How do you simplify 52\div 16\cdot ( 1+ 1)?

Sep 22, 2017

$6.5$.

Explanation:

Order of Operations:
Parenthesis/Brackets, Exponents, Multiplication/Division, Addition/Subtraction or otherwise known as BEDMAS or PEDMAS. Whatever you choose, they mean the same things.

First thing to do here is to here is to solve the things in parenthesis.

$52 \div 16 \cdot \left(1 + 1\right) = 52 \div 16 \cdot \left(2\right)$

Then, do Multiplication and Division from Left to Right.
$52 \div 16 \cdot \left(2\right) = \frac{52}{16} \left(2\right) = \frac{52}{8} = \frac{13}{2} = 6.5$

Sep 22, 2017

It depends...

Explanation:

Given:

$52 \div 16 \cdot \left(1 + 1\right)$

Parentheses always enforce order of operations, so we might as well evaluate the content of the parentheses first to get:

$52 \div 16 \cdot 2$

There are essentially two choices here: to perform the division first or the multiplication.

Which is correct?

Interpretation 1 - PEMDAS, BIDMAS or BODMAS

In PEMDAS and similar conventions, multiplication and division have the same priority and are evaluated left to right.

So in our example, we would perform the division first and the multiplication second, simply working from left to right:

$52 \div 16 \cdot 2 = \frac{52}{16} \cdot 2 = \frac{13}{4} \cdot 2 = \frac{13}{2}$

Interpretation 2 - Historical

Historically the obelus $\div$ was used to indicate that the whole expression on the left should be divided by the whole expression to its right. So with this interpretation we evaluate $52$ and $16 \cdot 2$ first, then divide the first result by the second, as follows:

$52 \div 16 \cdot 2 = \frac{52}{16 \cdot 2} = \frac{52}{32} = \frac{13}{8}$

But which is right?

Conventions for order of operations are intended to help disambiguate otherwise ambiguous expressions, but that will only work if the writer and the reader both understand the conventions in use.

In the given example, we have not been asked to used PEMDAS or similar. The writer may have had some other convention in mind.

In practice, it would be better for the writer to use more parentheses to avoid ambiguity, unless the conventions in use are well understood.