Exploring Properties of Real Numbers in Algebraic Proofs

Why is it important to rigorously justify the steps in simplifying an algebraic expression?

• To confuse the students

• To make the process faster

• To ensure the simplification is correct

• To avoid using properties of real numbers

What is the purpose of a two-column proof?

• To skip steps in the solution

• To list all possible solutions

• To show the steps and reasons for each step in a logical manner

• To confuse the reader

What property justifies that 7 times 5/8 is the same as 5/8 times 7?

• Commutative property of multiplication

• Associative property of addition

• Distributive property

• Identity property of multiplication

What does the associative property of multiplication allow you to do?

• Subtract numbers

• Add numbers together

• Change the order of numbers

• Change the grouping of numbers

How is subtraction defined in terms of addition?

• Subtracting is the same as multiplying by zero

• Subtracting is the same as adding the same number

• Subtracting is the same as dividing by one

• Subtracting is the same as adding the opposite

What does the inverse property of multiplication state?

• Multiplying a number by its reciprocal gives one

• Multiplying by two gives double the number

• Multiplying by one gives the same number

• Multiplying by zero gives zero

What is the identity property of multiplication?

• Multiplying by two gives double the number

• Multiplying by one gives the same number

• Multiplying by negative one gives the opposite number

• Multiplying by zero gives zero

How can the commutative property of addition be used to simplify expressions?

• By changing the order of the numbers being added

• By changing the grouping of the numbers being added

• By multiplying the numbers

• By dividing the numbers

What does the closure property of addition state?

• The sum of two real numbers is always zero

• The sum of two real numbers is always a fraction

• The sum of two real numbers is always an integer

• The sum of two real numbers is always a real number

How is the expression 10X + (-2) simplified to 10X - 2?

• By using the commutative property

• By using the associative property

• By using the definition of subtraction

• By using the closure property