ratios. what does a ratio do? o a ratio compares values. o it tells us how much of one thing there...
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Ratios
What does a ratio do?O A ratio compares values.
O It tells us how much of one thing there is compared to another thing.
O There are 3 orange squares to 1 yellow square
How to show a ratioO Ratios can be shown in different
ways:
O Using the : to separate the values 3:1
O You can also use the word to 3 to 1
Ratios can be increased (scaled up)
O We can multiply ratios in order to scale them up.O What happens if we multiply or scale
up 3:1 by 2?
3:1
O Here the ratio is also 3 orange squares to 1 yellow square, even though there are more squares.
Using Ratios
Football Example:O A quarterback throws the ball 10
times in the first quarter of the game and 6 of his passes are caught.
O If he has the same results in the remaining three quarters of the football game what are his final numbers?
Answer:
Part-to-Part RatiosO Part-to-Part:
O The ratio of boy to girl puppies is 2:3O The ratio of girl to boy puppies is 3:2
Part-to-Whole RatiosO Part-to-Whole:
O The ratio of boys to all puppies is 2:5O The ratio of girls to all puppies is 3:5
Singer Example
Singer RatiosO The ratio of Katy Perry to Justin
Bieber is 1:2O The ratio of Justin Bieber to Katy
Perry is 2:1
O The ratio of Katy Perry to all singers is 1:3
O The ratio of Justin Bieber to all singers is 2:3
ScalingO You can use ratios to scale drawings
up or down (by multiplying or dividing).
Lobo Louie ExampleO The height to width ratio of Lobo
Louie’s head is 2:3O So for every 2 feet of height there
should be 3 feet of width.O But if we wanted to use inches
instead we would scale up by 12.O Then are ratio would become 24:36.O Lobo Louie has a big head!
Business ExampleO Let’s start a lemonade business!O We know that it takes 2 sugar
packets for every 5 lemons to make 1 cup of lemonade.
O How many sugar packets and lemons do we need to serve 20 customers?
Answer
Proportions
What does a proportion do?
O A proportion says that two ratios (or fractions) are equal.
1-out-of-3 is equal to 2-out-of-6
The ratios are the same, so they are in proportion.
How to show a Proportion
OProportions can be shown in different ways:
O Fraction form
O Word form 1 out of 2
Using ProportionsO When things are "in
proportion" then their relative sizes are the same.
O Here you can see that the ratios of head length to body length are the same in both drawings.
O So they are proportional. (Both fractions can reduce to ½.)
Example:
Answer:Now we solve it mathematically:
So you should draw the head 21 long.
How tall is the tree?
Alex tried using a ladder, tape measure, ropes and various other
things, but still couldn't work out how tall the tree was.
How tall is the tree?Alex has a clever idea: proportions!
He measures a stick and its shadow (in meters), and also the shadow of the tree, and this is what he gets:
How tall is the tree?Alex writes the "Height to Length" ratio for both objects:
How tall is the tree?
Example
Maggie and her little sister Minnie are in proportion.
What is Minnie's height?
What is Minnie’s height?
Health Example
If the records at the Humane Society show that they have 9 cats for every 10 dogs.
OThe ratio of cats to dogs can be written:
9 to 10 or 9:10.
Health ExampleIf the records at the Humane Society show that they have a total of 40 dogs
The total number of cats at the Humane Society can be found by using a proportion:
Total # of cats =
Health Example
About 4 in every 5 puppies in Albuquerque are taken to Animal Humane to be vaccinated.
If we were all puppies in this classroom, how many of us would be vaccinated at Animal Humane?