Part of an Amount - Examples, Exercises and Solutions

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.

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: $\frac{4}{6}$.

The task is to determine which of the given figures correctly represents the decimal fraction 0.1.

To interpret 0.1, we recognize it as $\frac{1}{10}$. This indicates that in a graphical representation of 10 equal parts, 1 part should be shaded. Each figure is assumed to be divided into such equal parts.

Let's analyze the options:

• Choice 1: Shows 10 equal divisions with 1 part shaded. This potentially represents 0.1 since it shades exactly 1 of 10 parts.
• Choice 2: Shows 10 equal divisions with more than 1 part shaded. Thus, it represents more than 0.1.
• Choice 3: Shows 10 equal divisions with numerous parts shaded. It represents a number greater than 0.1.
• Choice 4: Shows a full shading, representing 1 (i.e., shading all 10 parts), clearly not 0.1.

Hence, the correct choice that correspond to 0.1 is Choice 1. This figure accurately shades exactly 1 out of 10 equal segments.

Therefore, the solution to the problem indicates that choice 1 correctly represents the decimal fraction 0.1.

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 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 solve the problem of identifying which figure represents seven tenths, follow these steps:

• Step 1: Understand that the problem requires identification of a geometric representation for the fraction $\frac{7}{10}$ or decimal 0.7.
• Step 2: Each figure is divided into ten equal segments, representing one tenth each.
• Step 3: Carefully count the number of segments filled or shaded in each figure.

Now, let's apply these steps:

Step 1: We note that each figure is evenly divided into ten parts.

Step 2: By inspecting each option, you can see which has exactly seven segments shaded. This corresponds directly to seven out of ten segments, or seven tenths.

Step 3: Upon review, the figure corresponding to choice 3 shows exactly seven shaded segments out of ten.

Therefore, the solution to the problem is eminently found as choice 3, representing seven tenths.

To solve this problem, let's analyze the shaded area in terms of grid squares:

• Step 1: The top rectangle in the grid is completely filled. Let's count the shaded squares horizontally: There are 10 squares across aligned vertically in 1 row, giving $1$ as the shaded area.
• Step 2: The bottom rectangle is partially filled. Observe it spans $6$ squares horizontally by $1$ square height in the grid row. The shaded area will, therefore, be $0.6$ as it spans only $60\%$ of the horizontal extent.
• Step 3: Add both shaded areas of the rectangles from step 1 and step 2: $1$ (top) and $0.6$ (bottom).

Thus, the total shaded area is $1 + 0.6 = 1.6$.

Therefore, the solution to the problem is $1.6$.

To solve this problem, let's carefully examine the decimal number $0.73$ digit by digit:

• The first digit after the decimal point is $7$.
• The second digit after the decimal point is $3$.

We observe that there are no digits in the sequence of $0.73$ that are the number '1'. Therefore, there are no '1's in the decimal number $0.73$.

Thus, the number of ones in the number $0.73$ is 0.

The correct choice, given the options, is choice id 1: 0.

To solve this problem, let's follow the outlined plan:

• Step 1: Count the number of shaded sections.
• Step 2: Count the total number of sections in the rectangle.
• Step 3: Express the number of shaded sections as a fraction of the total sections.
• Step 4: Convert this fraction to a decimal to find the numerical value.

Now, let's apply these steps:
Step 1: The given diagram shows that there are 4 vertical stripes shaded.
Step 2: The total number of vertical stripes (including both shaded and unshaded) is 10.
Step 3: The fraction of shaded area is $\frac{4}{10}$.
Step 4: Convert $\frac{4}{10}$ to a decimal. This equals $0.4$.

Therefore, the numerical value of the shaded area is 0.4.

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 a few simple steps to calculate the shaded area by counting strips and converting to a decimal:

• Step 1: Identify the total number of vertical strips in the entire rectangle. From the diagram, there are 10 strips in total.
• Step 2: Count the number of shaded vertical strips. According to the diagram, 5 strips are shaded.
• Step 3: Write the fraction of the shaded area relative to the total area. The fraction is $\frac{5}{10}$.
• Step 4: Simplify the fraction, which is already simplified, and then convert it to a decimal. $\frac{5}{10} = 0.5$.

Therefore, the solution to the problem is $0.5$.

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 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'll follow these steps:

• Step 1: Identify the total number of divisions in the grid.
• Step 2: Count the number of shaded divisions.
• Step 3: Calculate the fraction of the shaded area relative to the total.

Now, let's work through each step:
Step 1: The grid is divided into 10 equal vertical columns.
Step 2: Of these columns, 1 column is shaded.
Step 3: Since there are 10 columns in total, the shaded area represents $\frac{1}{10}$ of the total area.

Finally, the fraction $\frac{1}{10}$ can be expressed as the decimal $0.1$.

Therefore, the numerical value of the shaded area is $0.1$.