Part of an Amount - Examples, Exercises and Solutions

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

• Step 1: Understand the problem of finding the number of tenths in 1.3.
• Step 2: Note that the decimal number 1.3 is composed of the whole number 1 and the decimal fraction 0.3.
• Step 3: Recognize that the tenths place is the first digit after the decimal point.

Now, let's work through each step:

Step 1: The problem asks us to count the number of tenths in the decimal number 1.3. This involves understanding the place value of each digit.

Step 2: In the decimal 1.3, the digit '1' represents the whole number and does not contribute to the count of tenths. The digit '3' is in the tenths place.

Step 3: Since the digit '3' is in the tenths place, it denotes 3 tenths or the fraction $\frac{3}{10}$.

Therefore, the number of tenths in 1.3 is $3$.

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

• Examine the given number 0.4.
• Identify and list all digits represented in this decimal.
• Count the occurrences of the digit '1'.

Now, let's work through each step:
Step 1: The number given is 0.4. This number is composed of the digits '0', '.', and '4'.
Step 2: Identify any '1's among these digits. There are no '1's in this sequence of digits.
Step 3: Thus, the count of the digit '1' in the number 0.4 is zero.

Therefore, the number of ones in the number 0.4 is $0$.

To solve this problem, we'll examine the given decimal number, $0.07$, to identify how many '1's it contains.

Let's break down the number $0.07$:

• The digit to the left of the decimal is $0$, which is the ones place. It is not '1'.
• The first digit after the decimal point is $0$, which represents tenths. This is also not '1'.
• The next digit is $7$, which represents hundredths. This digit is also not '1'.

None of the digits in the number $0.07$ are equal to '1'.

Therefore, the number of ones in $0.07$ is 0.

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

• Step 1: Define the place value of each digit in the decimal number.
• Step 2: Identify the specific digit in the hundredths place.
• Step 3: Determine the number of hundredths in 0.96.

Now, let's work through each step:

Step 1: Consider the decimal number $0.96$. In decimal representation, the digit immediately after the decimal point represents tenths, and the digit following that represents hundredths.

Step 2: In the number $0.96$, the digit $9$ is in the tenths place, and the digit $6$ is in the hundredths place.

Step 3: Therefore, the number of hundredths in $0.96$ is $6$.

Thus, the solution to the problem is that there are 6 hundredths in the number $0.96$.

To solve this problem, we need to examine the decimal number $0.81$ and count the number of '1's present:

• The first digit after the decimal point is $8$.
• The second digit after the decimal point is $1$.

Now, count the number of '1's in $0.81$:

There is only one '1' in the entire number $0.81$ because it appears only once after the decimal point.

Thus, the total number of ones in $0.81$ is 0, since the task is to count ones in the whole number, and there are no ones in the integer part of $0$, nor in the remaining digits $8$.

Therefore, the solution to the problem is $0$, which corresponds to choice 3.

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 $3$.