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.

The question requires combining two skills,

First identifying the fractions and then comparing them.

In the first stage, we need to identify which fraction is shown in each option.

To do this, we need to write in the denominator (bottom number) the total number of squares in the shape,

and in the numerator (top part) the number of colored squares.

Let's check each option and see that:

a. 5/5

b. 2/5

c. 2/3

d. 4/6

We are asked to find the fraction that is greater than 5/6.

The easiest fraction to compare with is d, since both have the same denominator.

When two fractions have the same denominator, the one with the larger numerator is greater,

therefore 4/6 is less than 5/6 and option d is eliminated.

The next easiest option to calculate is option a.

Any number divided by itself equals 1,

therefore 5/5 is 1. We can also do this in reverse, to bring the fraction to a denominator of 6,

1 equals 6/6.

6/6 is greater than 5/6, so we know that option a is correct,

but let's continue and check the other options.

Option b is the next option, and to check it we'll use a different method - comparing to one-half.

We know that 5/6 is greater than half because half of six is 3/6.

Option b, as can be seen in the drawing or calculated, is less than half,

therefore option b must be less than 5/6.

To understand option c we need to bring both fractions to the same denominator.

The existing fraction is 2/3, and to bring it to the same denominator as 5/6, we need to multiply it by 2.

Remember that when we convert to a common denominator we multiply both numerator and denominator.

Therefore:

2*2/3*2=4/6

We already calculated in option d that 4/6 is less than 5/6, so option c is also eliminated.

Thus, the only correct answer is option a.

And that's the solution!