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When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?Original Equation:First Step:subtraction property of equalityassociative property of multiplicationassociative property of additionaddition property of equality
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Q. When solving an equation, Francesca's first step is shown below. Which property justifies Francesca's first step?Original Equation:First Step:subtraction property of equalityassociative property of multiplicationassociative property of additionaddition property of equality
- Identify Change Nature: To determine which property of addition is used, we need to look at the nature of the change made to the equation. The original equation has a sum within a sum, and Francesca's first step involves changing the grouping of the numbers that are being added. This is a key characteristic of the associative property of addition, which states that the way in which numbers are grouped in an addition problem does not change the sum.
- Associative Property Explanation: The associative property of addition allows us to change the grouping of the terms in an addition expression. In the context of the equation, it means that is equivalent to , and both expressions will yield the same result when simplified.
- Other Options Explanation: The other options provided are not applicable to this situation:- The subtraction property of equality is used when subtracting the same value from both sides of an equation.- The associative property of multiplication is similar to the associative property of addition but applies to multiplication.- The addition property of equality is used when adding the same value to both sides of an equation.
