Preface xvStudy Skills That Point Out Common Student Mistakes
In Chapter 1, we have included four Study Skills
Checklistsdesigned to actively show students how
to effectively use the key features in this text.
Subsequent chapters include one checklist just
before the Chapter Summary and Reviewthat
provides another layer of preparation to promote
student success. These Study Skills Checklistswarn
students of common errors, giving them time to
consider these pitfalls before taking their exam.
Comprehensive End-of-Chapter Summary
with Integrated Chapter Review
The end-of-chapter material has been
redesigned to function as a complete study
guide for students. New chapter summaries
that include definitions, concepts, and
examples, by section, have been written.
Review problems for each section
immediately follow the summary for that
section. Students will find the detailed
summaries a very valuable study aid when
preparing for exams.CHAPTER 5 SUMMARY AND REVIEWSECTION 5.1 Ratios and RatesRatiosare often used to describe important
relationships between two quantities.
A ratiois the quotient of two numbers or the
quotient of two quantities that have the same
units.
Ratios are written in three ways:as fractions,in
words separated by the word to, and using a
colon.DEFINITIONS AND CONCEPTS EXAMPLESThe ratio 4 to5 can be written as.The ratio 5 :12 can be written as. (^12) ^5
4
5
To write a ratio as a fraction,write the first
number (or quantity) mentioned as the
numerator and the second number (or
quantity) mentioned as the denominator. Then
simplify the fraction, if possible.
Write the ratio 30 to 36 as a fraction in simplest form.
The word toseparates the numbers to be compared.
^56
To simplify, factor 30 and 36. Then remove the common
factor of 6 from the numerator and denominator.
30
36
5 61
61 6
Write each ratio as a fraction in simplest form.
1.7 to 25 2. 15 16
3.24 to 36 4. 21 14
5.4 inches to 12 inches 6.63 meters to 72 meters
7.0.28 to 0.35 8.5.11.
- 11.15 minutes : 3 hours 12.8 ounces to 2 pounds
2 31 to 2 32 4 61 (^3 )
Write each rate as a fraction in simplest form.
13.64 centimeters in 12 years
14.$15 for 25 minutes
Write each rate as a unit rate.
15.600 tickets in 20 minutes
16.45 inches every 3 turns
17.195 feet in 6 rolls
18.48 calories in 15 pieces
REVIEW EXERCISES
STUDY SKILLS CHECKLIST
Working with Fractions
Before taking the test on Chapter 3, make sure that you have a solid understanding of the
following methods for simplifying, multiplying,dividing, adding, and subtracting fractions.Put a
checkmark in the box if you can answer “yes” to the statement.
1
I know that to add or subtract fractions, they must
have a common denominator. To multiply or divide
fractions, they do notneed to have a common
denominator.
Need an LCD Do not need an LCD
I know how to find the LCD of a set of fractions
using one of the following methods.
- Write the multiples of the largest denominator
in increasing order, until one is found that is
divisible by the other denominators. - Prime factor each denominator. The LCM is a
product of prime factors, where each factor is
used the greatest number of times it appears in
any one factorization.
I know how to build equivalent fractions by
multiplying the given fraction by a form of 1.
^1015^23 ^5523 ^23 (^55)
11
40
5
8
4
7
2
9
9
20
7
12
2
3
1
5
I know how to simplify fractions by factoring the
numerator and denominator and then removing
the common factors.
When multiplying fractions, I know that it is
important to factor and simplify first, before
multiplying.
Factor and simplify first Don’t multiply first
To divide fractions, I know to multiply the first
fraction by the reciprocal of the second fraction.
7
8 ^
23
24 ^
7
8 ^
24
23
^3 ^5 ^360560
(^1) 3 81
2 81 51 7
15
16
24
35
15 24
16 35
15
16
24
35
15 24
16 35
^2125
^2
(^1) 3 7
21 5 5
4250 ^22 ^35 ^77