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Question:I'm doing my homework and i stumbled on a few questions that look like this.... 5(74), (62)8, etc...
I'm supposed to "rewrite each expression using the distributive property, then simplify".
I did some addition problems with this like 4(3+5). I multiply 4 by each number in the parentheses then add right? I got 12+20=32 for that problem. Is it right? And if so, do i do the same thing for subtraction problems except subtract it instead of adding?
I know.... Pretty basic stuff but i wanna be sure.
Answers:you are right my friend In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example: 2 (1 + 3) = (2 1) + (2 3). In the lefthand side of the above equation, the 2 multiplies the sum of 1 and 3; on the righthand side, it multiplies the 1 and the 3 individually, with the results added afterwards. Because these give the same final answer (8), we say that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.
Answers:you are right my friend In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra. For example: 2 (1 + 3) = (2 1) + (2 3). In the lefthand side of the above equation, the 2 multiplies the sum of 1 and 3; on the righthand side, it multiplies the 1 and the 3 individually, with the results added afterwards. Because these give the same final answer (8), we say that multiplication by 2 distributes over addition of 1 and 3. Since we could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers distributes over addition of real numbers.
Question:I moved up a math class this year in school. I'm now at the top which means we go a lot quicker when learning stuff. Right now we are focusing on distributive property and I keep on getting confused. I'll include my answers, explain why they're wrong please because I'm sooo unsure of what to do. Can someone please explain to me the answers and how they got there (simplify distributive property) to the following:
1) 8c +11  6c
my answer: 13c because 8c+11=19c6c=13c
2) 15d  9 + 2d
my answer: 8d because 159=6d+2d
3) 24bb
my answer: I have no clue how to use the distributive property for this.
4) 12s  4t + 7t  3s
my answer: 13stst....which is SO wrong... got my answer because... 129=8+7t=163s=13
5) (5m + 5n) + (6m 4n)
my answer: 22mn because 5+6= 11m 5+4= 9n 11+9=20+ (119=)2 + 22
6) 2(4x + 3y)
my answer: 14yx because 2*4 =8x +2*3=6y 8+6=14yx
7) 13st + 5  9st
my answer: 27st because 13+9 = 22st + 5 = 27st
8) 2(3n  n)
my answer: 6n  n because 2 * 3= 6n  n
9) 2 + 7q + 3r + q
my answer: 56zq because 7 * 7= 49zq + 7zq
10) 4(2a 3b)
my answer: 4ab because 4 *2= 8a  (4*3=)12b 8a  12b = (negative) 4ab
11) 2 + 7q + 3r +q
my answer: 12rqq because 9q + 12rqq (DONT UNDERSTAND THIS ONE AT ALL) my answers are all wrong :x idk how i got into the top math class.... i suck at math
Answers:1) 8c +11  6c You need to remember that you can only add and subtract numbers that have the same variable. This is called combining like terms. So, 8c and 11 cannot be added to get 19c. Instead, these will remain separate in your answer. The 6c CAN be taken from the 8c because it does have the same variable. So, 8c6c=2c. Thus, your final answer should be 2c + 11 or the other way around. 2) 15d  9 + 2d The same concept applies here as in number one. 15d + 2d = 17d. Your final answer should be 17d 9. 3) 24bb This is also the same concept. 24b b = 23b. The answer is 23b. 4) 12s  4t + 7t  3s Now, here you have two variables which are s and t. These need to remain separate like the ones above. Take all your ones with the s variable and subtract them. 12s 3s = 9s. Then do the same for the ones with the variable t. Now, look at the 4t. You ll see a minus sign in front of it. This indicates that the number after it is negative. So, you add the opposite. You change the minus into a plus sign and place a negative sign in front of the 4t. You ll end up with 9s + 4t + 7t. Now add your t variables and you will get 3t. Your final answer is 9s + 3t. 5) (5m + 5n) + (6m 4n) There is a rule to when you can drop the parenthesis and it is if all the numbers inside the parenthesis have been simplified as much as possible. Such is the case with this problem. Your problem will look like this 5m + 5n + 6m 4n. Now use the same principle used above and combine like terms. Your m s should add up to 11m because 5m + 6m = 11m. Do the same for the n s. 5n 4n = n. NEVER make the mistake and put 1n because that is incorrect. 1n = n, so put n! Your final answer is 11m + n. 6) 2(4x + 3y) You have yet to have used the distributive property in the above problems. This is where it comes into play. You take the 2 on the outside and multiply it to each of terms on the inside of the parenthesis. So start out with 2*4x. Now, you may be confused because this looks like it you are not combining like terms. When you combine like terms like we did above it only applies for addition and subtraction. Multiplication and division have its own set of rules. Back to the problem, 2*4x = 8x. You simply multiply 2 and 4 and leave the x alone. It just gets bumped next to your number. Then do 2*3y. This gets you 6y. Your answer is 8x + 6y. 7) 13st + 5  9st If you see variables together like the st in this problem, you should consider it as one whole variable. So, 13st 9st = 4st. Your final answer should be 4st + 5. 8) 2(3n  n) This is not the distributive property. If you look closely, you ll see inside the ( ). You ll see that you can simplify 3n n. Do that and you will get 5n. Now multiply 2*5n and you will get 10n. 9) 2 + 7q + 3r + q This is back to the basics. Simplify all like terms. Your 2 cannot be simplified, so leave that there. Your 7q and q can be added together, so do that and you will get 8q. The 3r also cannot be simplified so leave that alone too. Your final answer is 2 + 8q + 3r. 10) 4(2a 3b) Distributive Property again! Take the 4 and multiply it by all the terms inside. You will get 4*2a = 8a. Do the same for the other term 4*3b = 12b. The final answer, when you put it together should be 8a 12b. Remember to keep the variables where they are at on either side of the addition or subtraction sign. Otherwise, you ll get the wrong answer because 8a 12b is not the same as 12b 8a. 11) 2 + 7q + 3r +q I think you copied this one down twice on accident. Email me if you have any more math questions in the future. I am always glad to help. I forgot to mention I am also in an accelerated class, but I'm in High School.
Answers:1) 8c +11  6c You need to remember that you can only add and subtract numbers that have the same variable. This is called combining like terms. So, 8c and 11 cannot be added to get 19c. Instead, these will remain separate in your answer. The 6c CAN be taken from the 8c because it does have the same variable. So, 8c6c=2c. Thus, your final answer should be 2c + 11 or the other way around. 2) 15d  9 + 2d The same concept applies here as in number one. 15d + 2d = 17d. Your final answer should be 17d 9. 3) 24bb This is also the same concept. 24b b = 23b. The answer is 23b. 4) 12s  4t + 7t  3s Now, here you have two variables which are s and t. These need to remain separate like the ones above. Take all your ones with the s variable and subtract them. 12s 3s = 9s. Then do the same for the ones with the variable t. Now, look at the 4t. You ll see a minus sign in front of it. This indicates that the number after it is negative. So, you add the opposite. You change the minus into a plus sign and place a negative sign in front of the 4t. You ll end up with 9s + 4t + 7t. Now add your t variables and you will get 3t. Your final answer is 9s + 3t. 5) (5m + 5n) + (6m 4n) There is a rule to when you can drop the parenthesis and it is if all the numbers inside the parenthesis have been simplified as much as possible. Such is the case with this problem. Your problem will look like this 5m + 5n + 6m 4n. Now use the same principle used above and combine like terms. Your m s should add up to 11m because 5m + 6m = 11m. Do the same for the n s. 5n 4n = n. NEVER make the mistake and put 1n because that is incorrect. 1n = n, so put n! Your final answer is 11m + n. 6) 2(4x + 3y) You have yet to have used the distributive property in the above problems. This is where it comes into play. You take the 2 on the outside and multiply it to each of terms on the inside of the parenthesis. So start out with 2*4x. Now, you may be confused because this looks like it you are not combining like terms. When you combine like terms like we did above it only applies for addition and subtraction. Multiplication and division have its own set of rules. Back to the problem, 2*4x = 8x. You simply multiply 2 and 4 and leave the x alone. It just gets bumped next to your number. Then do 2*3y. This gets you 6y. Your answer is 8x + 6y. 7) 13st + 5  9st If you see variables together like the st in this problem, you should consider it as one whole variable. So, 13st 9st = 4st. Your final answer should be 4st + 5. 8) 2(3n  n) This is not the distributive property. If you look closely, you ll see inside the ( ). You ll see that you can simplify 3n n. Do that and you will get 5n. Now multiply 2*5n and you will get 10n. 9) 2 + 7q + 3r + q This is back to the basics. Simplify all like terms. Your 2 cannot be simplified, so leave that there. Your 7q and q can be added together, so do that and you will get 8q. The 3r also cannot be simplified so leave that alone too. Your final answer is 2 + 8q + 3r. 10) 4(2a 3b) Distributive Property again! Take the 4 and multiply it by all the terms inside. You will get 4*2a = 8a. Do the same for the other term 4*3b = 12b. The final answer, when you put it together should be 8a 12b. Remember to keep the variables where they are at on either side of the addition or subtraction sign. Otherwise, you ll get the wrong answer because 8a 12b is not the same as 12b 8a. 11) 2 + 7q + 3r +q I think you copied this one down twice on accident. Email me if you have any more math questions in the future. I am always glad to help. I forgot to mention I am also in an accelerated class, but I'm in High School.
Question:
Answers:no. only multiplication over addition X + X = x(1+1) however 2+(x*x) does not equal (2+x)(2+x)
Answers:no. only multiplication over addition X + X = x(1+1) however 2+(x*x) does not equal (2+x)(2+x)
Question:Question 1 (Multiple Choice Worth 2 points)
Simplify 6(2r 5) + 2r
4r 30
4r + 30
14 r 30
12 r 30
Question 2 (Multiple Choice Worth 1 points)
Simplify (6p + 12)
6p 12
6p + 12
6p + 12
6p 12
Question 3:
simplify 5x  10 / 5
x 10
5x 2
x 2
x 5
Question 4 (Multiple Choice Worth 2 points)
Identify which distributive property problem below would help you solve the following scenario: Your Math class has 32 students. You would like to treat the class to cookies. You would like each person to have 5 cookies. Which expression would be a quick way to figure out how many cookies you would need to bake?
5(32 + 2)
5(30 + 2)
5(32 2)
5(30 2)
Question 5 (Multiple Choice Worth 1 points)
Simplify 4(9y + 2)
36y + 16
36y + 2
36y + 8
36y + 6
Question 6 (Multiple Choice Worth 1 points)
Simplify (g 16)
g 16
g 4
g + 4
g + 16
Question 7 (Essay Worth 2 points)
Prove, in complete sentences, whether the left expression is equal to the right expression and discuss which property applies.
2(x 3) 2x 6
Answers:the distributive law(property) states that a(b+c) = ab + ac 1) 14r  30 2) 6p  12 3) x  2 4) 5(30 + 2) 5) 36y + 8 6) g  16 7) the property is the distributive law of multiplication over addition. imagine the bracket is like a basket. 2(x3) means you have two of these baskets each with an x and a 3. So if there are 2 of these then overall there are 2x's and 2 (3)'s (ie: 2x and 6)
Answers:the distributive law(property) states that a(b+c) = ab + ac 1) 14r  30 2) 6p  12 3) x  2 4) 5(30 + 2) 5) 36y + 8 6) g  16 7) the property is the distributive law of multiplication over addition. imagine the bracket is like a basket. 2(x3) means you have two of these baskets each with an x and a 3. So if there are 2 of these then overall there are 2x's and 2 (3)'s (ie: 2x and 6)
From Youtube
The Distributive Property of Multiplication Problem 1 :www.greenemath.com In this video we look at three examples of how to use the distributive property to simplify an expression.
Math Made Easy: Multiplication: Mutiplicative Identity and Distributive Property :In this video, I define the multiplicative identity and distributive property of multiplication and show you how to use these properties to solve multiplication problems. If you are a teacher or student looking for online resources to help you understand other things you're having trouble with, go to my website: sites.google.com