefore, the fractional part is $\frac{3}{4}$.

Putting it all together, the mixed number is $3 \frac{3}{4}$.

Thus, the fraction $\frac{15}{4}$ as a mixed number is $\mathbf{3 \frac{3}{4}}$.

To write the improper fraction $\frac{18}{5}$ as a mixed number, we perform the following steps:

• Step 1: Divide the numerator by the denominator. Calculate $18 \div 5$.
• Step 2: Determine the quotient and remainder. The division $18 \div 5$ gives a quotient of 3 and a remainder of 3.
• Step 3: Express this result as a mixed number. The quotient 3 becomes the whole number, and the remainder 3 is the numerator of the fraction part, with the denominator 5 retained.

These steps yield the mixed number $3\frac{3}{5}$. By examining the choices provided, we confirm that choice 1, $3\frac{3}{5}$, is the correct option.

Therefore, the fraction $\frac{18}{5}$ as a mixed number is $3\frac{3}{5}$.

To solve this problem, we'll convert the fraction $\frac{20}{4}$ into its simplest form:

• Step 1: Perform the division of the numerator by the denominator.
  $\frac{20}{4}$ can be simplified by dividing 20 by 4.
• Step 2: Calculate $20 \div 4 = 5$.
• Step 3: Since there is no remainder, $\frac{20}{4}$ simplifies to the whole number 5.

Thus, the fraction $\frac{20}{4}$ as a mixed number is simply the whole number $5$.