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 $\frac{8}{10}$.

We can see that there are three shaded parts out of six parts in total,

that is - 3/6

But this is not the final answer yet!

Let'snotice that this fraction can be reduced,

meaning, it is possible to divide both the numerator and the denominator by the same number,

so that the fraction does not lose its value. In this case, the number is 3.

3:3=1
6:3=2

And so we get 1/2, or one half.
And if we look at the original drawing, we can see that half of it is colored.

To solve this problem, follow these steps:

• Step 1: Examine each figure to determine the total number of equal parts.
• Step 2: Identify how many parts are shaded in red for each figure.
• Step 3: Calculate the fraction of the shaded area over the total area for each figure.
• Step 4: Determine which figure has the fraction $\frac{3}{4}$ shaded in red.

Now, let's work through these steps:

Step 1: Upon examining the figures provided:

• Figure A is divided into 4 equal parts, with 1 part shaded.
• Figure B is divided into 4 equal parts, with 2 parts shaded.
• Figure C is divided into 4 equal parts, with 3 parts shaded.
• Figure D is divided into 4 equal parts, with all 4 parts shaded.

Step 2: Calculate the shaded fraction for each figure:

• Figure A: $\frac{1}{4}$ shaded.
• Figure B: $\frac{2}{4} = \frac{1}{2}$ shaded.
• Figure C: $\frac{3}{4}$ shaded.
• Figure D: $\frac{4}{4} = 1$ shaded.

Step 3: Identify which figure has $\frac{3}{4}$ of its area shaded:

• Only Figure C has $\frac{3}{4}$ of its area shaded in red.

Therefore, the solution to the problem is that Figure C correctly shows $\frac{3}{4}$ of its area shaded in red.

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

• Step 1: For each shape, count the total number of equal segments.
• Step 2: Count the number of segments that are painted.
• Step 3: Calculate the fraction of the painted area by dividing the number of painted segments by the total number of segments.
• Step 4: Identify the shape where the fraction of painted area is $\frac{2}{5}$.

Now, let's work through each step:

Step 1: Let's examine the shapes given in the choices.

Step 2: For choice 3, the shape has 5 equal segments. Two of these segments are painted.

Step 3: Calculate the fraction for choice 3:

$\frac{\text{Number of painted parts}}{\text{Total number of parts}} = \frac{2}{5}$

Step 4: Therefore, choice 3 is the correct shape with $\frac{2}{5}$ of the area painted.

Therefore, the solution to the problem is the shape from choice 3, where $\frac{2}{5}$ of the area is painted.

To solve this problem, we'll determine which shape has a fraction of $\frac{2}{7}$ of its sections painted:

• Step 1: Analyze the given choices to determine the total number of sections in each shape.
• Step 2: Count the number of painted sections in each shape.
• Step 3: Calculate the fraction of painted sections for each shape.
• Step 4: Identify which, if any, of the fractions is equal to $\frac{2}{7}$.

Let's go through these steps with the shapes provided:

Choice 1: This shape is divided into 5 sections (3 empty, 2 painted):

The fraction of painted sections $= \frac{2}{5}$.

Choice 2: This shape is divided into 7 sections (5 empty, 2 painted):

The fraction of painted sections $= \frac{2}{7}$.

Choice 3: This shape is divided into 7 sections, same as choice 2:

The fraction of painted sections $= \frac{2}{7}$.

Choice 4: This shape is divided into 7 sections (5 empty, 2 painted):

The fraction of painted sections $= \frac{2}{7}$.

Both Choice 2 and Choice 4 have exactly the fraction $\frac{2}{7}$ of the sections painted. Since we are looking for one choice, we’ll choose the first (Choice 2) based on its placement in the sequence.

Therefore, the shape which represents a fraction of the painted part of $\frac{2}{7}$ is found in Choice 2.

To solve this problem, we'll analyze each representation:

• Step 1: Identify the divisions and colored sections in each representation.
• Step 2: Convert the colored sections to fractions relative to the total divisions.
• Step 3: Compare each fraction with $\frac{3}{5}$.

Let's apply these steps:

Choice 1: The rectangle is divided into 5 parts with 3 parts colored on the left and 1 part colored on the right, so this represents $\frac{3}{5} + \frac{1}{5} = \frac{4}{5}$. This is greater than $\frac{3}{5}$.

Choice 2: The rectangle shows 1 part colored out of 5 total, $\frac{1}{5}$, which is less than $\frac{3}{5}$.

Choice 3: Similar to Choice 2, it shows 1 part colored out of 5 total, $\frac{1}{5}$, which is also less than $\frac{3}{5}$.

Choice 4: Two sections each representing $\frac{1}{5}$, totaling $\frac{2}{5}$, which is less than $\frac{3}{5}$.

Therefore, the correct choice is Choice 1 where the painted part, $\frac{4}{5}$, is greater than $\frac{3}{5}$.

To find the shape where the colored section accounts for more than $\frac{1}{5}$ of the whole, we'll follow these steps:

• Step 1: Count the total number of sections in each shape.
• Step 2: Count the number of sections that are colored.
• Step 3: Calculate the fraction represented by the colored sections.
• Step 4: Compare this fraction with $\frac{1}{5}$.

Let's apply this to the given choices:

**Choice 1:**
The shape is comprised of 6 sections, with 2 sections being colored.
The fraction of the shape that is colored is $\frac{2}{6} = \frac{1}{3}$.
Since $\frac{1}{3}$ is greater than $\frac{1}{5}$, this choice meets the condition.

**Choice 2:**
The shape is similar but has only 1 section colored out of 6 in total.
The fraction is $\frac{1}{6}$, which is less than $\frac{1}{5}$. This does not satisfy the condition.

**Choice 3:**
Here, 1 out of 5 sections is colored.
The fraction is $\frac{1}{5}$, which is exactly $\frac{1}{5}$ but not more than $\frac{1}{5}$.

**Choice 4:**
This shape has 1 out of 6 sections colored.
The fraction is $\frac{1}{6}$, which is less than $\frac{1}{5}$.

Therefore, in the example corresponding to Choice 1, the colored sections indeed account for more than $\frac{1}{5}$ of the entire shape.

The correct answer is Choice 1.

Let's solve the problem by following these steps:

• Step 1: Identify the total and painted sections in each illustration.
• Step 2: Calculate the fraction of painted sections.
• Step 3: Compare each fraction to $\frac{1}{9}$.

Now, let's analyze each choice:

Choice 1: The illustration shows one painted section out of 9 total sections, so the fraction is $\frac{1}{9}$.

Choice 2: The illustration shows three painted sections out of 9 total sections, so the fraction is $\frac{3}{9} = \frac{1}{3}$.

Choice 3: The illustration shows one painted section out of 9 total sections, which equals $\frac{1}{9}$.

Choice 2's $\frac{1}{3}$ is greater than $\frac{1}{9}$ since $\frac{1}{3} = \frac{3}{9}$.

Thus, the configuration in Choice 2 represents a painted part that is greater than $\frac{1}{9}$.

Therefore, the option with a painted part greater than $\frac{1}{9}$ is Choice 2.

To solve the problem, we need to determine which option displays parts painted more than $\frac{2}{5}$.

• Step 1: Each option shows an arrangement divided into 5 boxes. We seek parts painted red exceeding $\frac{2}{5}$.

• Step 2: Analyze each visual:
  -- Option 1, 1 block painted out of 5, fraction = $\frac{1}{5}$.
  -- Option 2, 2 out of 5 blocks painted, fraction = $\frac{2}{5}$.
  -- Option 3, 3 blocks painted out of 5, fraction = $\frac{3}{5}$.
  -- Option 4, 1 block painted out of 5, fraction = $\frac{1}{5}$.

• Step 3: Compare $\frac{3}{5}$ in Option 3 with $\frac{2}{5}$.

Therefore, the only choice where the painted part is greater than $\frac{2}{5}$ is Option 3.