Question

Create a model for each expression below. Then, write another equivalent expression using the distributive property.

Answer 1

Answer and  explanation:

To find : Create a model for each expression below. Then, write another equivalent expression using the distributive property ?

Solution :  

1) $3(x+y)$

Step 1 - First we create a model of x+y.

Ste 2 - The expression 3(x+y) tells us that we have 3 of the (x+y)’s.

Create a model that shows 3 groups of (x+y).

Step 3 - Count x’s and y’s,

3x's and 3y's.

Step 4 - We grouped together the x’s, and then grouped together the y's.

Step 5 - Write the expression as

$3(x+y)=3x+3y$

Refer the attached figure below.

2) $4(2h+g)$

Step 1 - First we create a model of 2h+g.

Ste 2 - The expression 4(2h+g) tells us that we have 4 of the (2h+g)’s.

Create a model that shows 4 groups of (2h+g).

Step 3 - Count 2h’s and g’s,

4(2h)'s and 4(g)'s.

Step 4 - We grouped together the 2h’s, and then grouped together the g's.

Step 5 - Write the expression as

$4(2h+g)=8g+4g$

Refer the attached figure below.