What you need to do
In these exercises, your goal is to name the algebraic property that explains each step of an expression or equation. You are not just simplifying; you are showing why a step is valid.
Common properties to look for
- Commutative property: terms can switch order in addition or multiplication.
- Associative property: grouping can change in addition or multiplication.
- Distributive property: a factor multiplies each term inside parentheses.
- Identity property: adding 0 or multiplying by 1 keeps the value the same.
- Inverse property: a number and its opposite, or reciprocal, combine to give the identity.
A good method
- Look at what changed from one line to the next.
- Ask: did the order change, the grouping change, or was something expanded or factored?
- Match the change to the correct property.
- If the work continues to a final simplified result, simplify carefully after identifying the properties.
Check your answer
Make sure the property you name really matches the exact step. If two steps are similar, identify the one that best explains the change. A quick check is to verify that both sides still have the same value after the transformation.
Tip
When possible, use precise names such as “commutative property of addition” or “distributive property,” rather than a vague description.