Understanding Fractions Using Shaded Shapes

Q1. What fraction of each shape is shaded?

Background

Topic: Fractions and Visual Representation

This question is testing your ability to interpret fractions by looking at shaded portions of geometric shapes. It helps you understand how fractions represent parts of a whole.

Key Terms:

• Fraction: A way to represent a part of a whole, written as $\frac{a}{b}$ where $a$ is the number of shaded parts and $b$ is the total number of equal parts.

• Numerator: The top number in a fraction, representing the shaded (or selected) parts.

• Denominator: The bottom number in a fraction, representing the total number of equal parts.

Step-by-Step Guidance

1. Count the total number of equal sections in each shape. This will be your denominator ($b$).

2. Count the number of shaded sections in each shape. This will be your numerator ($a$).

3. Write the fraction for each shape as $\frac{a}{b}$, where $a$ is the number of shaded parts and $b$ is the total number of parts.

4. Check if the fraction can be simplified by finding the greatest common divisor (GCD) of $a$ and $b$.

Try solving on your own before revealing the answer!

Final Answer:

For the first shape (octagon), there are 8 sections and 4 are shaded, so the fraction is $\frac{4}{8}$, which simplifies to $\frac{1}{2}$.

For the second shape (circle), there are 8 sections and 2 are shaded, so the fraction is $\frac{2}{8}$, which simplifies to $\frac{1}{4}$.

We counted the shaded and total sections, then wrote and simplified the fractions.