Which property is illustrated by the equation (a b) c=c (a b)

Both statements are true in part because of the order of operations. Interested in mathematical properties? Check out some other cool properties, like the reflexive , symmetric , and transitive properties! Both of these properties state this. Thus the goal is usually to choose an order that is easier. It may take some practice to recognize which order is the easiest.

We can multiply the smaller numbers together first. We could also multiply the two negative numbers together first. 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. The answer looks like this:. The only fiddly part was moving the " — 5 b " from the middle of the expression in the first line of my working above to the end of the expression in the second line.

Just don't lose that minus sign! I'll do the exact same steps I've always done. The only difference now is that I'll be writing down the reasons for each step. Page 1 Page 2. All right reserved. Web Design by. Skip to main content. Purplemath There are three basic properties of numbers, and your textbook will probably have just a little section on these properties, somewhere near the beginning of the course, and then you'll probably never see them again until the beginning of the next course.

What does the distributive property signify? What is the distributive property of 15 21? What is the distributive property of 9 15? What is the distributive property of 35 14? What is the distributive property of 35 50? What is the distributive property of 24 36? What is the distributive property of 55 35? How do you use the distributive property to express 24 40? Substitute for x.

Use the associative property of multiplication to regroup the factors so that 4 and are next to each other. Multiplying 4 by first makes the expression a bit easier to evaluate than multiplying by Answer when.

Identify compatible numbers. Use the commutative property of addition to group them together. Add the rest of the terms. When you use the commutative property to rearrange the addends, make sure that negative addends carry their negative signs. 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?