Which diagram represents a fraction equivalent to 75%?

Question

A bar diagram with 14 shaded squares and 6 unshaded squares.
A bar diagram with 8 shaded squares and 2 unshaded squares.
A bar diagram with 15 shaded squares and 5 unshaded squares.
A bar diagram with 7 shaded squares and 3 unshaded squares.

Answer 1

To determine which diagram represents a fraction equivalent to 75%, we need to calculate the fraction represented by each diagram.

75% as a fraction is equivalent to \( \frac{75}{100} \), which simplifies to \( \frac{3}{4} \).

Now, let's analyze the given options:

1. 14 shaded squares and 6 unshaded squares.

   • Total squares = 14 + 6 = 20
   • Shaded fraction = \( \frac{14}{20} = \frac{7}{10} \) (not equivalent to 75%)

2. 8 shaded squares and 2 unshaded squares.

   • Total squares = 8 + 2 = 10
   • Shaded fraction = \( \frac{8}{10} = \frac{4}{5} \) (not equivalent to 75%)

3. 15 shaded squares and 5 unshaded squares.

   • Total squares = 15 + 5 = 20
   • Shaded fraction = \( \frac{15}{20} = \frac{3}{4} \) (equivalent to 75%)

4. 7 shaded squares and 3 unshaded squares.

   • Total squares = 7 + 3 = 10
   • Shaded fraction = \( \frac{7}{10} \) (not equivalent to 75%)

The only diagram that represents a fraction equivalent to 75% is the one with 15 shaded squares and 5 unshaded squares.