Ratios in Simplest Form
Jen Kershaw
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Printed: September 1, 2013
AUTHOR
Jen Kershaw
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C ONCEPT
Concept 1. Ratios in Simplest Form
1
Ratios in Simplest Form
Here you’ll learn to write ratios in simplest form.
Remember Casey and the milk comparison from the Identify and Write Equivalent Ratios Concept?
Well, Casey is pleased that she has been able to write the ratios, but wonders if these is an easier way to compare
them. This is where simplifying ratios comes in.
Pay attention in this Concept and you will learn how simplifying ratios can help us to compare and draw
conclusions. Then we’ll come back and help Casey compare her ratios.
Guidance
Sometimes, a ratio does not represent a clear comparison. If you look at one of the ratios in the practice problems
you just finished you will see what I mean. The ratio of orange marbles to total marbles was 2 to 22. We can simplify
a ratio just as we would a fraction. Let’s look at the ratio 2 to 22 in the fraction form of the ratio.
2
22
We simplify a ratio in fraction form in the same way that we would simplify a fraction. We use the greatest
common factor of both the numerator and the denominator. By dividing the numerator and the denominator
by the GCF we can simplify the fraction.
The GCF of both 2 and 22 is 2.
2÷2
1
=
22 ÷ 2 11
The simplest form of the ratio is 1 to 11. We can write this in three ways 1 to 11, 1:11 and
simplify a ratio in fraction form, we also write an equivalent form of the original ratio.
1
11 .
When we
2
1
=
11 22
Simplify these ratios on your own. If the ratio is not written in fraction form, you will need to do that first.
Example A
2
10
Solution:
1
5
Example B
6 to 8
Solution: 3 to 4
1
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Example C
5:20
Solution: 1:4
Now let’s think about Casey and the milk.
Casey can write this comparison three different ways.
4 to 2
4
2
4:2
If Casey simplifies these ratios, what conclusions can she draw?
4 to 2 simplifies to 2 to 1
4 2
=
2 1
4:2=2:1
Casey concludes that there are twice as many non-organic brands as there are organic. When she shows her
teacher, Ms. Gilson challenges Casey to do some research about organic brands of milk to bring to the grocery
store manager. Casey rises to the challenge!!
Vocabulary
Ratio
a comparison between two quantities; can be written three different ways.
Equivalent
equal
Simplify
to make smaller
Greatest Common Factor
the largest number that will divide into two or more numbers evenly.
Guided Practice
Here is one for you to try on your own.
Write the following ratio in simplest form.
12
18
Answer
We can simplify this ratio just as we would a fraction because it is in fraction form. The greatest common factor of
both 12 and 18 is 6. We divide both the numerator and the denominator by 6.
2
3
2
is our answer.
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Concept 1. Ratios in Simplest Form
Video Review
MEDIA
Click image to the left for more content.
James Sousa,Exampleof Writing a Ratio as aSimplified Fraction
MEDIA
Click image to the left for more content.
James Sousa,AnotherExampleof Writing a Ratio as aSimplified Fraction
Practice
Directions: Simplify each ratio. Write your answer in fraction form.
1. 2 to 4
2. 3:6
3. 5 to 15
4. 2 to 30
5. 10 to 15
6.
4
6
7. 3:9
8. 6:8
9.
2
8
10.
4
16
11. 10 to 12
12. 7:21
13. 12:24
14. 25 to 75
15.
16.
17.
27
30
48
60
18
80
3