The problem the others seem to have missed is that your statement is ambiguous. The problem is NOT in the order of operations.
6÷2(1+2)
this can be interpreted two ways
6÷(2(1+2))
or
(6÷2)(1+2)
The (1+2) is changed to 3 in both cases, but it is still ambiguous
the first is 6/(2*3) = 6/6 = 1
the second is 3*3 = 9
learn to use parans correctly to avoid ambiguous statements. It's difficult sometimes, as the way it appears in the text book must be translated to one line statements.
Once you have computed the sum in parentheses, you have a 3-factor product:
.. 6*(1/2)*3
The rules of the Order of Operations tell you to evaluate the product by performing multiplication/division left to right. The associative and commutative properties of multiplication say you can compute the product of these factors in any order.
If you follow PEMDAS (and use your parenthesis correctly), there's only one right answer.
6÷2×(1+2)
6÷2×3
3×3
9
By default, math operations in which the order doesn't matter (division and multiplication are at the same "level") are performed left to right. If you want a different answer, you need to use parenthesis to control that.
Answers & Comments
one.
6 ÷ 2(1 + 2) = 9. Add first (parentheses), divide next (6 ÷ 2), then multiply.
If this were 6 ÷ (2 (1 + 2)), this is 1.
6÷2(1+2) = 6÷2(3) = 3(3) = 9
If it had been written 6÷(2(1+2)), then it would be 1:
6÷(2(1+2)) = 6÷(2(3)) = 6÷6 = 1
The problem the others seem to have missed is that your statement is ambiguous. The problem is NOT in the order of operations.
6÷2(1+2)
this can be interpreted two ways
6÷(2(1+2))
or
(6÷2)(1+2)
The (1+2) is changed to 3 in both cases, but it is still ambiguous
the first is 6/(2*3) = 6/6 = 1
the second is 3*3 = 9
learn to use parans correctly to avoid ambiguous statements. It's difficult sometimes, as the way it appears in the text book must be translated to one line statements.
8
There is ONE way to do this, but you MUST follw the LOrder of Operation, which are:
1. Parentheses
2. Exponents and Roots
3. Multi[plication and Division
4. Addition and subtreaction
5. Left to right
Now, in your example there are on exponents and roots, so we can forget them.
SO,. the first thing you do is ANYTHING INSIDE PARENTHESIS:
6 / 2 * (1+2) = 6 / 2 * (3)
Second, do all multiplication and division:
BUT THERE ARE TWO, one multiplication and one division.
So do them LEFT TO RIGHT
6 / 2 * 3 = (6/2) * 3 = 3 * 3
3 * 3 = 9
The CORRECT answer is 9.
If you don't follow the Orders of Operation, then you get 1 -- which is wrong.
Once you have computed the sum in parentheses, you have a 3-factor product:
.. 6*(1/2)*3
The rules of the Order of Operations tell you to evaluate the product by performing multiplication/division left to right. The associative and commutative properties of multiplication say you can compute the product of these factors in any order.
6 ÷ 2(1+2) = 6 ÷ 2 x 3
= 6 ÷ 6
= 1
If you follow PEMDAS (and use your parenthesis correctly), there's only one right answer.
6÷2×(1+2)
6÷2×3
3×3
9
By default, math operations in which the order doesn't matter (division and multiplication are at the same "level") are performed left to right. If you want a different answer, you need to use parenthesis to control that.