# How do you simplify 48÷2(9+3) using order of operations?

May 15, 2016

$288$ if using PEMDAS or similar.

$2$ if using one of several other common conventions.

#### Explanation:

If by "order of operations" you mean the conventions described by PEMDAS, then refer to the answer:

What else might "order of operations" mean?

Historically, when it was introduced, the obelus $\div$ meant to divide the whole expression on the left by the whole expression on the right.

If we followed that convention of order of operations then we would evaluate the expression $2 \left(9 + 3\right) = 2 \cdot 12 = 24$ then divide $48$ by $24$ to get $2$.

Alternatively, if we followed a convention that multiplication by juxtaposition has higher priority than other forms of multiplication or division then again we would evaluate the product $2 \left(9 + 3\right) = 24$ first and end up with the result $2$. How might such a convention be justified? Consider the expression $a \div 2 b$. This is normally understood to mean $a \div \left(2 b\right)$ If we were really stubborn about PEMDAS, then we might insist on the interpretation: $\left(a \div 2\right) \cdot b$. I guess that we don't do this because we consider $2 b$ a single term.

Strictly followed, PEMDAS does not distinguish between multiplication by juxtaposition and any other kind of multiplication. so using PEMDAS we end up doing the division $48 \div 2 = 24$ before multiplying by $\left(9 + 3\right) = 12$, resulting in the value $24 \cdot 12 = 288$.