Math  /  Algebra

QuestionAnswer the questions below about Line 1 and Line 2 shown below. (8+7)+38+(7+3)\begin{array}{l} (8+7)+3 \\ 8+(7+3) \end{array}
Line 1
Line 2
Answer Attempt 1 out of 2
The expression was rewritten using the \square (8+7)+3(8+7)+3 equals \square +3 which equals \square . 8+(7+3)8+(7+3) equals 8+8+ \qquad which equals \square .

Studdy Solution

STEP 1

1. We are given two expressions: Line 1: (8+7)+3(8+7)+3 and Line 2: 8+(7+3)8+(7+3).
2. The task is to identify the property used to rewrite the expressions and complete the calculations.

STEP 2

1. Identify the mathematical property used.
2. Rewrite the expressions using the identified property.
3. Calculate the values of the expressions.

STEP 3

The expressions (8+7)+3(8+7)+3 and 8+(7+3)8+(7+3) are examples of the associative property of addition. This property states that the way in which numbers are grouped in addition does not affect the sum.

STEP 4

Using the associative property, rewrite the expressions: - Line 1: (8+7)+3(8+7)+3 can be rewritten as 8+(7+3)8+(7+3). - Line 2: 8+(7+3)8+(7+3) can be rewritten as (8+7)+3(8+7)+3.

STEP 5

Calculate the values of the expressions: - For Line 1: (8+7)+3=15+3=18(8+7)+3 = 15+3 = 18. - For Line 2: 8+(7+3)=8+10=188+(7+3) = 8+10 = 18.
The expression was rewritten using the associative property of addition. (8+7)+3(8+7)+3 equals 15+315+3 which equals 1818. 8+(7+3)8+(7+3) equals 8+108+10 which equals 1818.

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