Apply the Properties of Operations to Generate Equivalent Expressions: CCSS.Math.Content.6.EE.A.3 - 6th Grade Math

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Question

Expand:

Answer

Distribute the by multiplying it by each term inside the parentheses.

$5\cdot 2=10$

and

$5\cdot y=5y$

Therefore, 5(2 + y) = 10 + 5y.

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Question

Which of the following is equivalent to ?

Answer

We need to distribute -3 by multiplying both terms inside the parentheses by -3.:

.

Now we can multiply and simplify. Remember that multiplying two negative numbers results in a positive number:

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Question

Distribute:

Answer

Remember that a negative multiplied by a negative is positive, and a negative multiplied by a positive is negative.

Distribute the through the parentheses by multiplying it by each of the two terms:

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Question

Simplify the expression:

Answer

To solve this question you must use the distrubitive property by multiplying x by -2 and the 2 by -2, making sure to distribute the negative as well. This gives you:

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Question

Which answer correctly simplifies this expression?

Answer

To simplify this expression, use the distributive property. This means that we have to multiply the 2 times both terms inside the parentheses. , and . So, our answer is .

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Question

Simplify the following expression:

Answer

Apply the distributive property of multiplication to remove the parenthesis from the given expression. Multiply the term outside of the parenthesis to each of the terms inside the parenthesis.

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Question

Simplify the following expression using the distributive property.

Answer

Distributive property is used to multiply a single term by two or more terms inside a set of parenthesis. Multiply the outside term (5) by 7 first.

$5\times7x=35x$

Then multiply the outside term (5) by 9.

$5\times9=45$

Combine the two remaining terms by keeping the sign that was originally inside the parenthesis.

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Question

Solve the equation using the distributive property.

Answer

First, we must use the distributive property on both sides of the equation.

The distributive property states:

Therefore:

Now, we can solve the expression like a two-step equation with variables on both sides. Do not forget the properties of equality and perform the same operations on both sides.

Subtract from both sides.

${\color{Red} -2q }$ ${\color{Red} -2q}$

Simplify.

Now, the problem is a one-step equation.

Add to both sides.

${\color{Red} + 15}$ ${\color{Red} + 15}$

Solve.

Check the answer by substituting it back into the original equation. Both sides should equal to each other.

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Question

Name the property used to solve the problem.

Answer

Multiplying each term on the outside of the parenthesis by each term on the inside refers to the distributive property.

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Question

Simplify using the distributive property:

Answer

First, we must use the distributive property on both sides of the equation.

The distributive property states:

In other words, we can take the factor on the outside of the parentheses and multiply it by each term inside the parentheses.

Therefore:

$2(x - 4)=(2 \times x) + (2 \times -4)$

$(2 \times x) + (2 \times -4)=2x + -8$

Simplify.

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Question

Simplify the following:

Answer

This is applying to distrubtive property and then combining like terms.

First you distrubute the negative to the two terms in the first parentheses, so:

Then do the same for the four:

Finally, combine like terms to get:

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$4\times2=8$

$4\times x=4x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$2\times7=14$

$2\times x=2x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$3\times6=18$

$3\times x=3x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$1\times5=5$

$1\times x=x$

Now we have

This expression is simplified because we cannot add to because we cannot add a number to a variable.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$5\times2=10$

$5\times x=5x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$6\times7=42$

$6\times x=6x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$7\times3=21$

$7\times x=7x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$8\times4=32$

$8\times x=8x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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Question

Select the expression that is equal to

Answer

To solve this problem we need to use the distributive property. This property is used to multiply a term outside of a set of parentheses by each of the terms in the parentheses.

$9\times5=45$

$9\times x=9x$

Now we have

This expression is simplified because we cannot add to because has a variable attached to it.

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