What does a ratio do? • A ratio compares values. • It tells us how much of one thing there is compared to another thing. • There are 3 orange squares to 1 yellow square
How to show a ratio • Ratios can be shown in different ways: • Using the : to separate the values 3:1 • You can also use the word to 3 to 1
Ratios can be increased (scaled up) • We can multiply ratios in order to scale them up. • What happens if we multiply or scale up 3:1 by 2? 3:1 • Here the ratio is also 3 orange squares to 1 yellow square, even though there are more squares. 2 6
Using Ratios 4 : 5 x2 x2 8 : 10
Football Example: • A quarterback throws the ball 10 times in the first quarter of the game and 6 of his passes are caught. • If he has the same results in the remaining three quarters of the football game what are his final numbers?
Part-to-Part Ratios • Part-to-Part: • The ratio of boy to girl puppies is 2:3 • The ratio of girl to boy puppies is 3:2
Part-to-Whole Ratios • Part-to-Whole: • The ratio of boys to all puppies is 2:5 • The ratio of girls to all puppies is 3:5
Singer Ratios • The ratio of Katy Perry to Justin Bieber is 1:2 • The ratio of Justin Bieber to Katy Perry is 2:1 • The ratio of Katy Perry to all singers is 1:3 • The ratio of Justin Bieber to all singers is 2:3
Scaling • You can use ratios to scale drawings up or down (by multiplying or dividing).
Lobo Louie Example • The height to width ratio of Lobo Louie’s head is 2:3 • So for every 2 feet of height there should be 3 feet of width. • But if we wanted to use inches instead we would scale up by 12. • Then are ratio would become 24:36. • Lobo Louie has a big head!
Business Example • Let’s start a lemonade business! • We know that it takes 2 sugar packets for every 5 lemons to make 1 cup of lemonade. • How many sugar packets and lemons do we need to serve 20 customers?
What does a proportion do? • A proportion says that two ratios (or fractions) are equal. 1-out-of-3is equal to 2-out-of-6 The ratios are the same, so they are in proportion.
How to show a Proportion • Proportions can be shown in different ways: • Fraction form • Word form1 out of 2
Using Proportions • When things are "in proportion" then their relative sizes are the same. • Here you can see that the ratios of head length to body length are the same in both drawings. • So they are proportional. (Both fractions can reduce to ½.)
Example: We want to draw the dog's head, and we need to know how long it should be: Write the proportion with the help of the 1/2 ratio from above:
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? To solve, we multiply both sides by 2.9: Answer: the tree is 5.4 m tall. And he didn't even need a ladder!
Example Maggie and her little sister Minnie are in proportion.What is Minnie's height?
Health Example If the records at the Humane Society show that they have 9 cats for every 10 dogs. • The ratio of cats to dogs can be written: 9 to 10 or 9:10.
Health Example If the records at the Humane Society show that they have a total of 40 dogs The total number of catsat 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?