Question

which best describes one way to show \frac{1}{3} shaded?
draw a circle and cut it into 3 unequal parts. shade 1 part.
draw a circle and cut it into 3 equal parts. shade 2 parts.
draw a circle and cut it into 3 unequal parts. shade 3 parts.
draw a circle and cut it into 3 equal parts. shade 1 part.

Explanation:

Step1: Recall the concept of fractions

A fraction \(\frac{a}{b}\) represents \(a\) parts out of \(b\) equal parts. For \(\frac{1}{3}\), we need \(1\) part out of \(3\) equal parts.

Step2: Analyze each option

• Option 1: Cutting into unequal parts. Fractions require equal - sized parts. So this is incorrect.
• Option 2: Shading 2 parts out of 3 equal parts gives \(\frac{2}{3}\), not \(\frac{1}{3}\). Incorrect.
• Option 3: Shading 3 parts (the whole circle) when parts are unequal. Not \(\frac{1}{3}\). Incorrect.
• Option 4: Cutting into 3 equal parts and shading 1 part. This gives \(\frac{1}{3}\) as \(\frac{1}{3}=\frac{\text{Number of shaded parts}}{\text{Total number of equal parts}}\). Correct.

Answer:

Draw a circle and cut it into 3 equal parts. Shade 1 part.