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Here are a few recommended readings before getting started with this lesson.
Diego is going through some old stuff in storage. He discovers an entire rack of vinyls! There are 200 in total and they belong to his dad. Diego asks his father how long this collection took to gather.
Multiplication and division are inverse operations. They can be used to solve equations by the following properties of equality.
Given an equation, multiplying each side of the equation by the same number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b, then a×c=b×c.
Dividing each side of an equation by the same nonzero number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b and c=0, then a÷c=b÷c.
LHS/5=RHS/5
Cross out common factors
Simplify quotient
Calculate quotient
undoeach other. Consider the given equation.
LHS⋅35=RHS⋅35
Commutative Property of Multiplication
ba⋅ab=1
a⋅1=a
a⋅cb=ca⋅b
Multiply
Calculate quotient
Diego finds himself wondering about the speed at which a record rotates. His father tells Diego that the record rotates 190 times while playing a song on the album. Diego later reads online that a record rotates 95 of a full rotation every second it plays.
Identify the coefficient of the variable. Multiply both sides of the equation by the reciprocal of the coefficient.
LHS⋅59=RHS⋅59
Commutative Property of Multiplication
ba⋅ab=1
a⋅1=a
a⋅cb=ca⋅b
Multiply
Calculate quotient
Solve the equations using the Multiplication Property of Equality or the Division Property of Equality. If necessary, round answers to two decimal places.
Many real-life situations can be algebraically modeled by equations. These equations can involve a variable that represents an unknown quantity. Consider modeling the following situation.
Diego categorizes his father's record collection by genre. He finds out that there are 8 different genres, each with the same number of records. The collection contains 200 records. How many records are there in each genre? |
LHS/8=RHS/8
Cross out common factors
Simplify quotient
Calculate quotient
Diego's father's old turntable is broken. Diego is so eager to listen to the records that he decides to make some money to buy the replacement parts. The parts that Diego needs to buy costs $96. Diego's neighbor offers him $8 per walk to walk her dog.