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Chapter 7: Problem 16

Change the percent to a simplified fraction or mixed number. $$32 \%$$

Short Answer

Expert verified
32% is \( \frac{8}{25} \).

Step by step solution

01

- Write the percentage as a fraction

Start by writing 32% as a fraction. Since percentages are out of 100, we can write 32% as \( \frac{32}{100} \).
02

- Simplify the fraction

Next, simplify the fraction \( \frac{32}{100} \) by finding the greatest common divisor (GCD) of 32 and 100. The GCD of 32 and 100 is 4.
03

- Divide the numerator and denominator by the GCD

Divide both the numerator and the denominator by the GCD (which is 4): \( \frac{32 \div 4}{100 \div 4} \). This results in \( \frac{8}{25} \).

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Key Concepts

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

simplifying fractions
Simplifying fractions is a crucial skill in math. It means reducing a fraction to its simplest form. To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, if you have the fraction \( \frac{32}{100} \), this can be simplified. We'd need to find the GCD of 32 and 100.
greatest common divisor
The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD involves:
  • Listing the factors of both numbers
  • Comparing the factors and identifying the largest one
For the numbers 32 and 100, their factors are:
32: 1, 2, 4, 8, 16, 32
100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The largest number in both lists is 4, making 4 the GCD.
writing percentages as fractions
Converting a percentage to a fraction is simple. Start by writing the percentage over 100. For instance, 32% becomes \( \frac{32}{100} \). From here, you simplify the fraction by finding the GCD of the numerator and the denominator and dividing both by that GCD. Using the GCD of 4, we simplify \( \frac{32}{100} \) to \( \frac{8}{25} \). Hence, 32% as a simplified fraction is \( \frac{8}{25} \).

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