You're treating the ÷ (aka /) like everything on the left of it is the numerator (top) and everything to the right is a denominator (bottom).
When equations like this are written in a single line, you don't assume this, you only assume that the numbers touching the division are part of the fraction. So the 6 is the top, 2 is the bottom. What you did is 6/(2(1+3)). The trick part is that you'd probably know this if the original was written as (6/2)×(1+2)
You were taught to use the distributive property first, which is weird because it makes these calculations harder. It makes later algebra (with letters instead of numbers) easier which I'm guessing is why you were taught that way.
The distributive property comes from how addition and multiplication interact with each other, since the 2(1+2) is actually the same as 2×(1+2), we just don't usually write the × explicitly.
You should do operations IN the brackets first, but your distributive thing is equivalent if you're careful. The distribution is equivalent to doing a ×, and it doesn't take priority over other × operations, or the ÷ operation. × and ÷ are done in order as they appear left to right if using BEDMAS.
Brackets first, then exponents, then division/multiplication (in order as they appear left to right) and then addition/subtraction (in order as they appear)
In this bullshit trick question, the ÷ and the implied × in 2(1+2) are the same 'priority' in the usual order of operations, so you just do them in order as they appear left to right.
Way I was taught to do BEDMAS (order of operations):
= 6÷2(1+2)
= 6 ÷ 2 × 3
= 3 × 3
= 9
If I wanted to use your distributive property with fractions then I'd do:
deleted by creator
We were taught when you put a number in front of brackets 2(1+2) it means to distribute it as in (2x1)+ (2x2) = 2+4 = 6
Since it is written 6/2(1+2) it is also written as
6
2(1+2)
Thus the separation. So the end 6/6 = 1
You're treating the ÷ (aka /) like everything on the left of it is the numerator (top) and everything to the right is a denominator (bottom).
When equations like this are written in a single line, you don't assume this, you only assume that the numbers touching the division are part of the fraction. So the 6 is the top, 2 is the bottom. What you did is 6/(2(1+3)). The trick part is that you'd probably know this if the original was written as (6/2)×(1+2)
You were taught to use the distributive property first, which is weird because it makes these calculations harder. It makes later algebra (with letters instead of numbers) easier which I'm guessing is why you were taught that way.
The distributive property comes from how addition and multiplication interact with each other, since the 2(1+2) is actually the same as 2×(1+2), we just don't usually write the × explicitly.
You should do operations IN the brackets first, but your distributive thing is equivalent if you're careful. The distribution is equivalent to doing a ×, and it doesn't take priority over other × operations, or the ÷ operation. × and ÷ are done in order as they appear left to right if using BEDMAS.
Brackets first, then exponents, then division/multiplication (in order as they appear left to right) and then addition/subtraction (in order as they appear)
In this bullshit trick question, the ÷ and the implied × in 2(1+2) are the same 'priority' in the usual order of operations, so you just do them in order as they appear left to right.
Way I was taught to do BEDMAS (order of operations):
= 6÷2(1+2) = 6 ÷ 2 × 3 = 3 × 3 = 9If I wanted to use your distributive property with fractions then I'd do:
= 6÷2(1+2) = (6/2)(1+2) = 1(6/2) + 2(6/2) = 6/2 + 12/2 = 18/2 = 9Distributive property no fractions:
= 6÷2(1+2) = 3(1+2) = 3(1)+3(2) = 3+6 = 9Thank you. Nice formatting.
deleted by creator