Remind students that the Associative Property moves the parentheses but does not change the position of the numbers. Do you know what the Associative Property states?

The Commutative Property changes the positions of the numbers; Provide graphic organizers, such as those shown below, to help students understand the properties and how they are used to simplify numeric and algebraic expressions; Be sure to give students plenty of opportunity to use concrete materials and pictorial representations of algebraic expressions before moving to the symbolic.

According to the order of operations, multiplication does come before addition so your observation is correct. The algebra tiles show that there are 3 x s and 15 units.

To prove two expressions are equivalent, properties and theorems must be used. How do you suggest we write the expression?

Changes additions to multiplications. Remind students that in exponential notation, the base is a repeated factor, and does not indicate repeated addition. And how do you know?

Subtraction and division are not commutative. I have an idea. Is there another way to write the expression that may be a little less confusing. Is 3x equivalent to x3? In our rectangle product, our partial products are 3x and That means that both the x and the 5 get multiplied by 3. In the algebraic expression x5, the multiplication is implied.

Like we usually write 3x, not x3. You do have a point. Ask the student to demonstrate that two expressions [e. What would that be? Let me give you an example of the distributive property using numbers.

This provides an opportunity to show that the properties actually do act the same way with numbers and algebraic expressions. For example, 6y means 6 times whatever value the variable y has.

Examples of Student Work at this Level The student writes expressions that are not equivalent to the given expression. Then you add 3 times 5, or These students may benefit from discussion about how x is not usually used to represent multiplication in algebraic expressions to avoid confusion with the variable x, and that a dot is often used when a multiplication symbol is needed to prevent confusion.

So what you did was grouped the "like" terms.

It is true that in algebra, when we write quantities right next to each other without any symbol in between, multiplication is implied. Because of the commutative property.

You could add all the x s together and add all the 1 s together.Use the commutative law of addition to write an equivalent expression. 3) 9 + xy 4) 7a + 9b Use the commutative law of multiplication to write an equivalent expression.

5) uv 6) s + 8t Insert, or = to make the statement true. 7) -|-6| _____. Question use the commutative property of addition to write an equivalent expression to 7x+8y.

use the associative property of addition to write an equivalent expression to 3x+(5y+6) use the commutative property of multiplication to write an equivalent expression to (3a)(4b).

Commutative law of multiplication. Intro to commutative property of multiplication. Use the commutative law of addition-- let me underline that-- the commutative law of addition to write the expression 5 plus 8 plus 5 in a different way and then find the sum.

Now, this commutative law of addition sounds like a very fancy thing, but all it. Use the associate and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Use the communative law of multiplication to write an equivalent expression. x+3y Math prove that the cancellation law of multiplication is equivalent in a commutative ring to the assertion that the product of non-zero factors is not zero.

SOLUTION: Use the commutative law of multiplication to write an equivalent expression. 4(a + b) Algebra -> Customizable Word Problem Solvers -> Misc -> SOLUTION: Use the commutative law of multiplication to write an equivalent expression.

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