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. To simplify 4 • (-3) • 5, we can first use the commutative property of multiplication to rearrange the terms in any order. Next, we can use the associative property of multiplication to group the terms in pairs. This gives us (-3 • 4) • 5. Finally, we can use the distributive property to simplify (-3 • 4) to -12. So the expression simplifies to -12 • 5. The properties used are the commutative property of multiplication, the associative property of multiplication, and the distributive property.
2. To simplify (2.25 • 23) • 4, we can use the associative property of multiplication to group the terms in any way. Next, we can use the commutative property of multiplication to rearrange the terms. This gives us (23 • 2.25) • 4. Finally, we can multiply 23 and 2.25 to get 51.75. So the expression simplifies to 51.75 • 4. The properties used are the associative property of multiplication and the commutative property of multiplication.
3. This expression is already simplified.
4. To simplify 5 • 12 • (-2), we can use the associative property of multiplication to group the terms in any way. Next, we can multiply 5 and 12 to get 60. Finally, we can multiply 60 and -2 to get -120. So the expression simplifies to -120. The property used is the associative property of multiplication.
5. To simplify 35(26)(0), we can use the zero property of multiplication, which states that any number multiplied by 0 is 0. So the expression simplifies to 0. The property used is the zero property of multiplication.