Because the coefficient 1 is implied, students will benefit from the teacher writing the coefficient 1 whenever it is implied to make it explicit. For example, 6y means 6 times whatever value the variable y has. So far we have: Well, I remember that the fastest way to find the area of a rectangle is to multiply the length by the width.

In our rectangle product, our partial products are 3x and The associative property is about grouping. How did the two x s get lost? How does the distributive property work? According to the order of operations, multiplication does come before addition so your observation is correct. How do you suggest we write the expression?

Is there another way to write that expression that may be a little simpler? Please identify which properties justify your thinking.

Because we usually write the numbers first. Yes, but remember - the commutative property only works for multiplication and addition. Remind students that the Associative Property moves the parentheses but does not change the position of the numbers.

What are you suggesting? First you multiply 3 by x, which is 3x. It is true that in algebra, when we write quantities right next to each other without any symbol in between, multiplication is implied. Students will benefit from a discussion of what the word equivalent means.

Show me what you mean. The algebra tiles show that there are 3 x s and 15 units. Like we usually write 3x, not x3. If you substitute a number in for x, like 2, you get 6 for both expressions.

The key words to remember are order for the Commutative Property and grouping for the Associate Property. Subtraction and division are not commutative. In mathematics we have a property that says that when you multiply, the order of the factors does not matter.

That means that both the x and the 5 get multiplied by 3. Because of the commutative property. I see 2 y s, another x, 4 ones, and 11 ones. So how can we use the associative property to find more equivalent expressions for the area of our rectangle?

When I add 50 and 10 together I get 60, which is the same result I get for 5 x 12 using any strategy. Is 3x equivalent to x3? I know that properties are somewhat like laws; they always work. Give me an example. So what you did was grouped the "like" terms. How can we rewrite the expression to make it accurate and show that the 3 needs to get distributed, or multiplied by both 5 and the x?

Vignette In the Classroom In this vignette, students use associative, commutative, and distributive properties to generate equivalent algebraic expressions for the area of a rectangle. The picture supports your idea. You get the same thing. But why does the distributive property work?In this problem we have to transform expressions using the commutative, associative, and distributive properties to decide which expressions are equivalent.

Common mistakes are addressed, such as not distributing the 2 correctly. Practice identifying equivalent expressions involving the addition and subtraction of negative numbers. Write an equivalent expression for n x a using only addition Get the answers you need, now!/5(18).

Practice determining whether or not two algebraic expressions are equivalent by manipulating the expressions. These problems require you to combine like terms and apply the distributive property. Practice: Equivalent expressions. Next tutorial. Interpreting linear expressions.

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Write an equivalent addition expression

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