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Here are a few recommended readings before getting started with this lesson.
Zain and Jordan planned an adventure across a vast desert landscape. They will cycle for three days until they reach a huge music festival! The first two days, Zain and Jordan need to cycle the same distance each day. On the third day, they will have 10 miles remaining to be cycled.
The total distance Zain and Jordan cycle during the trip is 60 miles. If they miscalculate their trip, they will miss the festival!
Equations can be named according to the minimum number of inverse operations needed to solve them.
LHS+3=RHS+3
Add terms
LHS/2=RHS/2
ca⋅b=ca⋅b
Calculate quotient
Identity Property of Multiplication
Zain and Jordan are cycling along. Already on their first day, they ran into a problem! Zain's tire got a terrible flat and they do not have a spare to replace it. They need to buy a new tire.
They head into town to buy extra tires to be better prepared.
LHS/3=RHS/3
Cross out common factors
Cancel out common factors
Calculate quotient
undoeach other. Consider the given equation. Here, the variable m is divided by 2 and then 5 is added to the result.
On the second day of this ride to the festival, Zain and Jordan begin to wonder about some of the data from their ride.
LHS⋅-45=RHS⋅-45
Commutative Property of Multiplication
ba⋅ab=1
a⋅cb=ca⋅b
Multiply
-b-a=ba
Calculate quotient
LHS−x=RHS−x
Subtract terms
LHS⋅(-1)=RHS⋅(-1)
-a(-b)=a⋅b
ca⋅b=ca⋅b
x=30
ca⋅b=ca⋅b
Multiply
Calculate quotient
Subtract term
Solve the equations by using the Properties of Equality. If necessary, give answers as decimals rounded to two decimal places.
Zain and Jordan continued cruising along their cycling trip. The beauty of the ride became even more noticeable as they could hear songbirds! Some birds sang perched atop a power line.
A few more birds flew in and joined the flock. As a result, the number of birds doubled. Then, 4 birds flew away. In the end, 8 birds were left singing on the power line.
LHS/2=RHS/2
Cross out common factors
Cancel out common factors
Calculate quotient
Zain and Jordan successfully reached the music festival! The line to enter the festival is super long. Each came up with their own way to describe the difference between the time they expected to wait in line and the time they will actually have to wait.
LHS/2=RHS/2
Cross out common factors
Cancel out common factors