Part of an Amount: Identify the greater value

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.

To solve this problem, we'll visually evaluate the proportion of the painted area relative to the entire space for each choice and compare it with $\frac{1}{3}$.

• First, observe each provided choice, ensuring painted portions are clearly defined.
• Count how many sections each graphic is divided into. The total sections represent the whole area.
• Determine the number of sections painted in red. This represents the painted area.
• Calculate the fraction of the painted area by dividing the number of painted sections by the total number of sections.
• Compare these fractions with $\frac{1}{3}$:
• Choice 1: 1 section painted out of 3 total sections, $\frac{1}{3}$
• Choice 2: 1 section painted out of 3 total sections, $\frac{1}{3}$
• Choice 3: 2 sections painted out of 3 total sections, $\frac{2}{3}$
• According to the calculations, Choice 3 results in a painted fraction of $\frac{2}{3}$, which is greater than $\frac{1}{3}$. Therefore, Choice 3 has the painted part greater than $\frac{1}{3}$.

Hence, the way in which the painted part is greater than $\frac{1}{3}$ is represented by Choice 3.