Lynn Marecek, MaryAnne Anthony-Smith
ISBN #9781938168994
1st Edition
5,729 Questions
Homework Questions
This chapter section emphasizes that percents are a way of expressing ratios with a denominator of 100. It covers converting percents to fractions and decimals and vice versa, and applies these conversions to practical situations such as calculating tips, sales taxes, and interest. The key takeaway is that a clear understanding of percent conversion is essential for accurately solving real-world math problems.
1
Understand the definition of percent as a ratio with a denominator of 100.
2
Convert percents to fractions and decimals and vice versa.
3
Translate word problems into percent equations using algebra.
4
Apply percent calculations to real-world scenarios such as sales tax, tips, and commissions.
CONCEPT
DEFINITION
Percent
A ratio expressed with a denominator of 100, indicated by the symbol %.
Fraction
A way to represent part of a whole; in percent conversions, the percent is initially written as a fraction with a denominator of 100.
Decimal
A number that represents a fraction in base ten; to convert a percent to a decimal, move the decimal point two places to the left.
Base
The total or whole amount to which the percent is applied, such as a meal bill or total savings.
In the following exercises, write each percent as a ratio. In 2014 , the unemployment rate for those with only a high school degree was 6.0$\%$
In the following exercises, write each percent as a ratio. In $2015,$ among the unemployed, 29$\%$ were long term unemployed.
In the following exercises, write each percent as a ratio. The unemployment rate for those with Bachelor's degrees was 3.2$\%$ in 2014 .
In the following exercises, write each percent as a ratio. The unemployment rate in Michigan in 2014 was 7.3$\%$
In the following exercises, write as (a) a ratio and (b) a percent 57 out of 100 nursing candidates received their degree at a community college.
QUESTION
How do you convert 36% to a simplified fraction?
STEP-BY-STEP ANSWER:
Step 1: Write the percent as a ratio with denominator 100, which gives 36/100. Step 2: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, 4, resulting in 9/25. Final Answer: 9/25.
Converting a Percent to a Fraction
What is the tip when leaving 20% on an $80 bill?
Step 1: Convert the percent to a decimal by moving the decimal point two places left (20% becomes 0.20). Step 2: Multiply the base amount ($80) by the decimal 0.20. Step 3: Compute the multiplication: 0.20 x 80 = 16. Final Answer: The tip amount is $16.
Calculating a Tip Using Percent