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Activity 2: Find the fraction of shaded objects for each part. Simplify your answers.
Mathematics
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6 stepsYou're referring to "Activity 2" at the bottom of the page. Let's find the fraction of shaded objects for each part.
- a)
Count the total number of shapes.
There are 4 rows with 5 pentagons in each row. Total shapes = $4 \times 5 = 20$.Count the number of shaded shapes.
In each row, 3 pentagons are shaded. Number of shaded shapes = $4 \times 3 = 12$.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)
Count the total number of shapes.
There are 4 rows with 6 circles in each row. Total shapes = $4 \times 6 = 24$.Count the number of shaded shapes.
In each row, 2 circles are shaded. Number of shaded shapes = $4 \times 2 = 8$.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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