Here are the key steps to solving proportions: 1. Write the proportion as a fraction equal sign. 2. Isolate the variable by multiplying/dividing both sides by the same value. 3. Solve for the variable. 4. Check your solution by plugging it back into the original proportion. Practice these steps on your homework problems. Let me know if you have any other questions!

1. Section 3-5
Proportions

2. Essential Question
How do you write and solve proportions?
Where you’ll see this:
Art, machinery, manufacturing, business,
physics, retail

3. Vocabulary
1. Proportion:
2. Means:
3. Extremes:
4. Cross-products:

4. Vocabulary
1. Proportion: An equation where two ratios are
the same
2. Means:
3. Extremes:
4. Cross-products:

5. Vocabulary
1. Proportion: An equation where two ratios are
the same
2. Means: The “inside” values of a proportion
3. Extremes:
4. Cross-products:

6. Vocabulary
1. Proportion: An equation where two ratios are
the same
2. Means: The “inside” values of a proportion
3. Extremes: The “outside” values of a proportion
4. Cross-products:

7. Vocabulary
1. Proportion: An equation where two ratios are
the same
2. Means: The “inside” values of a proportion
3. Extremes: The “outside” values of a proportion
4. Cross-products: Multiplying the extremes and
the means

8. Proportion

9. Proportion
Compares ratios

10. Proportion
Compares ratios
Ratios are equal

11. Proportion
Compares ratios
Ratios are equal
Words:

12. Proportion
Compares ratios
Ratios are equal
Words: a is to b as c is to d

13. Proportion
Compares ratios
Ratios are equal
Words: a is to b as c is to d
Colons:

14. Proportion
Compares ratios
Ratios are equal
Words: a is to b as c is to d
Colons: a:b = c:d

15. Proportion
Compares ratios
Ratios are equal
Words: a is to b as c is to d
Colons: a:b = c:d
Fractions:

16. Proportion
Compares ratios
Ratios are equal
Words: a is to b as c is to d
Colons: a:b = c:d
a c
Fractions: =
b d

17. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36

18. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36

19. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x

20. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x

21. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x = 24(24)

22. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x = 24(24)
36x = 576

23. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x = 24(24)
36x = 576
36 36

24. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x = 24(24)
36x = 576
36 36
x = 16

25. Example 1
Solve the proportion and check the solution.
x 24
a. =
24 36
36x = 24(24)
36x = 576
36 36
x = 16
Check.

26. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12

27. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12

28. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12)

29. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12)

30. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12) = 28x

31. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12) = 28x
168 = 28x

32. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12) = 28x
168 = 28x
28 28

33. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12) = 28x
168 = 28x
28 28
x =6

34. Example 1
Solve the proportion and check the solution.
14 28
b. =
x 12
14(12) = 28x
168 = 28x
28 28
x =6
Check.

35. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?

36. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c
=
grams g

37. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= =
grams g 15 75

38. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= =
grams g 15 75

39. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= = 6000 = 15c
grams g 15 75

40. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= = 6000 = 15c
grams g 15 75 15 15

41. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= = 6000 = 15c
grams g 15 75 15 15
c = 400

42. Example 2
The cheese that Fuzzy Jeff bought contains
about 80 calories in 15 grams. Fuzzy Jeff ate
75 grams of the cheese. About how many
calories was that?
calories c 80 c
= = 6000 = 15c
grams g 15 75 15 15
c = 400 Fuzzy Jeff had 400 calories

43. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x

44. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x

45. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)

46. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)

47. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144

48. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144
+8x +8x

49. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144
−144 +8x +8x −144

50. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144
−144 +8x +8x −144
336 = 56x

51. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144
−144 +8x +8x −144
336 = 56x
56 56

52. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
8(60 − x ) = 48(x + 3)
480 − 8x = 48x + 144
−144 +8x +8x −144
336 = 56x
56 56
x =6

53. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
x =6

54. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
x =6
8 48
=
6 + 3 60 − 6

55. Example 3
Solve the proportion and check.
8 48
=
x + 3 60 − x
x =6
8 48
=
6 + 3 60 − 6
8 48
=
9 54

56. Homework

57. Homework
p. 124 #1-47 odd
"Far better it is to dare mighty things, to win
glorious triumphs even though checkered by
failure, than to rank with those poor spirits who
neither enjoy nor suffer much because they live
in the gray twilight that knows neither victory
nor defeat." - Theodore Roosevelt