I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.
No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.
Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation. One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4by a divisor (2; "I took away half of my 48.").
I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:
48÷2=48/2
48÷2(9+3)â 48/2(9+3)
After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:
The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.
NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:
48
----
2(9+3)
This would then simplify to
48
----
2(12)
Then
48
----
(24)
Which is equal to
2.
We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.
I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.
No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.
Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation. One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4
I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:
48÷2=48/2
48÷2(9+3)â 48/2(9+3)
After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:
The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.
NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:
48
----
2(9+3)
This would then simplify to
48
----
2(12)
Then
48
----
(24)
Which is equal to
2.
We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.
Question is why are you multiplying before you divide when the division sign comes before the multiplication sign in the equation?
Question is why are you multiplying before you divide when the division sign comes before the multiplication sign in the equation?
See the way it's written above. Mathematical questions can be solved many different ways, and each way should yield the right answer. If you look at the entire thing as a fraction, it makes more sense. Because the division sign comes before the 2(9+3), then that would be in the denominator, while the 48 would be in the numerator. Solving from there is easy. Check it out above.
See the way it's written above. Mathematical questions can be solved many different ways, and each way should yield the right answer. If you look at the entire thing as a fraction, it makes more sense. Because the division sign comes before the 2(9+3), then that would be in the denominator, while the 48 would be in the numerator. Solving from there is easy. Check it out above.
Read my above post. It addresses this issue and shows how it works out to 2. In the end, the ÷ sign and the / sign mean the same thing, and I proved it above.Originally Posted by Millzhouse719
See what your saying with the / and the ÷ sign but do not think it is the issue in this topic. The biggest issue in here is that once we do (9+3) is it just 12 or (12). If it is 48÷2x12= 288 or 48÷2(12). I was taught that the parentheses stays with the sign even after we do the problem. So I will go with 2 for the sake of how I was taught.
Read my above post. It addresses this issue and shows how it works out to 2. In the end, the ÷ sign and the / sign mean the same thing, and I proved it above.Originally Posted by Millzhouse719
See what your saying with the / and the ÷ sign but do not think it is the issue in this topic. The biggest issue in here is that once we do (9+3) is it just 12 or (12). If it is 48÷2x12= 288 or 48÷2(12). I was taught that the parentheses stays with the sign even after we do the problem. So I will go with 2 for the sake of how I was taught.
I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.
No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.
Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation. One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4
I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:
48÷2=48/2
48÷2(9+3)â 48/2(9+3)
After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:
The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.
NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:
48
----
2(9+3)
This would then simplify to
48
----
2(12)
Then
48
----
(24)
Which is equal to
2.
We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.
I refute your refutation on the grounds that both signs actually hold the same mathematical meaning. They are actually interchangeable in a way.
No, 48÷2 is spoken as 48 divided by 2.
48/2 is spoken as 48 halves.
Just because both 48 halves are 2 wholes and 48 divided by 2 equals 2 doesn't mean that the symbols for division and fraction are interchangeable in an equation. One is the addition of fractions of a whole ("I have 48 halves.") and the other is the division of a dividend (4
I've only read the first page and the last two pages so the sample size is small, but I have yet to read an opinion that would dissuade me from my belief that:
48÷2=48/2
48÷2(9+3)â 48/2(9+3)
After my immediate refutation, I reconsidered this and thought he was right. HOWEVER, I realized soon afterwards that they are indeed the same, and here is why:
The problem states: 48÷2(9+3). We already proved that through distribution, this problem can be written as 48÷((2*9)+(2*3)). This then simplifies to 48÷(18+6), which simplifies to 48÷(24), which is equal to 2.
NOW, we have the issue of, "What if you interpret this as a fraction?" Above, HoldenMichael writes 48/2, and that makes sense.... but the real problem is that Holden forgets to write the rest of the problem in the denominator. There is nothing that separates the (9+3) from being in the denominator along with the 2. So in reality, if one would look at the ÷ as a / sign, the problem would look like this:
48
----
2(9+3)
This would then simplify to
48
----
2(12)
Then
48
----
(24)
Which is equal to
2.
We have now proven that the answer is 2, 2 different ways solidly. We have also given valid reasons and proof as to why calculators and other mathematical engines are unreliable. These methods also are not based on whether Multiplication goes before Division, which I think we are all now in consensus that it doesn't. If you would like to argue further, please disprove both of these methods.
