Transcript Solving Proportions

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 15
12 students out of 20
15 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 $2.00
6 balloons $4.00
9 balloons $6.00
12 balloons $8.00
15 balloons $10.00
18 balloons $12.00
21 balloons $14.00
24 balloons $16.00
24 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
Reduce
5/3
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