RATIOS

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RATIOS
3 to 10
1,000,0001
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2 to 1
7 to 9
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A ratio is a comparison of 2 things.
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A fraction is an example of a ratio because a
fraction compares a part to a whole.
4 2 part

6 3 whole
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A ratio, however, does not always compare a
part to a whole.
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A ratio can compare anything.
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A ratio can compare a part to a part.
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For example, open a bag of MMs, and you could
make many comparisons.
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What is the ratio of red MMs to blue MMs?
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2 to 1 or 21
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What is the ratio of blue MMs to red MMs?
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1 to 2 or 12
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What is the ratio of red MMs to yellow MMs?
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2 to 2 or 1 to 1 or 22 or 11 Ratios can be
simplified just like fractions.
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Lets look at another example of ratios.
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Suppose that you went fishing. You cast your net
and caught 3 fish.
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Here are your 3 fish. (2 green fish and 1 blue
fish)
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You could conclude that for every 2 green fish,
there is 1 blue fish.
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This is a 2 to 1 ratio. (21)
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This is the same as a ratio of 4 to 2. (42)
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Or 6 to 3. (63)
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Or 8 to 4. (84)
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Or 10 to 5. (105)
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Or 12 to 6. (126)
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Or 14 to 7. (147)
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Wow! Thats a lot of fish.
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Just like fractions, ratios are usually
represented in their simplest form.
2 to 1 or 21
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Ratios help scientists answer real-world
questions.
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Lets investigate.
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Suppose that you wanted to estimate the number of
fish in a small lake.
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We could ask local anglers to help catch, tag,
and release fish back into the lake.
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Suppose that we tagged exactly 100 fish in the
lake.
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Lets again call on the help of some
conservationists.
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Suppose that our fisher friends caught a total
of 30 fish. 10 of these fish had been tagged,
and 20 of the fish had not been tagged. Based on
this ratio of 1 to 2, can you determine how many
fish are in the lake?
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The ratio of tagged fish to untagged fish is 1 to
2.
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If we caught 1 tagged fish for every 2 untagged
fish, and we know that there are 100 tagged fish
in the lake, then how many untagged fish should
be in the lake?
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Thats right! There should be 200 untagged fish
in the lake.
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So how many total fish should be in the
lake?
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100 tagged fish 200 untagged fish 300 total
fish
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Businesses use ratios all the time.
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For example, the motto for Kelloggs Raisin Bran
cereal has always been, Two scoops of raisins in
every box.
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Now, we dont know exactly how big a scoop is,
but someone needs to make sure that there is a
sufficient number of raisins in each box.
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Obviously, there are machines that put the cereal
and raisins in the box. However, someone needs
to program and calibrate these machines.
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If the machines were not calibrated correctly,
you might just get bran with three raisins.
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Someone needs to make sure that the ratio of
raisins to cereal is correct. Otherwise,
customers will not be happy with the product.
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Discussion Questions

• Are all fractions considered to be ratios?
• Are all ratios considered to be fractions?
• Can a probability be represented as a ratio?
• What is the benefit of putting a ratio in its
  simplest form?
• Where do we use ratios in the real world?