Basic Mathematics for College Students

Caution! Example 3 shows that order is important when writing a ratio. The

width-to-length ratio is while the length-to-width ratio is.

2 Simplify ratios involving decimals and mixed numbers.

12

5

5

12

5.1 Ratios 417

EXAMPLE (^4) Write the ratio 0.3 to 1.2 as a fraction in simplest form.
StrategyAfter writing the ratio as a fraction, we will multiply it by a form of 1 to
obtain an equivalent ratio of whole numbers.
WHYA ratio of whole numbers is easier to understand than a ratio of decimals.
Solution
The ratio 0.3 to1.2 can be written as.
To write this as a ratio ofwhole numbers,we need to move the decimal points in
the numerator and denominator one place to the right. Recall that to find the
product of a decimal and 10, we simply move the decimal point one place to the
right. Therefore, it follows that is the form of 1 that we should use to build into
an equivalent ratio.
1
Multiply the ratio by a form of 1.
Simplify the fraction:^312 ^3.
1
31  4 
1
 (^4)

1

4

 

Do the multiplications by moving each decimal point one

 (^) place to the right. 0.3  10 3 and 1.2  10 12.

3

12

Multiply the numerators.

(^) Multiply the denominators.

0.3

1.2



0.3# 10

1.2# 10

10

10

0.3

1.2



0.3

1.2



0.3

1.2^

10

10



0.3

1.2



Self Check 4

Write the ratio 0.8 to 2.4 as a

fraction in simplest form.

Now TryProblems 29 and 33

“A more personal classroom atmosphere can sometimes be an easier adjustment

for college freshmen. They are less likely to feel like a number, a feeling that

can sometimes impact students’ first semester grades.”

FromThe Importance of Class Size by Stephen Pemberton

The data below come from a nationwide study of mathematics programs at

two-year colleges. Determine which course has the lowest student-to-

instructor ratio. (Assume that there is one instructor per section.)

THINK IT THROUGH Student-to-Instructor Ratio

Source: Conference Board of the Mathematical Science, 2005 CBMS Survey of Undergraduate Programs ( The

data has been rounded to yield ratios involving whole numbers.)

Basic Elementary Intermediate

Mathematics Algebra Algebra

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