Finding Equivalent Equations

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

Use the distributive property to simplify: 5(2f + 4)

Back

10f + 20

Front

How do you find the balance in a checking account after deposits and withdrawals?

Back

You add the deposit amount to the initial balance and subtract the withdrawal amount. For example, if Larry had $84, made a deposit of $21, and a withdrawal of $3, the expression is 84 + 21 - 3.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variables involved.

Front

Identify the equivalent expressions: 9(6 + x) and 9 ⋅ 6 + 9 ⋅ x

Back

These expressions are equivalent because of the distributive property.

Front

What is the result of simplifying (10 - 6) ÷ y and 10 - (6 ÷ y)?

Back

These expressions are not equivalent because the first expression simplifies to (4/y) while the second simplifies to (10 - 6/y).

Front

What is the expression for finding the equivalent of (6 ÷ 2) - (8 x 12)?

Back

The equivalent expression is (3) - (8 x 12).

Front

What is the first step in using the distributive property?

Back

The first step is to multiply the term outside the parentheses by each term inside the parentheses.

Front

What is an example of an expression that is not equivalent?

Back

The expressions 4 + (3 ⋅ y) and (4 + 3) ⋅ y are not equivalent because the first simplifies to 4 + 3y, while the second simplifies to 7y.

Front

How do you check if two expressions are equivalent?

Back

You can check by substituting the same value for the variables in both expressions and seeing if they yield the same result.