1. A ratio compares two things.
It can compare part to part, a part to the whole, or the whole to a part.
The word “to” compares the two terms in a ratio.
The numbers and words MUST be in the same order!

2. You can write a ratio three different ways.
In words: 4 to 3
Using a colon: 4:3
Like a fraction 4/3
In this ratio we are comparing the number of pink squares to the number of blue squares.

3. RATIO If a recipe says, “For every cup of rice, add 2
cups of water” that’s a ratio.
In school, if there is 1 teacher to every 5 students,
that’s a ratio, too.
A ratio is a handy way to express the relationship between numbers.
RATIO

4. If you've spent any time in the kitchen, then you already know quite a bit about ratios.
A rice recipe calls for 2 cups of water to 1 cup rice.
The ratio of water to rice is 2 to 1.

5. What is the ratio of oil to vinegar in a salad dressing recipe that calls for 2 tablespoons oil to 1 tablespoon vinegar?
Separate your numbers by the word "to."

6. The ratio of oil to vinegar in the salad dressing
is 2 to 1.
We can also write this with a colon as 2:1.

7. A biscuit recipe calls for 7 cups flour
and 1 cup shortening.
What is the ratio of flour to shortening? Write the ratio with a colon.
Don't add any spaces between the numbers and the colon.

8. ANSWER
7:1

9. Ratios can also be written as fractions.
A tortilla recipe calls for 4 cups flour and 1 cup water. The ratio of flour to water would be 4 to 1, or 4:1.
As a fraction we write this as 4/1.

10. A stew recipe calls for 5 cups carrots and 2 cups onions
A stew recipe calls for 5 cups carrots and 2 cups onions. Write the ratio of carrots to onions as a fraction
A stew recipe calls for 5 cups of carrots and 2 cups of onions.

11. ANSWER
5/2
is the same as
5:2
and
5 to 2.

12. A recipe for orange juice calls for 3 cups water and 1 cup orange juice concentrate.
                                                                                                                                                                     
A recipe for orange juice calls for 3 cups water and 1 cup orange juice concentrate.
Write the ratio of water to concentrate as a fraction.

13. Good job. 3 to 1 is the same as 3/1.

14. What if we want to double the amount of orange juice we make?
The original recipe calls for 3 cups water and 1 cup orange juice concentrate.
The ratio of water to concentrate is 3:1.
To double the recipe, we multiply both terms (in ratios we call the numbers "terms") in the 3:1 ratio by 2 (because we’re making twice as much).
This is called an equivalent ratio. Two ratios that equal the same thing.

15. The new ratio is 6:2.

16. If we triple the recipe, what is the ratio of water to concentrate?
Write the ratio as a fraction.

17. ANSWER
9/3

18. What if we want to make 5 times the original amount of orange juice?
The original recipe calls for 3 cups water and 1 cup orange juice concentrate. The ratio of water to concentrate is 3:1.

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Working with Ratios: Activity 1 of 3
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What if we want to make 5 times the original amount of orange juice? The original recipe calls for 3 cups water and 1 cup orange juice concentrate. The ratio of water to concentrate is 3:1.
To make 5 times the recipe, we multiply both terms in the 3:1 ratio by 5. The new ratio is 15:5.
                                                                                                                                                                     
If we make 4 times as much orange juice, what is the ratio of water to concentrate? Write the ratio with a colon.
Don't type any spaces between the numbers and the colon.
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To make 5 times the recipe, we multiply both terms in the 3:1 ratio by 5. The new ratio is 15:5.

20. No matter how much orange juice we make, we still need 3 cups of water for every 1 quart of concentrate
So the ratio of 12 cups of water to 4 cups concentrate in the quadrupled recipe is the same as the ratio of concentrate to water in the original recipe.

21. In other words, the relationship between the two terms in the ratio 3:1 is the same as that in 12:4.
Just do the math! 3 is three times as much as 1, and 12 is three times as much as 4.
Since 3:1 and 12:4 have the same relationship, these two ratios are equal.

22. When two ratios are equal, we say they are in proportion.
In other words, a proportion is a mathematical statement that two ratios are equal.
Equivalent ratio = proportion

23. We write proportions like this:
3 to 1 equals 12 to 4
3:1 = 12:4
3/1 = 12/4

24. A recipe for chili calls for 5 oz beans and 2 oz beef
A recipe for chili calls for 5 oz beans and 2 oz beef. The ratio of beans to beef is 5:2. You want to quadruple the recipe to fill a big pot for a party.

25. Write the original beans to beef ratio and the quadrupled recipe ratio as a proportion. Don’t forget to write your answer with colons and the equal sign.

26. ANSWER
5:2 = 20:8

27. To figure out the new ratio you multiply both terms in the original recipe ratio 5:2 by 4.
Another way to write the same proportion is 20:8 = 5:2.

28. Which of the following is not a proportion?
B) 3:4 = 15:20
C) 7:6 = 14:12

29. ANSWER A In true proportions, both terms in one ratio must be
multiplied (or divided) by the same number to get the
terms of the second ratio.
If you do the math, you’ll see that 1:6 = 24:4 is not a
proportion.
1 x 24 = but 6 x 24 = not 4!

30. In Mrs. Jones’ class there are 20 students
In Mrs. Jones’ class there are 20 students. There are 12 boys and 8 girls. 7 students have brown hair, 10 have blonde hair and 3 have red hair. What is the ratio of students with blond hair to those that have red hair?

31. ANSWER 10:3

32. Martha has 10 dresses. 3 are red and the rest are blue
Martha has 10 dresses. 3 are red and the rest are blue. How many red dresses to blue dresses does she have?

33. ANSWER
3:7

34. Tom has 13 video games. 5 are action games, 2 are adventure and the rest are sports. How many sports games to action games does Tom have?

35. ANSWER
6:5

36. Ratios and Proportions in Word Problems
In problems involving proportions, there will always be a ratio statement.

37. Can you find the ratio statement?
An automobile travels 176 miles on 8 gallons of gasoline. How far can it go on a tankful of gasoline if the tank holds 14 gallons?

38. The ratio statement is:
176 miles
8 gallons

39. What information do we have remaining?
14 gallons

40. What information are we trying to find out?
miles

41. Since we don’t know miles what should we put in its place?
X or any letter because it’s the variable

42. So the proportion is: 176 miles = x miles 8 gallons 14 gallons
Math Note: Notice in the previous example that the numerators of the proportions have the same units, miles, and the denominators have the same units, gallons.

43. So the proportion is:
176 = x

44. Next step: Cross Multiply
8m = 176 x 14
8m = 2464

45. Then divide both 2464 and 8m by 8.
8m = m= 308 miles
8 8

46. On 14 gallons, the automobile can travel a distance of 308 miles.
ANSWER
On 14 gallons, the automobile can travel a distance of 308 miles.

47. STEP 1
Read the problem .

48. Identify the ratio statement. There will ALWAYS be one.
STEP 2
Identify the ratio statement.
There will ALWAYS be one.

49. STEP 3 Set up the proportion
Be sure to keep the identical units in the numerators and denominators of the fractions in the proportion.

50. Solve for x or the variable.
STEP 4
Solve for x or the variable.

51. Let’s try another
If it takes 16 yards of material to make 3 costumes of a certain size, how much material will be needed to make 8 costumes of that same size?

52. The ratio statement is:
What’ s the next step
Find the ratio statement.
The ratio statement is:

53. STEP 2 Find the proportion remember
Be sure to keep the identical units in the numerators and denominators of the fractions in the proportion.
yards yards
costumes costumes

54. Setting the proportion
16 yards = x yards
3 costumes 8 costumes
Identical units

55. Next step cross multiply
16 yards = y yards 3 costumes 8 costumes 3y = 16 x 8 3y = Y =

56. PRACTICE

57. Remember: Pounds across from pounds square feet across from feet.
If 5 pounds of grass seed will cover 1025 square feet, how many square feet can be covered by 15 pounds of grass seed?
Remember: Pounds across from pounds square feet across from feet.

58. ANSWER
3075 square feet

59. If a homeowner pays $8000 a year in taxes for a house valued at $250,000, how much would a homeowner pay in yearly taxes on a house valued at $175,000?

60. ANSWER
$5600

61. If a person earns $2340 in 6 weeks, how much can the person earn in 13 weeks at the same rate of pay?

62. ANSWER
$5070

63. If 3 gallons of waterproofing solution can cover 360 square feet of decking, how much solution will be needed to cover a deck that is 2520 square feet in size?

64. Answer
21 gallons

65. A recipe for 4 servings requires 6 tablespoons of shortening
A recipe for 4 servings requires 6 tablespoons of shortening. If the chef wants to make enough for 9 servings, how many tablespoons of shortening are needed?

66. Answer
13 or 13.5 tablespoons