Solving Proportions

What’s a proportion? A proportion is when 2 ratios are equivalent For example 5/6 = 15/18

How do you use proportions? Proportions are great for solving all types of problems! You will be introduced to 2 methods of solving proportions Making a table Using multiplication

Making a table In a seventh grade class 3 out of every 5 students ride the bus to school. How many students ride the bus if there are 25 students in the class? That’s a ratio! 3 : 5

Lets make a table! 3 students out of 5 6 students out of 10 9 students out of students out of students out of 25 There will be 15 students riding the bus in a class of 25 students.

How is the table made? Each step is acquired by adding the ratio to the previous answer!

Your turn! John, Jenny, and Henry bought 3 balloons and paid $2.00 for them all. They decide to buy enough balloons for the whole class. How much did they pay for 24 balloons? Make a table

How much did the balloons cost? 3 balloons $ balloons $ balloons $ balloons $ balloons $ balloons $ balloons $ balloons $ balloons cost $16.00

Using Multiplication To use multiplication, find a factor (number) that was used to multiply part of the proportion, then multiply the other part by that same factor

An example using multiplication If two machines can complete 6 tasks for every 5 days. How many tasks can these machines complete in 30 days? First set up your proportion Remember to have the same units in the same places tasks/days = tasks/days

Let’s solve it! 6 tasks/5 days = ? tasks/30 days Notice! You have to take 5 times 6 to get 30. Take 6 times 6 to get 36. The machine can complete 36 tasks in 30 days.

Your turn! At maximum speed, an elevator in a tall building can pass 50 floors in 30 seconds. How many floors can the elevator pass in 18 seconds. (Be careful, you might want to simplify the ratio first!)

Solution First, write the ratio 50 floors/30 seconds Reduce5/3 Write the proportion 5 floors/3 seconds = ? Floors/18 seconds What times 3 = 18? 6 x 3 = 18 Multiply 5 times that factor. 6 x 5 = 30 The elevator can pass 30 floors in 18 seconds