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Chapter 6: Problem 5

There are 1720 females among the 3200 students at the local community college. Express this ratio in each of the following forms. a. fraction b. reduced fraction c. decimal d. percent

Short Answer

Expert verified
Answer: The ratio of females to the total number of students at the community college in percentage is 53.75%.

Step by step solution

01

Calculating the Fraction

The number of females is 1720. The total number of students is 3200. So, the ratio can be written as the fraction: $$\frac{1720}{3200}$$
02

Reducing the Fraction

In order to reduce the fraction, we need to find the Greatest Common Divisor (GCD) of the numerator (1720) and the denominator (3200). The GCD of 1720 and 3200 is 40. Dividing both the numerator and the denominator by 40, we get the reduced fraction: $$\frac{1720/40}{3200/40} = \frac{43}{80}$$
03

Converting Fraction to Decimal

To convert the reduced fraction to a decimal, divide the numerator (43) by the denominator (80). $$\frac{43}{80}= 0.5375$$
04

Converting Decimal to Percent

To convert the decimal to a percentage, multiply it by 100. $$ 0.5375 \times 100 = 53.75\% $$ In conclusion: a. Fraction: $$\frac{1720}{3200}$$ b. Reduced Fraction: $$\frac{43}{80}$$ c. Decimal: 0.5375 d. Percent: 53.75%

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