4.4c Class Activity: Solving Proportions
The following proportion compares two quantities:
!
!
=
!
!
means “3 is to what number, as 5 is to 9?”
What is another comparison that could be made between the two quantities?
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!!
!
!
!
!
Now consider the equation ! = !.!!Whether the numbers came from a ratio with like units, a rate with unlike
units, or fractions, we can solve this equation for x using the multiplication property of equality. Example #1
shows a path for the solution. Write a justification of why each step shows an equation with the same solution
as the previous step.
Example #1: Write a justification for each step, using algebraic properties.
Equation
! !
=
! !
! !
! = ! !
! !
!" !"
=
!
!
!"
!=
!
Justification
For the proportions below, solve using properties of equality. You may reverse the order of the ratio
comparison.
1.
2.
3.
!
!
=
!
!"
!
!
!
=!
!
=!
!
!
!
4.
5.
6.
7WB4 - 116
!
=
!
!
!
!
!
=!
!"
!
!
!
=!
©2014 University of Utah Middle School Math Project in partnership with the
Utah State Office of Education. Licensed under Creative Commons, cc-by.
!
4.4c Homework: Solving Proportions
Solve each proportion using properties of equality.
1.
2.
!
=
!
!"
!
!
!
!
= !"
!
4.!! =
!
!
!
!
!
=!
!
5.
!
!
3.
!
!
=!
!.!
6.
!
!
=
!"
!
After solving problems # 1 – 6, go back and solve the problems from section 4.4b (where you wrote proportion
equations but did not yet solve).
!
!
7WB4 - 117
©2014 University of Utah Middle School Math Project in partnership with the
Utah State Office of Education. Licensed under Creative Commons, cc-by.
!