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.
4/5x5/4x-3
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.