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

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

How do you simplify the expression: 30 ÷ (3 + x)?

Back

The expression simplifies to 30 ÷ (3 + x), which cannot be simplified further without specific values for x.

Front

What is an equivalent expression for 30 ÷ (3 + x)?

Back

30 ÷ (3 + x) is equivalent to (3 + x) ÷ 30.

Front

What is the result of the expression: 84 + 21 - 3?

Back

The result is 102.

Front

What is the difference between addition and subtraction in an expression?

Back

Addition combines values, while subtraction removes a value from another.

Front

Which expressions are equivalent: 12 - (y ⋅ 2) and 12 - (2 ⋅ y)?

Back

Yes, both expressions are equivalent because multiplication is commutative.

Front

What is the purpose of using parentheses in mathematical expressions?

Back

Parentheses indicate which operations should be performed first in an expression.

Front

How do you evaluate the expression: 9(6 + x)?

Back

You distribute 9 to both terms inside the parentheses: 9 * 6 + 9 * x = 54 + 9x.