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Here are a few recommended readings before getting started with this lesson.
Two numerical expressions are equivalent if one of the expressions is obtained from the other by applying properties of addition and multiplication. Knowing this, match each expression in the left column with the equivalent expression.
Two expressions are equivalent when one of them is obtained by applying properties of addition and multiplication to the other. For each pair of given expressions, determine whether they are equivalent. In the affirmative case, name the property that transforms one expression into the other.
If two real numbers are equal, then one can be substituted for another in any expression.
If a=b, then a can be substituted for b in any expression.
Apply the Substitution Property of Equality to determine who got the correct answer. Start by substituting 77 for F into the conversion formula. Then, substitute the values Tadeo and Magdalena found for C. If a true statement is obtained, the corresponding value is a solution; otherwise, it is not.
C=23
ca⋅b=ca⋅b
Multiply
Calculate quotient
Add terms
C=25
ca⋅b=ca⋅b
Multiply
Calculate quotient
Add terms
In addition to the commutative and associative properties, multiplication has another useful property that helps in the process of simplifying expressions with parentheses. This property is called the Distributive Property.
Multiplying a number by the sum of two or more addends produces the same result as multiplying the number by each addend individually and then adding all the products together.
At Ali's fruit store, strawberries are on sale! Today they are $0.60 cheaper per pound than usual. Magdalena stopped at the store on her way home from school and bought eight pounds of strawberries. She paid a total of $14.40.
Distribute 8
Multiply
LHS+4.8=RHS+4.8
LHS/8=RHS/8
Calculate quotient
After dinner, Magdalena works on a 3D model of a castle using cardboard for a history project. She wants the walls of the ramparts to be 7 inches wide. Additionally, she wants the value of the perimeter of the wall, in inches, to be the same as the value of its area, in square inches.
How high should the wall be?The area of the wall is 7x minus the area of the two small rectangles at the top. Equate the area expression with the perimeter of the wall. Then, solve the equation for x.
Top Length=11
\CommutativePropAdd
\AssociativePropAdd
Add terms
LHS−2x=RHS−2x
\CommutativePropAdd
Subtract terms
LHS+4=RHS+4
Add terms
LHS/5=RHS/5
Calculate quotient
Rearrange equation
Course 1 | |
---|---|
Ticket price | $15.00 |
Processing fee per ticket | $1.50 |
Service charge | $4.00 |
15t+1.5t+4=103
This equation models the situation in which Mark and his friends chose Course 1, got no discount, and paid $103.
Course 2 | |
---|---|
Ticket price | $18.00 |
Processing fee per ticket | $1.50 |
Service charge | $4.00 |
18t+1.5(t−5)+4=230.5
This equation models the situation in which Mark and his friends chose Course 2, got a discount, and paid $230.50.
\AssociativePropAdd
Add terms
LHS−4=RHS−4
LHS/16.5=RHS/16.5
Calculate quotient
Distribute 1.5
Multiply
\CommutativePropAdd
\AssociativePropAdd
Add and subtract terms
a+(-b)=a−b
LHS+3.5=RHS+3.5
LHS/19.5=RHS/19.5
Calculate quotient