Tell which property is illustrated by the statement

This is one of those times when it's best to be flexible. In the latter case, it's easy to see that the Distributive Property applies, because you're still adding; you're just adding a negative. The other two properties come in two versions each: one for addition and the other for multiplication. Yes, the Distributive Property refers to both addition and multiplication, too, but it refers to both of the operations within just the one rule.

The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. They want me to regroup things, not simplify things.

In other words, they do not want me to say " 6 x ". They want to see me do the following regrouping:. In this case, they do want me to simplify, but I have to say why it's okay to do Here's how this works:. Since all they did was regroup things, this is true by the Associative Property.

The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.

Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property. They want me to move stuff around, not simplify. In other words, my answer should not be " 12 x "; the answer instead can be any two of the following:.

Since all they did was move stuff around they didn't regroup , this statement is true by the Commutative Property. I'm going to do the exact same algebra I've always done, but now I have to give the name of the property that says its okay for me to take each step. Does anyone know all the answers or does it change the questions around so theres no cheating Decreasing linear 21 A. Yes;8 24 D.

No,y doesn't vary directly with x 26 A. Neither 34 C. Graph point at -2 36 A. Infinitely many 38 C. Graph shades to right of. Positive correlation 45 A. I can't be confident at all, this is about as close to a random guess you can get. Use to check You pick and choose! Good luck. Hu the answers are correct. My Answers were Associative Property of Addition 2.

Rational Numbers 3. Open Circle: -7 Left The correct answer is Use the commutative property to rearrange the expression so that compatible numbers are next to each other, and then use the associative property to group them. Check your addition and subtraction, and think about the order in which you are adding these numbers. Use the commutative property to rearrange the addends so that compatible numbers are next to each other. It looks like you ignored the negative signs here.

The Distributive Property. The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference.

The property states that the product of a sum or difference, such as 6 5 — 2 , is equal to the sum or difference of products, in this case, 6 5 — 6 2. The distributive property of multiplication can be used when you multiply a number by a sum. Alternatively, you can first multiply each addend by the 3 this is called distributing the 3 , and then you can add the products.

This process is shown here. The products are the same. Since multiplication is commutative, you can use the distributive property regardless of the order of the factors. The Distributive Properties. For any real numbers a , b , and c :.

Rewrite the expression 10 9 — 6 using the distributive property. The correct answer is 10 9 — 10 6. This is a correct way to find the answer.

But the question asked you to rewrite the problem using the distributive property. You changed the order of the 6 and the 9. Note that subtraction is not commutative and you did not use the distributive property. The 10 is correctly distributed so that it is used to multiply the 9 and the 6 separately. Distributing with Variables. As long as variables represent real numbers, the distributive property can be used with variables.

The distributive property is important in algebra, and you will often see expressions like this: 3 x — 5. If you are asked to expand this expression, you can apply the distributive property just as you would if you were working with integers.

Remember, when you multiply a number and a variable, you can just write them side by side to express the multiplied quantity.

Distribute the 9 and multiply. Substitute 2 for x , and evaluate. Would you get the same answer of 5? The example below shows what would happen. Substitute 2 for x. Combining Like Terms. The distributive property can also help you understand a fundamental idea in algebra: that quantities such as 3 x and 12 x can be added and subtracted in the same way as the numbers 3 and Combine the terms within the parentheses:. Do you see what happened?

The table below shows some different groups of like terms:. Groups of Like Terms. Whenever you see like terms in an algebraic expression or equation, you can add or subtract them just like you would add or subtract real numbers.

So, for example,. There are like terms in this expression, since they all consist of a coefficient multiplied by the variable x or y. Add like terms. It looks like you added all of the terms. The correct answer is 5 x. You combined the integers correctly, but remember to include the variable too!

When you combine these like terms, you end up with a sum of 5 x. It looks like you subtracted all of the terms from 12 x. The commutative, associative, and distributive properties help you rewrite a complicated algebraic expression into one that is easier to deal with.

When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied. When you rewrite an expression using an associative property, you group a different pair of numbers together using parentheses.