Without doing ANY calculations, determine whether each number sentence is true. EXPLAIN. Check your answer. You should have THREE explanations!
a) -50 (-800) = (-50 x -1000) + (-50 x 200)
b) -50 + (400 x 32) = (-50 + 400) x (-50 + 32)
c) 12 ÷ (-8 + 4) = (12 ÷ -8) + (12 ÷ 4)
a) -50 (-800) = (-50 x -1000) + (-50 x 200) yes
ReplyDeletethe 200+ (-1000) =-800 so it works
b) -50 + (400 x 32) = (-50 + 400) x (-50 + 32) no
It doesn’t work because you would have to multiply the 400 and the 32 first
c) 12 ÷ (-8 + 4) = (12 ÷ -8) + (12 ÷ 4) yes
It works because you can add the answers after you don’t have to add -8 and 4 first
A) The number sentence is not true, because adding a negative sign to the 1000 doesn’t automatically make it -800 after all the math. Plus after you multiply the -1000 and the 200 by -50, it’s going to come out less than the product of -50(-800).
ReplyDeleteB) The number sentence is true, because the second equation is just expanded form of the first equation. The -50 is distributed to the 400 and the 32, -50(400) x -50(32).
C) The number sentence is true, because just like B) the second equation is the expanded form of the first equation. The 12 is distributed to the -8 and the 4, 12(-8) divided by 12(4).
The first number sentence is true. I know this because its using the distributive property the right way. If you write (-50x-1000) + (-50x200) in standard form it would be -50(-1000+200), which simplified equals -50(-800). The second number sentence is not true. I know this because its using the distributive property, but its not using it the right way because the distributive property doesnt work with addition. -50+(400x32)=80, and (-50+400)x(-50+32)=-6,300 therefore they are not equal, making the statement false. The third number sentence is also not true. It is using the distributive property the wrong way just like in the second one, but this time its using it with division, which the distributive property doesnt work with. 12/(-8+4)=-3, and (12/-8)+(12/4)=(12/-8) + 3, which clearly doesnt equal -3, proving this number sentence is not true.
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ReplyDeleteA) This is true because, the -800 times the -50 would equal 40,000 (it came out positive because we multiplied a negative by a negative) and then when we multiply the -50 times 200 it would equal -10,000 plus the positive 50,000 which would make the sum 40,000.
ReplyDeleteB) This is false, because when we multiply 400 by 32 subtracting 50 we would get a number in the thousands, approximately 12, ooo or so, but as we multiply the sum of the -400 – 50 it would approximately be 300 with the sum of -32 plus 50 we would approximately get 18, so if you multiply them together we would get a number in the thousands, approximately 6000.
C) This is false, because when we divide 12 by 4 we would get 3, and that wouldn’t equal the sum of 12 divided by -8, it would approximately be -1.5 and then after you subtract that from 3 it would be a sum of 2.5.
A)This number sentence is true, because 5 *8=40 and essentially in the question it asked that except with a couple of extra 0’s at the end. Multiplying 50 and 1000 makes 50000 and if we subtract 10000(-50*200) we get 40000 which is the correct answer, so yes, this number sentence is true.
ReplyDeleteB)Yes, this number sentence is also true because we learned in class about expanded form. Expanded form allows us to do the math in a different and easier way while getting the same answer.
C)No, this number sentence is not true, because 12/-12=-1, where as the answer I got for the other one was 4.5. The two answers are very different and are not equal, thus, disproving the idea that this number sentence is true.
The first one is true because -1000 + 200= 800. So (-50 x -1000) + (-50 x 200) is equal to -1000 x 800.
ReplyDelete-50 + (400 x 32) is equal to (-50 +400) x (-50 + 32) because 400 + 32 = 432.
The last one is true because 12 x (-8 + 4) is equal to (12 / -8) + (12 / 4).
A) The number sentence is true, because distributive property was used correctly.
ReplyDeleteB) The number sentence is false, because the distributive property was used incorrectly.
C) The number sentence is false, because division doesn’t work with distributive property.
The first number sentence is true. 200 plus a negative 1000 equals 800. Therefore the number sentence is true. On problem B) It says -50 + (400 x 32) = (-50 + 400) x (-50 + 32) the number sentence is false. For the problem to be true you would have to change the problem to like the one is the first one. In order for it to be true you would have to make the problem -50(400+32). On problem c) it says 12/(-8+4)= (12/-8)+(12/4). The statement is false because you can’t distribute division, If you try to solve for both answers and they will both turn out differently.
ReplyDeleteNumber sentence a) is true because to use the distibutive property in a number sentence, you have to use multiplacation. To must use multiplacation to use the distributive property otherwise the answer will not be correct. Also this is the reason why that number sentence b) and c) are false. you cannot use the disstributive property with division or additon.
ReplyDeleteby the way Mrs.ryon, this is mio yamada.
In sentence a) it says that -50 (-800) = (-50 x -1000) + (-50 x 200) this is true because you can distribute the first equation, then when you solve both of the sentences you will come out with the same answers.
ReplyDeleteIn sentence b) it says that -50 + (400 x 32) = (-50 + 400) x (-50 + 32) this statement is false. In order for this statement to be true you would have to switch the operations in the first sentence. To make the sentence true it would have to state -50 (400 + 32).
In sentence c) it says that 12 ÷ (-8 + 4) = (12 ÷ -8) + (12 ÷ 4) this is also false. You cannot distribute with division, because if you do then when you go back to check both answers they will come out different.
Out of the three number sentences letter was the only number sentences that was correct and a true statement. One reason because it is a true sentence is because it is the only sentence that correctly uses the distributive property because it distributes its numbers by multiplication. The other two sentences use division and addition witch can not distribute the numbers. Another reason is a true because is a true statement on both sides and when simplified both sides have the same answer. The other two sentences do not have matching answers on both sides when simplified. The last reason why letter a is true because it is the only one that has addition inside the parenthesis and multiplication symbols outside the parenthesis so it is the only true statement out of the three number sentences.
ReplyDeleteLetter A is true. The distributive property was used right. It says -50 (-800) = (-50 x 1000) + -50 x 2000). I know this because -50 times – 800 is 40,000. Also (-50x1000) + -50x 2000) is 40,000 also, so therefore it’s true. Letter B is not true. It says -50 + (400 x 32) = (-50+400) x (-50 + 32). I know this because -50 + (400 x 32) is 12,750. The second part (-50+400) x (-50+32) is -560,000. So that number sentence is not true. Letter C is not true it’s false. It says 12÷ (-8+4) = (12÷-8) + (12 ÷4). The first part is 0.3 and it’s repeated. The second part is 4.5. Those numbers are not equal to each other, so this number sentence is not true.
ReplyDeleteLetter A is true. This is true because when put in standard form, -50(-800) does equal -50(-1,000)+-50(800). This is an example of the correct way to use the distributive property. However, letter B is not true. This is because the distributive property cannot be used with addition. Letter B is the same way, you cannot use the distibutive property with division either.
ReplyDeleteIn A) the number sentence would be true, because when you use the Distributive Property for -50 (-800) = (-50 x -1000) + (-50 x 200)they both give you the same answer which is 800.
ReplyDeleteIn B)the number sentence would be false, because these equations,-50 + (400 x 32) = (-50 + 400) x (-50 + 32) gave different answers and they did not equal. This makes it that the Distributive Property was not used correctly.
In C)the number is false because you cant use Distributive Property with division,only with multiplication.
a) -50(-800)=(-50x-1000)+(-50x200)is true becaues the number sentence(-50x-1000)+(-50x200)if you take out -1000+200 it would add up to negative 800 as it is in the first number sentence.another way to see that its true is that -50(-800)=40000 and (-50x-1000)+(-50x200)also equals40000, both anwsers are equivalent witch makes both number sentences true.
ReplyDeleteb) -50+(400x32)=(-50+400)x(-50+32)this number sentence is false because the fist number sentence -50+(400x32) adds up to 12,750 and(-50+400)x(-50+32)adds up to -6300, both anwsers are not equivalent which makes both number sentence false.
c) 12÷(-8 + 4)=(12÷-8)+(12÷4) this number sentence is true because of the Distributive Property.
a. yes it is true because if you use the distributive property (-50 times -1000) + ( -50 times 200) becomes
ReplyDelete-50( -1000 + 200) and if you use to order of operation the first step is the parentheses and when you do the parentheses it becomes -50(-800)
b. yes it is true because -50 + ( 400 times 32) is standard form and (-50 + 400) times (-50 + 32) is expanded form.
c. yes it is true because 12/( -8 + 4) is standard form and (12/-8)+(12/4) is expanded form
The first # sentence is not true because adding a negative sign to the 1000 doesn’t make it -800 The second one is not true this is because the distributive property cannot be used with addition.
ReplyDeletethe last one is not true because you cant use Distributive Property with division you can only use it with multiplication.
a is yes because 200 + (-1000) equals -800 so it works. B doesnt work -50 + (400x32) doesnt equal -50 + 400 x -50 + 32 each equation has a differnt answer. c works because the first equation is in standerd form the other equation is in expanded form so it works
ReplyDeletea)the firs number sentence is true because the distributive property works. (-50 x -1000) + (-50 x 200)is -50 x (-1000 + 200) witch then becomes -50 x -800.
ReplyDeleteb) the number sentence is not true because we are working on the distributive property of multiplication not addition.
c) the 12 is being distributed to the -8 and the 4, 12(-8) divided by 12(4) so yes its true.
a)A) -50 (-800) = (-50 x -1000) + (-50 x 200)
ReplyDeleteIt works because -50*-800 = 40,000. And -50*-1000 is 50000 add that to -50*200= -10000. So really you subtract 10000 from 50000, which gives you a grand total of 40000.
b)-50 + (400 x 32) = (-50 + 400) x (-50 + 32)
It doesn’t work because the addition sign in the first expression would have to switch with the multiplication sign in order to make it true. So the correct operation would be -50*(400+32) = (-50*400)+ (-50*32).
c)C) 12 ÷ (-8 + 4) = (12 ÷ -8) + (12 ÷ 4)
It doesn’t work because if you add -8+ 4 which = -4 then divide 12 you get -3. Now you start at the other end of the expression, divide 12 by -8and you get -1.5, add that to the next answer of 12 divided by 4 which is 3. So 3+-1.5= 1.5, therefore it does not work out.
A)-50(-800)=(-50 x -1000)+(-50 x 200) is not correct for the 200 is not negative which means that (-50 x -1000)+(-50 x 200)= 800. A positive 800 the oppsitive of a -800.
ReplyDeleteB)Correct, -50 + (400 x 32)is the simplfied version of (-50 + 400) x (-50 + 32).
C)Like in question (B) 12 ÷ (-8 + 4) is the simlfied version of (12 ÷ -8) + (12 ÷ 4) meaning that (C) is correct
a. True )-50(-800)=(-50 x -1000)+(-50 x 200). If you do this work -50(-800)= 40,000 and (-50 x -1000)= 50,000 and (-50 x 200)= -10,000 so then you - 50,000 - -10,000 = 40,000. This means that the distributive property works with multiplying.
ReplyDeleteb. Fails )-50 + (400 x 32) = (-50 + 400) x (-50 + 32) then you add first 50+(400x32) Then = 12,750. And then you do(-50+400)x(-50+32)and then you will get -6300. This means that the distributive property does not work with adding.
c. Fails ) .12 ÷ (-8 + 4) = (12 ÷ -8) + (12 ÷ 4) you start dividing 4 ÷ 12 and get 4 And then you do 12÷ -8 = -1.5 and then add up 4 + -1.5 = 2.5. This means that the distributive property does not work with dividing.