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.

Question

4/5x5/4x-3

Answer 1

To simplify the expression 4/5 * 5/4 * -3, we can use the properties of equality to cancel out common factors and simplify the calculation.

First, let's rewrite the expression:

(4/5) * (5/4) * (-3)

Now, let's identify and describe the properties used to simplify the expression:

1. Commutative property of multiplication: This property allows us to rearrange the order of the factors without changing the product.
- We can rearrange the expression as: (5/4) * (4/5) * (-3).

2. Multiplicative inverse property: The multiplicative inverse of a number is its reciprocal (when multiplied by its reciprocal, the product is 1).
- We can rewrite the expression as: (5/4) * (4/5) * (-3/1).

3. Identity property of multiplication: Multiplying any number by 1 does not change its value.
- We can simplify further: (5/4) * (4/5) * (-3/1) = (1 * 1 * -3) / (1 * 1) = -3.

Applying these properties, we can simplify the expression 4/5 * 5/4 * -3 to just -3.