Part of an Amount - Examples, Exercises and Solutions

Let's solve this problem step-by-step:

First, examine the grid and count the total number of sections. Observing the grid, there is a total of 6 columns, each representing equal-sized portions along the grid, as evidenced by vertical lines.

Next, count how many of these sections are colored. The entire portion from the first column to the fourth column is colored. This means we have 4 out of 6 sections that are marked red.

We can then express the colored area as a fraction: $\frac{4}{6}$.

To work out what the marked part is, we need to count how many coloured squares there are compared to how many squares there are in total.

If we count the coloured squares, we see that there are four such squares.

If we count all the squares, we see that there are seven in all.

Therefore, 4/7 of the squares are shaded in red.

Let's begin:

Step 1: Upon examination, the diagram divides the rectangle into 7 vertical sections.

Step 2: The entire shaded region spans the full width, essentially covering all sections, so the shaded number is 7.

Step 3: The fraction of the total rectangle that is shaded is $\frac{7}{7}$.

Step 4: Simplifying, $\frac{7}{7}$ becomes $1$.

Therefore, the solution is marked by the choice: Answers a + b.

To solve this problem, we will count the total number of equal sections in the grid and the number of these sections that the marked area covers.

• Step 1: Determine Total Sections. The grid is divided into several vertical sections. By examining the grid lines, we see that the total number of vertical sections is 7.
• Step 2: Determine Marked Sections. The marked (colored) part spans 3 of these vertical sections within the total grid.
• Step 3: Compute Fraction. The fraction of the total area covered by the marked part is calculated as the number of marked sections divided by the total number of sections: $\frac{3}{7}$.

Therefore, the fraction of the area that is marked is $\frac{3}{7}$.

To solve the problem of finding the fraction of the marked part in the grid:

The grid consists of a series of squares, each of equal size. The task is to count how many squares are marked compared to the entire grid.

• First, count the total number of squares in the entire grid.
• Next, count the number of marked (colored) squares.
• Then, calculate the fraction of the marked part by dividing the number of marked squares by the total number of squares.

Let's perform these steps:

The grid displays several rows of columns. Visually, there appear to be a total of 10 squares in one row with corresponding columns, forming a grid.

Count the marked squares from the provided SVG graphic:

• There are 4 shaded (marked) regions.

Total squares: 10 (lines are shown for organizing squares, as seen).

Calculate the fraction:

$\frac{\text{marked squares}}{\text{total squares}} = \frac{4}{10}$

Thus, the marked part of the shape can be given as a fraction: $\frac{4}{10}$.

To determine the fraction of the area that is shaded, we need to analyze the diagram carefully.

• Step 1: Count the total number of squares in the grid.
• Step 2: Count the number of shaded squares.
• Step 3: Calculate the fraction by dividing the number of shaded squares by the total number of squares.
• Step 4: Compare this fraction with the given choices.

Now, let's execute each step:

Step 1: The grid is structured in terms of columns and rows. Observing the entire structure, we find that there are clearly 10 columns and 1 row of squares, leading to a total of $10 \times 1 = 10$ squares in the grid.

Step 2: Each square width equals that of one column; 4 shaded sections fill up to 5 sections of columns horizontally:

• Two small shaded squares (1 width) plus one square is completely filled as part of two columns, making up 2 columns in total.
• One large shaded rectangle (5 width) fully occupies the width of a large single square (2 columns), counting as 5 columns (2 + 3 more), confirming 2 + 3 column segments cover it.

Step 3: Simplifies the amount as layed means $5$ shaded parts.

Step 4: Thus, the fraction calculated is $\frac{5}{10}$, which simplifies to $\frac{1}{2}$.

The correct answer choice corresponds to choices b and c as $\frac{5}{10}$ and $\frac{1}{2}$ are equivalent by simplification.

Therefore, the answer is:

Answers b and c

To determine the marked part, we need to calculate the fraction of the diagram that is shaded red.

First, we count the total number of rectangles in the diagram. There are 10 rectangles visible along a straight line.

Next, we count the number of rectangles shaded red. There are 8 red rectangles in the diagram.

Therefore, the fraction of the total diagram that is marked red is calculated as $\frac{\text{Number of Red Rectangles}}{\text{Total Number of Rectangles}} = \frac{8}{10}$.

This fraction simplifies to $\frac{4}{5}$, but the answer provided is in the form $\frac{8}{10}$, which is equivalent.

Therefore, the marked part of the diagram is $\frac{8}{10}$.

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