1. Understanding Ratios
By Mr. Santana

2. What is a Ratio?

3. What is a Ratio?
A ratio is a comparison of two or more amounts

4. What is a Ratio? A ratio is a comparison of two or more amounts
Like Girls to boys

5. What is a Ratio? A ratio is a comparison of two or more amounts
Like Girls to boys
Cats : Dogs

6. What is a Ratio? A ratio is a comparison of two or more amounts
Like Girls to boys
Cats : Dogs
Coins to Dollars

7. What is a Ratio?
For Example

8. What is a Ratio?
For Example
The ratio of moons to stars is…

9. What is a Ratio?
For Example
The ratio of moons to stars is
9:3

10. What is a Ratio?
And if we rearrange the items…

11. What is a Ratio?
The diagram will look like this.

12. What is a Ratio?
There are several ways to think about what this diagram represents.

13. What is a Ratio?
We can have
Stars to Moons

14. What is a Ratio?
We can have
Stars to Moons
or Moons : Stars

15. What is a Ratio? We can have Stars to Moons or Moons : Stars
or Moons to All

16. What is a Ratio? We can have Stars to Moons or Moons : Stars
or Moons to All
or All : Moons

17. What is a Ratio? We can have Stars to Moons or Moons : Stars
or Moons to All
or All : Moons
or Stars to All

18. 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

19. 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…

20. What is a Ratio?
Count the number of stars…

21. What is a Ratio?
There are three stars.

22. What is a Ratio?
Count the number of moons…

23. What is a Ratio?
There are nine moons.

24. 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

25. What is a Ratio?
Similarly, to get the ratio of stars to all is the same process…
Count each and you get
3:12

26. What is a Ratio? So the other ratios are… Moons to All = 9:12
All : Moons = 12/9
& All : Stars = 12:3

27. What is a Ratio?
We can also simplify the ratios by regrouping them…

28. What is a Ratio?
For example box each column

29. What is a Ratio?
For example box each column

30. What is a Ratio?
For example box each column

31. What is a Ratio?
For example box each column

32. What is a Ratio?
For example box each column

33. 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.

34. What is a Ratio?
You can also simplify the ratio by using division like with fractions.

35. What is a Ratio?
3 stars to 9 moons can be simplified if… 3 9

36. 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

37. 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

38. 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.

39. 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.

40. 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.

41. Let’s Practice a bit. Consider the diagram below…
What is the ratio of cats to dogs?
Dogs to the whole group?

42. Let’s Practice a bit. First rearrange the diagram…
What is the ratio of cats to dogs?
Dogs to the whole group?

43. 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?

44. Let’s Practice a bit.
What is the ratio of dogs to the whole group?

45. 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

46. 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

47. 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

48. 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