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Activity 2: Find the fraction of shaded objects for each part. Simplify your answers.

Mathematics

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You're referring to "Activity 2" at the bottom of the page. Let's find the fraction of shaded objects for each part.

  • a)
  1. Count the total number of shapes.

    There are 4 rows with 5 pentagons in each row.  
    Total shapes = $4 \times 5 = 20$.
    
  2. Count the number of shaded shapes.

    In each row, 3 pentagons are shaded.  
    Number of shaded shapes = $4 \times 3 = 12$.
    
  3. Write the fraction of shaded shapes and simplify.

    Fraction shaded = $\frac{\text{Number of shaded shapes}}{\text{Total number of shapes}} = \frac{12}{20}$.  
    To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 4.
    $$
    \frac{12 \div 4}{20 \div 4} = \frac{3}{5}
    $$
    The fraction of shaded shapes is $\boxed{\frac{3}{5}}$.
    
    • b)
  4. Count the total number of shapes.

    There are 4 rows with 6 circles in each row.  
    Total shapes = $4 \times 6 = 24$.
    
  5. Count the number of shaded shapes.

    In each row, 2 circles are shaded.  
    Number of shaded shapes = $4 \times 2 = 8$.
    
  6. Write the fraction of shaded shapes and simplify.

    Fraction shaded = $\frac{\text{Number of shaded shapes}}{\text{Total number of shapes}} = \frac{8}{24}$.  
    To simplify, divide both the numerator and the denominator by their greatest common divisor, which is 8.
    $$
    \frac{8 \div 8}{24 \div 8} = \frac{1}{3}
    $$
    The fraction of shaded shapes is $\boxed{\frac{1}{3}}$.
    
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