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When to use PEMDAS?

When there is more than one operation in a mathematical expression, we use the PEMDAS method.

PEMDAS in Math gives you a proper structure to produce a unique answer for every mathematical expression. 

There is a sequence of certain rules that need to be followed when using the PEMDAS method.

Once you get the hang of these rules, you can do multiple steps at once.

Example 1

 

 

\(18\div(8-2\times 3)\)

Solution:

\[\begin{align}18\div(8-2\times 3)&=18\div(8-6)\\&=18\div 2\\&=9\end{align}\]

\(18\div(8-2\times 3)=9\)

Example 2

 

 

\((4\times 3\div 6+1)\times 3^{2}\)

Solution:

\[\begin{align}(4\times 3\div 6+1)\times 3^{2}&=(12\div 6+1)\times 3^{2}\\&=(2+1)\times 3^{2}\\&=3 \times 3^{2}\\&=3 \times 9\\&=27\end{align}\]

\((4\times 3\div 6+1)\times 3^{2}=27\)

Example 3

 

 

\(4^{2}\div 2+4\times 3\)

Solution:

\[\begin{align}4^{2}\div 2+4\times 3&=16\div 2+4\times 3\\&=8+12\\&=20\end{align}\]

\(4^{2}\div 2+4\times 3=20\)

Practicing these questions might have made you understand that the order of operations in the PEMDAS rule is nothing but the order of operations that we use to solve difficult mathematical expressions.

Now, let us get back to the mathematical expression given to Ruhi and Ryan to solve, and decide who got the correct answer.

\[\begin{align}5+2 \times 3&=5+6\\&=11\end{align}\]

Thus, based on the order of operations, Ryan got the correct answer.

But, where did Ruhi go wrong? Let’s see.

According to the PEMDAS rule, addition is followed after multiplication.

But, Ruhi performed addition before multiplication. 

This step resulted in an incorrect answer.

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The presence of multiple brackets usually causes confusion.

If we don't know which bracket to solve first, it could lead to an incorrect answer.

We will now learn how to solve this expression with multiple brackets.

\[4 + 3[8 –2(6 – 3)] \div 2\]

We will begin with working from the inside of the brackets.

We will solve the inner-most bracket first and then move outside.

Starting with \(6 – 3 = 3\), we get:

\[4 + 3[8 – 2(3)] \div 2\]

Next, multiplying \(2 (3)=6\) or \(2 \times 3=6\), we get:

\[4 + 3[8 – 6] \div 2\]

There is one bracket left, \([8 – 6] = 2\)

\[4 + 3[2] \div 2\]

Solving \(3 [2]\) or \(3 \times 2 = 6\), we have:

\[4 + 6 \div 2\]

We can observe that all the expressions in the brackets are solved. 

Based on PEMDAS, we know that division comes next, hence, \(6 \div 2 = 3\)

\[4 + 3\]

And lastly, addition \(4 + 3 = 7\)

\(4 + 3[8 –2(6 – 3)] \div 2=7\)