Math

QuestionFind the missing values in the area model for the expression 10(8w+10)10(8w + 10).

Studdy Solution

STEP 1

Assumptions1. We are given an area model. . The area model represents the expression 10(8w+10)10(8w+10).
3. The area model is a rectangle, and the area of a rectangle is given by the product of its length and width.

STEP 2

The expression 10(8w+10)10(8w+10) can be expanded using the distributive property of multiplication over addition. This property states that a(b+c)=ab+aca(b + c) = ab + ac.
10(8w+10)=108w+101010(8w+10) =10 \cdot8w +10 \cdot10

STEP 3

Now, we can calculate each term separately.
108w=80w10 \cdot8w =80w1010=10010 \cdot10 =100

STEP 4

So, the expanded form of the expression 10(8w+10)10(8w+10) is10(8w+10)=80w+10010(8w+10) =80w +100

STEP 5

In the area model, one dimension of the rectangle represents the variable part (80w) and the other dimension represents the constant part (100).

STEP 6

The area of the rectangle is the product of its length and width, which is equal to the expression 10(8w+10)10(8w+10).
Area=80w×100Area =80w \times100

STEP 7

So, the missing values in the area model are80w and100.

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