How do you simplify 18div(9-6)(1+2) using PEMDAS?

May 14, 2016

Using PEMDAS:

$18 \div \left(9 - 6\right) \left(1 + 2\right) = 18$

Explanation:

PEMDAS is a mnemonic for the following conventions of order of operations:

P Parentheses.

E Exponents.

MD Multiplication and Division - evaluated left to right.

AS Addition and Subtraction - evaluated left to right.

Note that multiplication and division have the same priority and addition and subtraction have the same priority.

Given:

$18 \div \left(9 - 6\right) \left(1 + 2\right)$

We evalulate the two expressions in parentheses first to get:

$18 \div 3 \cdot 3$

Note that since we are using PEMDAS, division and multiplication have equal precedence and are evalulated from left to right.

So the next step involves dividing $18$ by $3$ to get:

$6 \cdot 3$

Finally:

$6 \cdot 3 = 18$

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Footnote

This is a different result from what you might expect. The multiplication of $\left(9 - 6\right) \left(1 + 2\right)$ by juxtaposition looks more 'binding', so you might expect that you should perform the multiplication first.

Historically, that might have been the way this expression would be evalulated, especially since the obelus $\div$ used to mean divide the whole expression on the left by the whole expression on the right.

However, note well that PEMDAS makes no distinction as to different kinds of division or multiplication. They all have the same priority and are evaluated left to right.