Comparison of Ratios in
Decimal Form
Jen Kershaw
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Printed: August 22, 2014
AUTHOR
Jen Kershaw
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C HAPTER
Chapter 1. Comparison of Ratios in Decimal Form
1
Comparison of Ratios in
Decimal Form
Here you’ll learn to write and compare ratios in decimal form.
Remember Joanna from the Ratios in Simplest Form Concept?
Joanna read the following fraction of books.
She read
1
4
1
4
books that she had intended to read. We can write that a decimal.
= .25
Kara read
1
3
books that she intended to read.
Can you compare these two ratios?
Pay attention and you will learn how to do this by the time this Concept is complete.
Guidance
Previously we worked on writing fractions in decimal form. Just like fractions can be written in decimal form, well,
ratios can be written in fraction form, so they can also be written as decimals. We can look at how to write a ratio as
a decimal too.
How do we write a ratio as a decimal?
To convert a ratio to decimal form, write the ratio as a fraction. Then divide the term above the fraction bar
by the term below the fraction bar.
Let’s look at how to do this.
Rewrite the ratio 1 to 4 in decimal form.
The ratio 1 to 4 can be expressed as the fraction 14 . This is our first step.
Next, divide the term above the fraction bar, 1, by the term below the fraction bar, 4.
1
4
= 4)1
Since 1 cannot be evenly divided by 4, rewrite 1 as a decimal with a zero after the decimal point You can do this
because 1 = 1.0 = 1.00 = 1.000. Before you divide, write a decimal point in the quotient directly above the decimal
point in the dividend. Then divide.
0.2
4)1.0
−8
2
Continue adding zeroes after the decimal point and diving until the quotient has no remainder.
1
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0.25
4)1.00
−8
20
−20
0
The decimal form of the ratio
1
4
is 0.25.
Rewrite the ratio 9:5 in decimal form.
The ratio 9:5 can be expressed as the fraction 95 .
Next, divide the term above the fraction bar, 9, by the term below the fraction bar, 5.
1
14) 9
−5
4
There is a remainder. So, add zeroes after the decimal point in 9 to continue dividing.
1.8
5)9.0
−5
40
−40
0
The decimal form of 9:5 is 1.8.
What about comparing? Can we use decimals to compare ratios?
Sometimes, you may want to compare two ratios and determine if they are equivalent or not. Rewriting both
ratios in decimal form is one way to do this.
Compare these two ratios and determine if they are equivalent
Rewrite
7
14
in decimal form.
0.5
5) 7.0
−70
0
−0
0
Rewrite
2
11
20
in decimal form.
7
14
and
11
20 .
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Chapter 1. Comparison of Ratios in Decimal Form
0.55
20)11.00
−100
100
−100
0
To compare the ratios in decimal form, give each decimal the same number of decimal places. In other words,
give 0.5 two decimal places: 0.5 = 0.50.
Now compare. Since both decimals have a 0 in the ones place and a 5 in the tenths place, compare the digits
in the hundredths place.
0.50
0.55
Since 0 < 5, 0.50 < 0.55. So, the ratios,
In fact,
7
14
<
7
14
and
11
20 ,
are not equivalent.
11
20 .
Write each ratio as a decimal.
Example A
5 to 10
Solution: .5
Example B
4 to 10
Solution: .4
Example C
Compare 6 to 10 and 1 to 4
Solution: >
Now back to the book comparison. Here is the original problem once again.
Joanna read the following fraction of books.
She read
1
4
1
4
books that she had intended to read. We can write that a decimal.
= .25
Kara read
1
3
books that she intended to read.
Can you compare these two ratios?
First, let’s write a statement so that we can compare the decimals.
3
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.25 and
1
3
= .33
One-third becomes a repeating decimal, but for our purposes we can round to the hundredths place.
.25 < .33
This is our answer.
Vocabulary
Ratio
a comparison between two quantities. Ratios can be written as a fraction, with a colon or by using the word
"to".
Simplify
to write in a simpler form by using the greatest common factor to divide the numerator and the denominator
of a fraction by the same number.
Decimal
a part of a whole written using a decimal point and the place value system.
Guided Practice
Here is one for you to try on your own.
Write this ratio as a decimal.
3
5
Answer
To do this, we divide 3 by 5.
3 ÷ 5 = .6
This is our answer.
Video Review
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5409
This is a James Sousa video on simplifying ratios in decimal and fraction form and is a supporting video to this Con
cept.
Practice
Directions: Write each ratio as a decimal. Round to the nearest hundredth when necessary.
4
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Chapter 1. Comparison of Ratios in Decimal Form
1. 1 to 4
2. 3 to 6
3. 3:4
4. 8 to 5
5. 7 to 28
6. 8 to 10
7. 9 to 100
8. 15:20
9. 18:50
10. 3 to 10
11. 6 to 8
12. 15 to 35
Directions: Compare the following ratios using <, >or =.
13. .55 ____1 to 2
14. 3:8 _____ 4 to 9
15. 1 to 2 _____ 4:8
5