Use properties of equality to simplify each of the following expressions so that you can simplify them in your head. Identify the properties used and describe how you used them.
1. 4 • (–3) • 5
2. (2.25 • 23) • 4
3.
4. 5 • 12 • (–2)
5. 35(26)(0)
1. 4 • (–3) • 5 = -12 • 5 = -60
Properties used: Multiplicative Property of Integers (product of two negative numbers is positive)
2. (2.25 • 23) • 4 = 51.75 • 4 = 207
Properties used: Associative Property of Multiplication (changing the grouping of factors does not change the product)
3. (4 + 8) • (3 – 2) = 12 • 1 = 12
Properties used: Distributive Property of Multiplication over Addition (a(b + c) = ab + ac)
4. 5 • 12 • (–2) = 60 • (–2) = -120
Properties used: Associative Property of Multiplication (changing the grouping of factors does not change the product)
5. 35(26)(0) = 0
Properties used: Zero Property of Multiplication (any number multiplied by 0 equals 0)