Math: Module 1 Lesson 4 Equivalent Ratios

Classwork Example 1 The morning announcements said that two out of every seven 6th graders in the school have an overdue library book. Jasmine said, “That would mean 24 of us have overdue books!” Grace argued, “No way. That is way too high.” How can you determine who is right?

Example 1 Is Jasmine’s statement true? What do we need to do in order to find out if this conclusion is mathematically correct?

Original ratio = 2:7 What does each number in the ratio represent? Example 1 Original ratio = 2:7 What does each number in the ratio represent?

Example 1 Original ratio = 2:7 If Jasmine concludes that 24 students have overdue books, what is the total number of students in the 6th grade at her school?

Example 1 To determine two sets of ratios to be equivalent, we can multiply the first ratio by the same positive number.

Exercise 1 Take 5-10 minutes to work on the remaining problems from example 1. Share answers with neighbors and debate if there are any disagreements.

Exercise 2 Use a tape diagram to support your work. Justify your answer by showing that the new ratio you created is equivalent to 5:6

Tape Diagram Walnuts Cashews

Tape Diagram Walnuts = ? = 54 Cashews

Exercise 2 Determine the amount of walnuts that are in the bag if there are 54 cashews. The ratio of number of walnuts to number of cashews is ___: 54. That ratio is equivalent to 5:6.

Tape Diagram Walnuts = 45 9 = 54 Cashews 9

Closing How can we use the description of equivalent ratios to find an equivalent ratio? What do the numbers in the boxes of the tape diagram represent in terms of the ratio?

Closing (Answer) How can we use the description of equivalent ratios to find an equivalent ratio? Ratios are equivalent if there is a positive number that can be multiplied by both quantities in one ratio to equal the corresponding quantities of the second ratio.

Closing What do the numbers in the boxes of the tape diagram represent in terms of the ratio? Inside each of the boxes, the positive number, c , comes from the value of one unit in the tape diagram.

Closing We can determine that to find an equivalent ratio, the positive number, c, must be the same in each box in the tape diagram. This can also be described as “constant”. If the number, c, is constantly the same number, then the ratios are equivalent.

Lesson Summary Two ratios A:B and C:D are equivalent ratios if there is a positive number, c, such that C = cA and D = cB.

Lesson Summary Ratios are equivalent if there is a positive number that can be multiplied by both quantities in one ratio to equal the corresponding quantities of the second ratio. This description can be used to determine whether two ratios are equivalent.