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Chapter 7: Problem 20

Change the percent to a simplified fraction or mixed number. $$150 \%$$

Short Answer

Expert verified
\(\frac{3}{2}\) or 1 \(\frac{1}{2}\)

Step by step solution

01

- Convert Percent to Fraction

To convert 150% to a fraction, write 150% as \(\frac{150}{100}\).
02

- Simplify the Fraction

Simplify \(\frac{150}{100}\) by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 150 and 100 is 50. Thus, we divide both the numerator and the denominator by 50: \(\frac{150 \div 50}{100 \div 50} = \frac{3}{2}\).
03

- Convert to Mixed Number (if needed)

Since \(\frac{3}{2}\) is an improper fraction, convert it to a mixed number. \(\frac{3}{2}\) can be written as 1 \(\frac{1}{2}\).

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Key Concepts

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

Converting Percent to Fraction
To convert a percent to a fraction, remember that 'percent' means 'per hundred'. For example, 150% means 150 per 100.
To change a percent to a fraction, follow these steps:
  • Write the percent as a fraction with 100 as the denominator. So, 150% becomes \(\frac{150}{100}\).
  • Simplify the fraction if needed.
These steps can be applied to any percentage.
Simplifying Fractions
Simplifying fractions involves reducing the fraction to its simplest form. This makes the fraction easier to work with and understand.
Here鈥檚 how you can simplify a fraction:
  • Find the Greatest Common Divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by their GCD.
So, for \(\frac{150}{100}\), the GCD of 150 and 100 is 50. When we divide both 150 and 100 by 50, we get \(\frac{3}{2}\).
Now, \(\frac{3}{2}\) is in its simplest form.
Mixed Numbers
A mixed number consists of a whole number and a proper fraction. It is used to represent improper fractions more intuitively.
When you have a fraction like \(\frac{3}{2}\), it鈥檚 an improper fraction because the numerator is larger than the denominator.
To convert \(\frac{3}{2}\) to a mixed number:
  • Divide the numerator by the denominator. The quotient will be the whole number part. So, \(\frac{3}{2}\) is 1 whole.
  • The remainder will be the numerator of the proper fraction. The denominator stays the same. Here, 3 divided by 2 is 1 with a remainder of 1, so we have 1 \(\frac{1}{2}\).
Therefore, \(\frac{3}{2}\) simplifies to the mixed number 1 \(\frac{1}{2}\).

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Most popular questions from this chapter

Convert the fraction to a percent. $$1 \frac{3}{4}$$

Explain the difference between \(\frac{1}{2}\) and \(\frac{1}{2} \%\)

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