Mixed Numbers and Fractions Greater than 1: Visual representation of a fraction

To solve this problem, we focus on visually representing the fraction $\frac{3}{4}$. This requires selecting the option where three out of four equal parts are highlighted or filled, representing the fraction correctly.

Step 1: Understand the fraction $\frac{3}{4}$ means we need three parts filled out of a total of four parts.

Step 2: Review each visual choice to see which diagram correctly highlights 3 out of 4 sections:

• Choice 1: Highlights the right semicircle which does not represent $\frac{3}{4}$.

• Choice 2: Highlights a quarter of the circle which represents $\frac{1}{4}$.

• Choice 3: Highlights half, representing $\frac{1}{2}$.

• Choice 4: Highlights three quadrants, which correctly depicts $\frac{3}{4}$.

Therefore, the correct visual representation of $\frac{3}{4}$ forms part of choice 4, where exactly three out of four sections are filled.

Thus, the option that visually represents the fraction $\frac{3}{4}$ is Choice 4.

To solve this problem, follow these steps:

• Step 1: Simplify the fraction $\frac{8}{40}$.
• Step 2: Visualize this fraction using the provided options.
• Step 3: Select the diagram that accurately represents the simplest form of the fraction.

Now, let's go through each step in detail:
Step 1: Simplify the fraction $\frac{8}{40}$.
- The GCD of 8 and 40 is 8.
- Simplify: $\frac{8}{40} = \frac{8 \div 8}{40 \div 8} = \frac{1}{5}$.

Step 2: Visualize $\frac{1}{5}$ on a circle.
- A circle divided into 5 equal sections, where 1 section is shaded, represents $\frac{1}{5}$.

Step 3: Compare with the given options.
- Look for the option that shows a circle divided into 5 equal parts with 1 part shaded.

The correct visual representation of $\frac{8}{40}$ (or $\frac{1}{5}$) is Option 2, which visually displays this as one out of five equal parts shaded in a circle.

Therefore, the solution to the problem is Option 2.

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

• Step 1: Simplify the given fraction $\frac{5}{10}$ to check for equivalencies.
• Step 2: Understand that $\frac{5}{10} = \frac{1}{2}$.
• Step 3: Analyze each visual option to identify a representation of one-half.

Now, let's work through each step:
Step 1: The given fraction is $\frac{5}{10}$. To simplify, divide both numerator and denominator by 5, resulting in $\frac{1}{2}$.
Step 2: Knowing $\frac{1}{2}$ refers to half a whole, look for the option where half of a circle is shaded.
Step 3: Consider the options given. Among the options, we identify the representation of half a circle being shaded, showing $\frac{1}{2}$.

Therefore, the solution to the problem corresponds with option 1, which represents the fraction $\frac{1}{2}$.

To solve this problem, we'll simplify the fraction and identify the visual representation:

• Step 1: Simplify the fraction $\frac{9}{81}$.
• Step 2: Recognize that $9$ is a common factor of both the numerator and the denominator.
• Step 3: Divide both $9$ and $81$ by their GCD, which is $9$.
• Step 4: The simplified form $\frac{9 \div 9}{81 \div 9} = \frac{1}{9}$.

Now, let's work through each step:
Step 1: Identify that $\frac{9}{81}$ can be simplified.
Step 2: Identify that the greatest common divisor between $9$ and $81$ is $9$.
Step 3: Perform the division: $\frac{9 \div 9}{81 \div 9} = \frac{1}{9}$.
Step 4: The simplified fraction represents one part out of nine equal parts in the visual representation.

Therefore, the solution to the problem is the visual representation that shows $\frac{1}{9}$, which is Choice 3.

To solve this problem, we need to visually identify the fraction $\frac{10}{8}$.

• Step 1: Simplify $\frac{10}{8}$. Since the greatest common divisor of 10 and 8 is 2, simplifying gives: $\frac{10}{8} = \frac{10 \div 2}{8 \div 2} = \frac{5}{4}$
• Step 2: Convert $\frac{5}{4}$ to a mixed number: Divide 5 by 4, which gives 1 whole and a remainder of 1, so: $\frac{5}{4} = 1 \frac{1}{4}$
• Step 3: Find the visual representation that shows 1 whole and $\frac{1}{4}$ of another. - Choice 4 shows two circles; the first is fully shaded (indicating 1 whole), and the second is $\frac{1}{4}$ shaded, visually representing $1 \frac{1}{4}$.

Therefore, the visual representation for the fraction $\frac{10}{8}$ is Choice 4, which matches the correct shading for $1 \frac{1}{4}$.

To solve this problem, we'll first convert the improper fraction $\frac{27}{12}$ into a mixed number. Dividing 27 by 12, we get:

• 27 ÷ 12 = 2 with a remainder of 3.

This means $\frac{27}{12} = 2 \frac{3}{12}$. We can simplify $\frac{3}{12}$ to $\frac{1}{4}$. Thus, the mixed number is $2 \frac{1}{4}$.

Next, we look for the visual representation that displays this value. A correct representation will show two full circles and an additional quarter of a circle shaded.

Reviewing the provided options, the correct option visually representing $\frac{27}{12} = 2 \frac{1}{4}$ is option 3, which shows two fully shaded circles and one circle shaded to one-quarter.

Therefore, the solution to the problem is choice 3.

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

• Step 1: Simplify the fraction $\frac{9}{6}$.
• Step 2: Convert the simplified fraction to a mixed number, if necessary.
• Step 3: Identify the corresponding visual representation from the options.

Let's proceed with each step:
Step 1: Simplify $\frac{9}{6}$.
To simplify, find the greatest common divisor (GCD) of 9 and 6, which is 3. Divide both the numerator and the denominator by 3:

$\frac{9}{6} = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}$

Step 2: Convert $\frac{3}{2}$ to a mixed number.
Since $\frac{3}{2}$ is an improper fraction, we can express it as a mixed number: 1 whole and $\frac{1}{2}$.
That is, $1 \frac{1}{2}$. This corresponds to one whole circle and a half of another circle.

Step 3: Identify the visual representation.
From the choices, identify which diagram shows one full circle shaded in red (representing the whole number 1) and half of another circle shaded in red (representing $\frac{1}{2}$).

The correct option visually representing $\frac{9}{6}$ or $1 \frac{1}{2}$, where there is one complete circle shaded and another half circle shaded, is Choice 2.

Therefore, the solution to the problem is Choice 2.

To visually represent $\frac{26}{12}$, we first convert it into a mixed number:

1. Divide 26 by 12. The quotient is 2, and the remainder is 2. Thus, $26 \div 12 = 2$ with a remainder of 2.
2. Express the remainder as a fraction: $\frac{2}{12}$. This can be simplified to $\frac{1}{6}$.
3. Combine: The mixed number is $2 \frac{1}{6}$.

Therefore, our task is to find the visual representation that depicts two whole circles (or any filled shape indicating the whole parts) and an additional $\frac{1}{6}$ of another.

Upon analyzing the choices, Option 1 is the correct visual representation. It shows:

• Two fully filled circular shapes for the two whole components, and
• An additional segment showing $\frac{1}{6}$ of a circular shape filled in.

Therefore, the correct visual representation of the fraction $\frac{26}{12}$ as a mixed number is accurately shown by Option 1.

To solve this problem, we need to find the visual representation corresponding to the fraction $\frac{25}{15}$.

• First, we simplify the fraction $\frac{25}{15}$. To do this, find the greatest common divisor (GCD) of 25 and 15.
• Upon using the Euclidean algorithm, we find that the GCD of 25 and 15 is 5.
• We divide both the numerator and the denominator of $\frac{25}{15}$ by 5: $\frac{25 \div 5}{15 \div 5} = \frac{5}{3}$.

The simplified fraction $\frac{5}{3}$ is an improper fraction, which means it can be expressed as a mixed number: $1\frac{2}{3}$.

Visually, $\frac{5}{3}$ means 1 full unit and $\frac{2}{3}$ of another unit. The visual representation will show at least one full portion and a part of another.

By reviewing the visual options provided, the correct representation is the one displaying shaded portions that sum up to one whole and two-thirds of another, which is given by option 2. Therefore, the solution to the problem is the visual representation found in choice 2.

Thus, the correct answer is the option that displays option 2.