Understanding Ratios By Mr. Santana
What is a Ratio?
What is a Ratio? A ratio is a comparison of two or more amounts
What is a Ratio? A ratio is a comparison of two or more amounts Like Girls to boys
What is a Ratio? A ratio is a comparison of two or more amounts Like Girls to boys Cats : Dogs
What is a Ratio? A ratio is a comparison of two or more amounts Like Girls to boys Cats : Dogs Coins to Dollars
What is a Ratio? For Example
What is a Ratio? For Example The ratio of moons to stars is…
What is a Ratio? For Example The ratio of moons to stars is 9:3
What is a Ratio? And if we rearrange the items…
What is a Ratio? The diagram will look like this.
What is a Ratio? There are several ways to think about what this diagram represents.
What is a Ratio? We can have Stars to Moons
What is a Ratio? We can have Stars to Moons or Moons : Stars
What is a Ratio? We can have Stars to Moons or Moons : Stars or Moons to All
What is a Ratio? We can have Stars to Moons or Moons : Stars or Moons to All or All : Moons
What is a Ratio? We can have Stars to Moons or Moons : Stars or Moons to All or All : Moons or Stars to All
What is a Ratio? We can have Stars to Moons or Moons : Stars or Moons to All or All : Moons or Stars to All or All : Stars
What is a Ratio? We already saw the ratio of moons to stars is 9:3. Well to find the ratio of stars to moons…
What is a Ratio? Count the number of stars…
What is a Ratio? There are three stars.
What is a Ratio? Count the number of moons…
What is a Ratio? There are nine moons.
What is a Ratio? So the ratio of stars to moons is 3:9. You could also represent this ratio like a fraction 3/9
What is a Ratio? Similarly, to get the ratio of stars to all is the same process… Count each and you get 3:12
What is a Ratio? So the other ratios are… Moons to All = 9:12 All : Moons = 12/9 & All : Stars = 12:3
What is a Ratio? We can also simplify the ratios by regrouping them…
What is a Ratio? For example box each column
What is a Ratio? For example box each column
What is a Ratio? For example box each column
What is a Ratio? For example box each column
What is a Ratio? For example box each column
What is a Ratio? There is 1 column of stars and 3 columns of moons. So… The ratio of stars to moons goes from 3:9 to 1:3.
What is a Ratio? You can also simplify the ratio by using division like with fractions.
What is a Ratio? 3 stars to 9 moons can be simplified if… 3 9
What is a Ratio? You divide each number by 3 because each shape was placed in a group of 3 (and both numbers are in the 3 times table). 3 9
What is a Ratio? 3 9 1 3 = 1 group of stars to 3 groups of moons And as before, 3 stars to 9 moons becomes… 3 9 1 3 = 1 group of stars to 3 groups of moons
What is a Unit Ratio? Oh, I know. Because the ratio is 1:3, I can also say for every star there are 3 moons.
In each row, there is 1 star for every 3 moons. What is a Unit Ratio? In each row, there is 1 star for every 3 moons.
What is a Unit Rate? Here, the simplified ratio, 1:3, is also a unit rate. It is a unit rate because the ratio has a one in it.
Let’s Practice a bit. Consider the diagram below… What is the ratio of cats to dogs? Dogs to the whole group?
Let’s Practice a bit. First rearrange the diagram… What is the ratio of cats to dogs? Dogs to the whole group?
Let’s Practice a bit. Count what you need to count and… What is the ratio of cats to dogs? The ratio of cats to dogs is 6:4 or 3:2 Dogs to the whole group?
Let’s Practice a bit. What is the ratio of dogs to the whole group?
Let’s Practice a bit. What is the ratio of dogs to the whole group? The ratio of dogs to the whole group is… 4:10 or 2:5
Simplify each ratio. 1) = 2) = 10 6 3 tables:15 people 1) = 2) = 3 tables:15 people For every _____ table(s) we can sit _____ people
Simplify each ratio. 1) = 2) = 10 5 6 3 3 tables:15 people 1) = 2) = 3 tables:15 people For every _____ table(s) we can sit _____ people
Simplify each ratio. 1) = 2) = 10 6 5 3 1 table : 5 people 1) = 2) = 1 table : 5 people 3 tables:15 people 1 5 For every _____ table(s) we can sit _____ people