Match each equation to the property it represents.6(9−2)=6(9)−6(2)
Equation: 6(9−2)=6(9)−6(2)
Property: Distributive Property
Equation: 6(9−2)=6(9)−6(2)
Property: Distributive Property
Explanation: The equation demonstrates the distributive property, which states that multiplying a number by the sum of two numbers is the same as multiplying the number by each of the two numbers and then adding the products. In this case, the left side of the equation shows the distributive property by multiplying 6 by the difference of 9 and 2, while the right side of the equation illustrates the distributive property by multiplying 6 by 9 and by 2 separately and then subtracting the results.
To match each equation to the property it represents, let's examine the given equations:
1. 6(9−2) = 6(9) − 6(2)
The distributive property states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results. In this case, we can distribute the 6 to both terms inside the parentheses:
6 * 9 − 6 * 2 = 54 − 12
Simplifying further, we get:
54 − 12 = 42
So, the equation 6(9−2) = 6(9) − 6(2) demonstrates the distributive property.