Book cover for Prealgebra

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

ISBN #9781938168994

1st Edition

5,729 Questions

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210,912 Students Helped

Homework Questions

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Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

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.

Learning Objectives

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.

Key Concepts

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.

Example Problems

Example 1

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$\%$

Example 2

In the following exercises, write each percent as a ratio. In $2015,$ among the unemployed, 29$\%$ were long term unemployed.

Example 3

In the following exercises, write each percent as a ratio. The unemployment rate for those with Bachelor's degrees was 3.2$\%$ in 2014 .

Example 4

In the following exercises, write each percent as a ratio. The unemployment rate in Michigan in 2014 was 7.3$\%$

Example 5

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.

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Step-by-Step Explanations

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

QUESTION

What is the tip when leaving 20% on an $80 bill?

STEP-BY-STEP ANSWER:

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

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Common Mistakes

  • Failing to divide by 100 when converting a percent to a decimal.
  • Misplacing the decimal point (e.g., moving it the wrong number of places).
  • Not simplifying fractions fully after converting from percent form.
  • Overlooking rounding instructions, especially when dealing with recurring decimals.