# Use distributive property to write an equivalent variable expression

Be sure the student understands that the Distributive Property applies to subtractions as well since any subtraction can be rewritten as an addition. I wish this program was around when I was in college. What is another strategy for finding perimeter of a rectangle. Remind students that the Associative Property moves the parentheses but does not change the position of the numbers.

One way to verify that two expressions are equivalent, is to simplify each expression. Remind students that in exponential notation, the base is a repeated factor, and does not indicate repeated addition.

Indicates he or she does not know. She worked 4 hours on Friday and 6 hours on Saturday. In the first expression you multiply 3 times 2, and in the second expression you multiply 2 times three.

For example, 6y means 6 times whatever value the variable y has. Finally, students put their conclusions to work by expanding and evaluating 4 more expressions.

Then take the sum of those two products. Use this connection to help students see the base as a repeated factor, with the exponent telling how many times the base is repeated. A quality student answer will be something like this: When we simplify an algebraic expression using properties, we can compare the original expression with the simplified expression to make sure they are equivalent.

Divides one of the terms, 16, by 4. Be sure the student understands that a demonstration that two expressions are equivalent for a variety of values does not constitute a proof that they are equivalent. Next I will present the area model. But are those two expressions equivalent. The last two problems involve 3 addends in parenthesis. Well, I remember that the fastest way to find the area of a rectangle is to multiply the length by the width. Are there like terms in this expression. If needed, I will make up another similar problem using the area model. Use Parentheses, Brackets and Braces in Numerical Expressions By datewhen given 10 numerical expressions with parentheses, brackets, and braces, name will correctly evaluate each expression by using the order Can we simplify this expression.

It's because you only multiplied the 5 by 3, and didn't multiply the x by 3. What would that be. Subtraction and division are not commutative. According to the order of operations, multiplication does come before addition so your observation is correct.

If you change the order of the numbers when performing those operations you'll get different answers. In our language we often simplify expressions. 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.

Students' previous experiences with exponents has most likely been connected to place value using base 10; e. I know that properties are somewhat like laws; they always work. The key words to remember are order for the Commutative Property and grouping for the Associate Property.

How are you doing. This step is especially important when negative signs are involved, because they can be a tad tricky. The distributive property lets you "distribute," or multiply a number over each addend of a sum and then add the products.

That means that both the x and the 5 get multiplied by 3. It's the commutative property. It is important for students to see that either method gives us the same simplified expression. As students are working on these, I will be watching to make sure values are being expanded correctly. The key words to remember are order for the Commutative Property and grouping for the Associate Property.

The associative property is about grouping. Guide the student to use the Distributive Property to rewrite expressions such as 7m + (7 x 3) as 7(m + 3). Describe this process as factoring since the expression is being rewritten as a product of the factors 7 and (m + 3).

Explain the usefulness of factoring by guiding the student through problem #2. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y +. SOLUTION: Use the distributive property to write an equivalent variable expression. Algebra -> Distributive-associative-commutative-properties-> SOLUTION: Use the distributive property to write an equivalent variable expression.2(z + 8) Log On.

Choose 3 expression from the blue box that have the same value as expressions 1, 2, and 3 shown in the pink box. 7(4+2) = (7 x 4) + (7 x 2) = 7 x 6 Together we will discover ways to show or Model. Solutions to the Above Questions. Solution Like terms have the same variable raised to the same power.

Hence. in the expression 7 x - 5 x + 6 + 3 x 7 x, - 5 x and 3 x are like terms The coefficients of the like terms 7 x, - 5 x and 3 x are 7, - 5 and 3 respectively. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Use distributive property to write an equivalent variable expression
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