Examples with solutions for Converting Decimal Fractions to Simple Fractions and Mixed Numbers: Graphical representation

Exercise #1

What part of the whole does the shaded (blue) area represent?

Step-by-Step Solution

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

  • Step 1: Count the total number of equal sections in the diagram.
  • Step 2: Determine how many sections are shaded in blue.
  • Step 3: Use the fraction formula shaded sectionstotal sections\frac{\text{shaded sections}}{\text{total sections}} to find the portion represented by the shaded area.
  • Step 4: Convert the fraction to a decimal.

Now, let's work through each step:

Step 1: Upon examining the diagram, we observe that the grid is divided into 10 vertical sections. Each section is presumably equal in area.

Step 2: There is 1 shaded section, which is the first vertical column on the left.

Step 3: Using the fraction formula, the part of the whole represented by the shaded section is 110\frac{1}{10}, because there is 1 shaded section out of 10 total sections.

Step 4: We convert the fraction 110\frac{1}{10} into its decimal form, which is 0.10.1.

Therefore, the solution to the problem is the shaded area represents 0.10.1 or 110\frac{1}{10} of the whole.

This corresponds to choice 3: 0.10.1 and 110\frac{1}{10}.

Answer

0.1 0.1 and 110 \frac{1}{10}

Exercise #2

What part of the whole does the shaded part (blue) represent?

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Count the total number of equal vertical sections in the grid.
  • Step 2: Count the number of shaded (blue) sections.
  • Step 3: Determine the fraction of the whole that is shaded.
  • Step 4: Simplify the fraction, if needed, and express it as a decimal.

Now, let's execute these steps:

Step 1: By examining the diagram, we observe there are 10 equal vertical sections in total.

Step 2: Of these sections, 2 are shaded blue.

Step 3: The fraction of the shaded area compared to the whole is 210\frac{2}{10}.

Step 4: Simplify 210\frac{2}{10} to 15\frac{1}{5}, but since we are asked to express it as part of 10 parts, 210\frac{2}{10} remains an accurate choice. The decimal equivalent is 0.20.2.

Therefore, the shaded part of the whole is 210\frac{2}{10} or 0.20.2.

Among the given choices, the correct answer is: 210\frac{2}{10} or 0.20.2.

Answer

210 \frac{2}{10} or 0.2 0.2

Exercise #3

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Determine the grid dimensions and count the total number of rectangles and how many of these are shaded.
  • Step 2: Compute the fraction of the area that is shaded.
  • Step 3: Convert this fraction to a decimal.

Now, let's work through each step:
Step 1: Upon examining the diagram, we see the whole is a 4x5 grid, hence
There are 4×5=204 \times 5 = 20 rectangles in total.
The blue shaded area occupies the entire left-most column of this 4-column grid, so 4 rectangles are shaded.

Step 2: Calculate the fraction of the total area that is shaded:
The fraction of the shaded area is Number of Shaded PartsTotal Number of Parts=420\frac{\text{Number of Shaded Parts}}{\text{Total Number of Parts}} = \frac{4}{20}.
Simplifying this gives 15\frac{1}{5}.

Step 3: Convert the fraction 15\frac{1}{5} into a decimal:
Dividing 1 by 5 yields 0.20.2.

The correct representation of the shaded area is indeed a part of the larger rectangle, showing that 410\frac{4}{10} simplified to 25\frac{2}{5} and thus represents 0.40.4 in decimal form.

Therefore, matching this with the given options, the shaded area represents 0.40.4 or 410\frac{4}{10} of the entire area.

Answer

0.4 0.4 or 410 \frac{4}{10}

Exercise #4

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, we will determine how much of the whole grid is represented by the shaded area.

The problem provides a 10x10 grid which contains 100 smaller squares in total. Our task is to determine how many of these squares are shaded.

Upon inspection, we count that 80 out of the 100 squares are shaded.

Therefore, the fraction of the whole that the shaded area represents is given by dividing the number of shaded squares by the total number of squares:

shaded squarestotal squares=810 \frac{\text{shaded squares}}{\text{total squares}} = \frac{8}{10}

Converting this fraction to a decimal gives 0.80.8.

Thus, the shaded area represents 810\frac{8}{10} or 0.80.8 of the whole.

Among the choices provided, the correct answer is: 0.8 0.8 or 810 \frac{8}{10} .

Answer

0.8 0.8 or 810 \frac{8}{10}

Exercise #5

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, we need to assess how much of the grid is shaded:

  • Step 1: Notice that the grid is evenly divided into smaller, equal-sized squares.
  • Step 2: Observe that every single section of the grid is shaded blue, with no portions left unshaded.
  • Step 3: Consider that when an entire segment, like a grid, is covered entirely by shading, it represents the whole, which is equivalent to 11 or the fraction 1010\frac{10}{10}.

Therefore, since the whole grid is shaded, the shaded area represents 11 or 1010\frac{10}{10} of the whole.

Answer

1 1 or 1010 \frac{10}{10}

Exercise #6

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

The large square grid is divided into smaller squares. Let's determine how many small squares there are in total.

  • Step 1: Count the number of small squares along one side. From the SVG image, each side seems to have 10 smaller squares (since each section appears uniform and there are grids within both, rows, and columns).

  • Step 2: Calculate the total number of smaller squares in the grid. Since it's a square, the total is 10×10=100 10 \times 10 = 100 small squares.

  • Step 3: Calculate what fraction of the whole one shaded square (the blue one) represents. The shaded area is one of these squares, so it represents 1100 \frac{1}{100} of the entire grid.

Therefore, the shaded area represents 0.01 0.01 or 1100 \frac{1}{100} of the whole grid.

Answer

0.01 0.01 or 1100 \frac{1}{100}

Exercise #7

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, we will determine the fraction of the grid that is shaded by following these steps:

  • Step 1: Determine the Layout of the Grid.
    The grid is divided into 5×105 \times 10 smaller squares (5 rows and 10 columns), resulting in a total of 50 squares.

  • Step 2: Count the Shaded Squares.
    The top row, which is fully shaded, consists of 8 shaded squares.

  • Step 3: Calculate the Fraction of the Shaded Area.
    The fraction that represents the shaded area is number of shaded squarestotal number of squares=8100\frac{\text{number of shaded squares}}{\text{total number of squares}} = \frac{8}{100}.

  • Step 4: Convert Fraction to Decimal.
    The fractional representation 8100\frac{8}{100} can also be expressed as a decimal, 0.080.08.

Therefore, the shaded area represents 8100\frac{8}{100} or 0.080.08 of the whole grid.

Answer

8100 \frac{8}{100} or 0.08 0.08

Exercise #8

How much of the whole does the shaded area (blue) represent?

Step-by-Step Solution

To solve this problem, we need to determine the fraction of the whole grid that is represented by the shaded (blue) area. The grid is a 10x10 layout, therefore containing a total of 10×10=10010 \times 10 = 100 equal-sized squares.

Step 1: We count the number of shaded squares in the grid. According to the illustration, there are 86 shaded squares.

Step 2: Calculate the fraction of the shaded area compared to the whole grid: Number of shaded squaresTotal number of squares=86100\frac{\text{Number of shaded squares}}{\text{Total number of squares}} = \frac{86}{100}.

Step 3: Convert this fraction into a decimal. Dividing the numerator by the denominator gives us 0.86 0.86 .

Therefore, the shaded area represents 86100\frac{86}{100} of the total grid, which is equivalent to 0.860.86.

This matches with the correct answer choice, which is: 0.860.86 or 86100\frac{86}{100}.

Answer

0.86 0.86 or 86100 \frac{86}{100}