Which diagram represents a fraction equivalent to 75

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which diagram represents a fraction equivalent to 75

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LectureNotes said which diagram represents a fraction equivalent to 75

A fraction equivalent to 75 would be 75/1, since 75 can be expressed as a fraction in this way. In a diagram, this fraction implies the whole is divided into one part, which represents the number 75.

However, if the goal is to represent a fraction equivalent to 75% (which is a common context), then we’re dealing with the fraction \frac{75}{100}, which simplifies to \frac{3}{4}. Here’s a breakdown of how to identify diagrams that could represent this fraction:

1. Pie Chart Representation

A common way to represent fractions is through pie charts:

  • Diagram Description: The pie is divided into four equal parts.
  • Fraction Equivalent to 75%:
    • 3 out of the 4 parts are shaded.
    • This visually represents the fraction \frac{3}{4}, equivalent to 75%.

2. Bar Model Representation

A bar model can also effectively show fractions:

  • Diagram Description: A rectangle is divided into four equal segments.
  • Fraction Equivalent to 75%:
    • 3 of the 4 segments are colored or shaded.
    • This again represents the fraction \frac{3}{4}, equivalent to 75%.

3. Number Line Representation

Number lines can visually express fractions as well:

  • Diagram Description: A number line is divided into four equal segments between 0 and 1.
  • Fraction Equivalent to 75%:
    • The point at 0.75 (or \frac{3}{4}) is marked.
    • This mark shows that 75% of the length from 0 to 1 is covered.

Simplification and Generalization

To accurately identify a fraction equivalent to any given number, simplify the fraction and look for visual representations that match the simplified form.

Here’s a generic formula approach:

  1. Convert a percentage to a fraction: 75\% = \frac{75}{100}
  2. Simplify the fraction: \frac{75}{100} = \frac{3}{4}
  3. Visual Representation:
    • Divide the whole into equal parts (4 for this case).
    • Shade/mark the simplified numerator parts (3 for this case).

Conclusion

The diagram that successfully represents a fraction equivalent to 75 or 75% would be one where out of every four parts, three are highlighted or shaded. This equivalence is fundamental in fraction representation and crucial for understanding various fraction simplifications.