what is the difference between the commutative distributive and associative properties when multiplying?

Answers

Answer 1
The associative rule is a rule about when it's safe to move parentheses around. You can remember that because the parentheses determine which expressions you have to do first--which numbers can associate with each other. It looks like this:

For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)

The commutative property is about which operations you can do backward and forward. You can remember this by thinking of people commuting to work: they go to work every morning, then they repeat the same operation backward when they commute home. It looks like this:

For addition: a + b = b + a
For multiplication: ab = ba

Finally, the distributive property tells you what happens when you distribute one operation against another kind in parentheses. It looks like this:

a * (b + c) = ab + ac

In other words, the a is "distributed" over the b and c.

Of course, you can make these work together:

a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).

Hope this helps.
Answer 2
Commutative Property. The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2.

Related Questions

Solve 14n+q=rt-4n for n

Answers

Hey there!

In order to solve this, all you need to do is cancel out terms until you have n on one side of the equal sign and everything else on the other side. 

14n + q = rt – 4n (add 4n to both sides to combine 4n and 14n)
18n + q = rt (subtract q from both sides)
18n = rt – q (divide both sides by 18)
n = (rt – q) ÷ 18

Hope this helped you out! :-)

The solution for n is [tex]\( n = \frac{{q - rt}}{{10}} \)[/tex].

To solve for n in the equation -14n + q = rt - 4n, we need to isolate n on one side of the equation.

First, let's gather all terms involving n on one side. Adding 4n to both sides of the equation, we get:

-14n + 4n + q = rt

Simplifying the left side, we have:

-14 + 4)n + q = rt

-10n + q = rt

Next, let's isolate n by moving the term q to the other side. Subtracting q from both sides, we have:

-10n = rt - q

Finally, to solve for n, divide both sides by -10:

[tex]\[ n = \frac{{rt - q}}{{-10}} \][/tex]

So, the solution for n is [tex]n = \frac{{q - rt}}{{10}} \)[/tex].

Which option below correctly describes the domain of and explains why the range of b is not all real numbers?

Answers

what are the options?^

How do you work out 49.2 x 10.3

Answers

Final answer:

To work out 49.2 x 10.3, you multiply the two numbers together.

Explanation:

To work out 49.2 x 10.3, you multiply the two numbers together.

Step 1: Multiply the whole numbers: 49 x 10 = 490

Step 2: Multiply the decimals: 0.2 x 0.3 = 0.06

Step 3: Add the results from step 1 and step 2: 490 + 0.06 = 490.06

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3(n - 1) = 5n + 3 - 2n

Answers

3(n - 1) = 5n + 3 - 2n
3n - 3 = 3n + 3
3n - 3n = 3 + 3
0 = 3 ...(incorrect)
This equation has no solution

the percent of increase is 16% if the new number is 522 find the original number

Answers

The original number is 438.48. Hope this helps!

Calculate the future value of an investment of $2300, after 7 months, earning 6.6% APR, compounded monthly, by compounding manually.

Answers

The future value of an investment, P after n years at an APR of r% compounded t times a year is given by
[tex]FV=P\left(1+ \frac{r}{t} \right)^{nt}[/tex]

Given an investment of $2300, after 7 months, earning 6.6% APR, compounded monthly, the future value is given by
[tex]FV=2,300\left(1+ \frac{0.066}{12} \right)^{12\left( \frac{7}{12}\right) } \\ \\ =2,300(1+0.0055)^7=2,300(1.0055)^7 \\ \\ =2,300\times1.03914=\$2,390.02[/tex]

0.39/0.75 as a decimal

Answers

If you are asking for .39 to be divided by .75 the answer is .52

A carpet costs $15 per square foot. If the area you want to carpet is 19.7 square meters, how much will it cost to buy the carpet?

Answers

$ 295 because you can multiple 15×19.7 is =295.5

The day this lesson was written, the world population was 6,672,678,672. The population of the United States was 304,276,585. What is the population on the day you read this? Put “world population clock” into your search engine and see for yourself.

PS: I've already done it, the population as of 13 of September is 7,532,064,512

Write down the current date and the current world population. Use a calculator to figure out what percentage it has increased since the day this lesson was written. Use this formula:(current population - former population) / former population) x 100.

Answers

7,532,073,340 as of 9/13/17 at 7:18amest.

7532073340-6672678672=859394668/66726786720.12878*100 = 12.88%

Hemal wanted to make dessert for her family. The recipe made 8 servings, but she only wanted to make enough for 5 people. If the recipe for 8 servings called for 2 cups of flour, how much flour would she need for 5 servings?

Answers

If 8 servings called for 2 cups. 4 servings calls for 1 cup. Then you would need one more serving of 1/4. 
So the answers is: You would need 1 and 1/4 cups of water for 5 servings.

A credit card states that your payment will be a minimum of $15 plus 1% of your unpaid balance. Your unpaid balance is $2,365.What is your payment this month?

Answers

Alright, to get 1% of his unpaid balance, we can make 1% = 0.01 by moving the decimal place 2 places over. Multiplying 0.01 by 2365 gets 1% of your unpaid balance=23.65. Since we have to add 15 as a base value, we have 
15+23.65=38.65

The soccer field at Mario's school has a area of 6,000 square miles.How can Mario show the area as a whole number multiplied by a power of ten

Answers

Well, there is multiple ways like:
600 x 10^1
60 x 10^2
6 x 10^3
.6 x ^4

Write each fraction in simplest form

Answers

9/18 simplified would be 1/2
29. = 1/2 in simplest form. Hope I helped

whats the soultion for 10000 ft/hr = mi/hr

Answers

Hi! There are 5,280 feet in a mile. Therefore, you need to divide 10,000 feet by 5,280 (to see how many miles there are per every 5280 feet) and you get 1.89 miles per hour.

Six rectangles have a area of 64 square units what is the perimeter

Answers

Solution:1. A= 64m^2, l = 12 mA = wl Solving for PP=2 l+2(A/ l) = 2·12+2·64/12 ≈ 34.66667 m
Solution:2. A= 64m^2, l = 4 mA = wl Solving for PP=2 l+2 (A/ l) = 2·4+2·64/4 ≈ 40 m
Solution:3. A= 64m^2, l = 24 mA = w l Solving for PP=2 l+2 (A/ l) = 2·24+2·64/24 ≈ 53.33333 m
Solution:4. A= 64m^2, l = 16 mA = w l Solving for PP=2 l+2 (A/ l) = 2·16+2·64/16 ≈ 40 m Solution:5. A= 64m^2, l = 8 mA = w l Solving for PP=2 l+2 (A/ l) = 2·8+2·64/8 ≈ 32 m 
Solution:6. A= 64m^2, l = 32 mA = w l Solving for PP=2 l+2 (A/ l) = 2·32+2·64/32 ≈ 68 m

Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. There are 15 questions on the test, and students are given 51 minutes to take it.

The system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.

m + f = 15

3m + 5f = 51

How many multiple-choice questions are on the test?

Answers

m + f = 15....multiply by -5
3m + 5f = 51
-----------------
-5m - 5f = - 75 (result of multiplying by -5)
3m + 5f = 51
----------------add
-2m = - 24
m = -24/-2
m = 12 <=== 12 multiple choice questions

There are 12 number of multiple-choice questions are on the test.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

Given that m, and the number of free-response questions, f, on the test.

m + f = 15.

Then multiply by -5

3m + 5f = 51

-----------------

-5m - 5f = - 75

3m + 5f = 51

Now add

-2m = - 24

m = -24/-2

m = 12

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While trying to explain a physics concept, a student said, "Stuff keeps doing what it's doing unless something messes with it." What law was the student summarizing? Explain your answer.
Your answer

When a soccer player kicks a ball, the ball accelerates. Explain what causes this acceleration in terms of forces.
Your answer

Describe three examples from sports in which a force changes the velocity of an object or a person.
Your answer

Explain which has greater inertia; a speeding car or a jet airplane sitting on the runway.
Your answer

Do forces always cause motion, explain?
Your answer

Answers

1) Newton's first law of motion
2)The soccer ball accelerates because of the force the soccer player exerts on the ball.
4)Inertia is the act of not doing anything. Therefore, the jet airplane sitting on a runway has the greatest inertia because it is literally doing nothing.
5)Forces DO NOT always cause motion. friction is a force that goes against a motion, this is a resistant force. 

Sorry but I wouldn't want to inaccurately answer #3, so I didn't do it.

Answer:

Step-by-step explanation:

1. Newton's first law of motion: Also called the law of inertia, states that "An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force"

2. According to Newton's second law "the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a)", meaning that when the soccer player kicks a ball, a force is acting on the ball, therefore increasing it's acceleration. After the force is applied, the gravity and the resistance of air will be the ones in charge of stopping the ball.

3. a) Baseball: The ball changes direction and speed when it's hit with the bat.

b) Bowling: When the ball hits the pins, the change from being at rest to a higher velocity.

c) Wrestling: The wrestler exerts a force on the oponent increasing or decreasing it's velocity.

4. The jet airplane has more inertia. Inertia is the resistance of an object to move if at rest, or to change its velocity and it is proportional to the mass of the object. Therefore, the jet airplane being heavier than the car will have more inertia. It has to be clear that it is not due to the fact that is at rest that is the one with more inertia, but mostly related to the mass. If the example was with two cars, one at constant velocity and the other at rest, both with the same mass, the one with greater inertia will be the one moving.

5. No, forces do not always cause motion. They have to be greater than the forces that oppose movement, such as friction, air resistance or gravity.

Write two expressions where the solution is 4

Answers

16 divided by 4 = 4

7 + 3 - 6 = 4

or

40 divided by 5 - 4 = 4

Answer:

[tex]2+2=4[/tex]

[tex]\frac{8}{2}=4[/tex]

Step-by-step explanation:

We are asked to write two expressions where the solution is 4.

We can write infinitely many solutions whose solution is 4. Some of the expressions are as follows:

[tex]3+1=4[/tex]

[tex]2+2=4[/tex]

[tex]\frac{8}{2}=4[/tex]

[tex]\frac{16}{4}=4[/tex]

[tex]8-4=4[/tex]

[tex]6-2=4[/tex]

[tex]2\cdot 2=4[/tex]

Therefore, all of these expressions satisfy the given condition.

Frank is building a table. He needs 4 pieces of wood for the table legs. Each piece of wood needs to be 7/8 of a foot long. What is the total amount of wood he needs for the legs?
A. 3 1/2 feet
B. 3 2/5 feet
C. 4 4/7 feet
D. 4 7/8 feet

Answers

Final answer:

The correct option is (A) 3 1/2 feet. To find the total amount of wood Frank needs for the table legs, multiply the length of one leg (7/8 foot) by 4, the number of legs, resulting in 3 1/2 feet of wood in total.

Explanation:

Frank needs four pieces of wood, each 7/8 of a foot long for the table legs. To find the total amount of wood required, we multiply the length of one piece by the number of pieces:

Multiply the length of one leg, 7/8 foot, by the number of legs, which is 4.
(7/8) foot x 4 = (7/8) x 4/1 = 28/8 = 3.5 feet

Therefore, Frank needs 3 1/2 feet of wood in total for the table legs.

What is the prime factorization of 375

Answers

Answer:

See the image for the answer.

Solve the equation, justify each step with an algebraic property
-7=-1+ x/3

Answers

-7=-1+x/3
-7+1=-1+x/3+1 Additive property of equality
-6=x/3 Combine Like Terms
-6(3)=x/3(3) Multiplicative property of equality
-18=x           Distribution

Hope this helped!
Final answer:

The solution to the equation -7=-1+ x/3 is obtained by adding 1 to both sides, then multiplying both sides by 3 to solve for x. This yields x = -18.

Explanation:

To solve the equation -7=-1+ x/3, we can first isolate the x term using the addition and multiplication properties of equality.

First, add 1 to both sides to cancel out -1 from the right side of the equation. This gives us -6= x/3. Then, multiply both sides by 3 to solve for x. This gives us -18=x.

Hence, the solution to the equation -7=-1+ x/3 is x=-18.

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200 divided by 19.30 to the nearest 10th

Answers

19.30 to the nearest tenth is 20   20/200 = 10?

multiple of pi plis xxx

Answers

 [tex] \pi [/tex] is an irrational number i.e. it cannot be written in the form of [tex] \frac{p}{q} [/tex] where p and q are integers and q is never equal to 0.

By multiples of [tex] \pi [/tex], we can write like:

1[tex] \pi [/tex] = [tex] \pi [/tex] = 3.14
2[tex] \pi [/tex] = 2*3.14 = 6.28
3[tex] \pi [/tex] = 3*3.14 = 9.42
In the same way, any integer n when multiplied by [tex] \pi [/tex], is a multiple of [tex] \pi [/tex]

Why is it important to have complex carbohydrates before a big race?

(Again, not math. I know, its to get the answer faster..)

Answers

Complex Carbs are very useful because they are healthy and do not interfere with a race. They turn those into glucose and helps the energy be saved longer. 
Complex Carbohydrates are made up of sugar molecules strung together in long chains. Both simple and complex carbs can be turned into Glucose which is used as short term energy. This short term energy is great for short races, for marathons I suggest more lipids as well. The act of eating a lot of carbs the night before a race is called "Carb Loading" 

Does the Commutative Property of Addition apply when you add two negative integer?

Answers

Yes because whether you flip two negative integers around, the answer would still remain the same since its addition.

For example:
-9+-3 = -12 = -3+-9
Yes
Hopefully this helps

A warehouse floor has a perimeter of 6,615 feet. What is the perimeter of the floor in yards ? oh and please tell me how you got the answer

Answers

Since there are 3 feet in 1 yard you need to divide 6,615 divided by 3 which equals 2205 yards.
1 Yard = 3 feet
or 3 feet = 1 yard

to convert 6615 feet into yard, you have to divide it by 3.

6615 feet = 6615/3 yard = 2205 yard.

Your answer is 2205 yards.

Hope it helps!

A relay race is 1/10 kilometer long. Four athletes will run an equal distance to complete the relay. How far does each athlete run ?

Answers

25 metres. Because 1/10th of a kilometre is a 100 metres. And four athletes divided by 100 metres is 25 metres.

Answer:

25 meters.

Step-by-step explanation:

Let us suppose each athlete run x km.

Hence, four athlete will run 4x km.

Now, the distance of the relay race is 1/10 km

Thus, we have

[tex]4x=\frac{1}{10}[/tex]

Divide both sides by 4

[tex]x=\frac{1}{40}km[/tex]

Now, 1 km = 1000 meters. Thus, we have

[tex]x=\frac{1}{40}\times1000\\\\x=25[/tex]

Thus, each athlete run 25 meters.

Nancy bought an extra-large bag of 1,500 beads to make necklaces. When she got home, she found another bag with 660 beads in it. If she uses all of the beads and uses 60 beads per necklace, how many necklaces can she make?

Answers

She can make 36 necklaces.

solve 3x/2 - 7=x/4 - 2 i know the answer is 4 but how do i solve this

Answers

First, multiply by 4 on both sides to eliminate the denominator, and you get...
6x-28 =x-8
Subtract x on both sides and add 28...
5x=20
Divide to isolate the variable...
x=4
Hope this helps

what is the answer to 2(0.5c−1.5)−6=−2 please show work!!!!

Answers

ANSWER: c = 7

WORK:
2(0.5c - 1.5) - 6 = -2
c - 3 - 6 = -2
c - 9 = -2
c - 9+9 = -2+9
c = 7
2(0.5c - 1.5) = -2 + 6

2(0.5c - 1.5) = 4

0.5c - 1.5 = 4/2

0.5c - 1.5 = 2

0.5c = 2 + 1.5

0.5c = 3.5

c = 3.5/0.5

Lastly simplify

Answer: c = 7.
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