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Chapter 6: Problem 8

Change \(60 \%\) to a fraction.

Short Answer

Expert verified
The fraction equivalent to \(60 \%\) is \(\frac{3}{5}\).

Step by step solution

01

Establish the Fraction from the Percentage

The given percentage is \(60\%\). To convert this into a fraction, '60' becomes the numerator and '100' is the denominator. This gives the fraction \(\frac{60}{100}\).
02

Simplify the Fraction

The fraction \(\frac{60}{100}\) can be simplified to its lowest terms by dividing both the numerator and the denominator by the greatest common factor. The largest number that divides both 60 and 100 evenly is 20. Dividing 60 by 20 gives 3 and dividing 100 by 20 gives 5. This simplifies the fraction to \(\frac{3}{5}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percent to Fraction
Understanding how to convert percentages to fractions is a fundamental math skill that can greatly simplify solving various problems. First, remember that a percentage represents a number out of 100. So, when converting, you start by writing the percentage as the numerator of a fraction, with 100 always being the denominator.

For example, to convert 60% to a fraction, you write it as \( \frac{60}{100} \). This fraction can then be simplified to make it easier to work with, which brings us to our next core concept: simplifying fractions.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form where the numerator and denominator are the smallest possible whole numbers. To do this, find the greatest common divisor (GCD) of both the numerator and denominator. This is the largest number that divides into both without leaving a remainder. Once found, divide both the numerator and denominator by the GCD.

In our example of \( \frac{60}{100} \), the GCD is 20. Dividing both by 20, we get a simplified fraction of \( \frac{3}{5} \). Simplifying makes fractions easier to use in further math operations.
Numerators and Denominators
When dealing with fractions, it's crucial to understand the roles of numerators and denominators. The numerator, the top number, indicates how many parts we have. The denominator, the bottom number, shows into how many equal parts the whole is divided.

In our original fraction \( \frac{60}{100} \), '60' is the numerator, showing the 'part' of the whole we're working with. '100' is the denominator, representing the entire 'whole' divided into 100 equal parts. Grasping this concept aids in performing correct mathematical operations with fractions.

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Most popular questions from this chapter

The focal length \(f\) of a lens is given by the formula $$\frac{1}{f}=\frac{1}{d_{1}}+\frac{1}{d_{2}}$$ where \(d_{1}\) is the distance from the object to the lens and \(d_{2}\) is the distance from the lens to the image. Solve the formula for \(f\).

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