Equivalent Expressions – Part 1
Overview
Equivalent expressions are expressions that are written differently but have the same value. Let’s look at an example…
Write an expression that is equivalent to 2 (3 + n).
We can use our knowledge of multiplication to recognize that 2 times 3 + n is the same as saying 2 groups of 3 + n.
We can represent the two groups with a model.
We can see by looking at the model that the expression could be written as
6 + 2n
We can check our answer with the distributive property.
2 (3 + n)
When using the distributive property, we distribute the 2 to each term within the
parenthesis. Doing this allows us to forgo the order of operations, which comes in
handy when we are working with variables.
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Use a model to illustrate 4(2 + p).
Answers may vary
Use a model to illustrate 3(x + 4).
Answers may vary
Combine like terms to find an equivalent expression for 2t + 4 + 3t – 2.
5t + 2
Combine 2t and 3t. Then combine 4 – 2.
Combine like terms to find an equivalent expression for 3y + 2t – t + 2y.
5y + t
Combine 3y + 2y. Then combine 2t – t.
Combine like terms to find an equivalent expression for 4s + 1 – s.
3s + 1
Combine 4s – s