Convert Grid Representations to Fractions: Interpreting Shaded Regions

Grid Fraction Representation with Mixed Layouts

Write the fraction shown in the drawing:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Write the mathematical representation of the given fraction
00:04 In black, the number of parts into which the whole is divided (denominator)
00:13 In red, the given number of parts (numerator)
00:20 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Write the fraction shown in the drawing:

2

Step-by-step solution

To solve this problem, we'll analyze the fraction depicted in the drawing of shaded rectangles.

Steps to find the fraction:

  • Step 1: Count the Total Number of Parts
    In the drawing, identify the number of divisions in each rectangle. It appears there are 9 total sections across all of the rectangles depicted.
  • Step 2: Count the Shaded Parts
    The number of shaded sections is key to identifying the numerator of the fraction. Count all visible shaded parts; there are 5 shaded sections in total.
  • Step 3: Formulate the Fraction
    Using the standard formula for fractions, we have:
    Fraction=Number of Shaded SectionsTotal Number of Sections\text{Fraction} = \frac{\text{Number of Shaded Sections}}{\text{Total Number of Sections}}
    Using our counted numbers, 59\frac{5}{9}.

Therefore, the fraction represented by the shaded sections in the drawing is 59\frac{5}{9}.

3

Final Answer

59 \frac{5}{9}

Key Points to Remember

Essential concepts to master this topic
  • Visual Analysis: Count total sections first, then shaded parts carefully
  • Counting Method: Separate grids: 4 sections (top) + 5 sections (bottom) = 9 total
  • Verification: Recount shaded parts: 3 top + 2 bottom = 5 shaded ✓

Common Mistakes

Avoid these frequent errors
  • Counting individual rectangles instead of total sections
    Don't count just the rectangles as units = wrong denominator! This ignores how each rectangle is divided into sections. Always count every individual section shown in the entire grid layout.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction as a mixed number:

\( \frac{6}{2}= \)

FAQ

Everything you need to know about this question

How do I know what counts as one section?

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Each section is a single divided part of the grid. Look for the grid lines - they separate individual sections. In this problem, there are 9 total sections across both rows.

What if the grid has different sized sections?

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All sections must be equal in size to represent a proper fraction. If sections look different sizes, double-check the grid lines and count more carefully.

Should I count empty sections too?

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Yes! The denominator includes all sections - both shaded and unshaded. Only the numerator counts just the shaded parts.

How can I double-check my counting?

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Try counting in different orders:

  • Count by rows (top row, then bottom row)
  • Count by columns (left to right)
  • Circle each section as you count
You should get the same total each way!

What does 59 \frac{5}{9} actually mean?

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It means 5 out of 9 equal parts are shaded. Think of it as: if you divided something into 9 equal pieces, 5 of those pieces would be colored in.

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