# Why do we multiply before adding when doing PEMDAS?

It makes a lot of sense to multiply before adding when we follow the order of operations or PEMDAS.

Say for example, you want to calculate 6 × 2 + 5

The order of operations tells us to  multiply 6 and 2 first. However, the following question remains:

Why can't we add 2 and 5 first and then multiply by 6?

In order to see why it makes sense to multiply 6 and 2 first and then add 5, we need to turn the expression 6 × 2 + 5 into a word problem.

Maria went to the supermarket and bought 6 bottles of water and 1 gallon of milk. If a bottle of water cost 2 dollars and a gallon of milk costs 5 dollars, how much money does she owe to the cashier.

The numerical expression for this word problem is 6 × 2 + 5

If you add 2 to 5 first and then multiply the result by 6, you will get 42 dollars. This does not make sense since that is way too much money for 1 gallon of milk and 6 bottles of water. What went wrong here?

After adding 2 and 5, we get 7. However, 7 includes the price of 1 gallon of water or 5 dollars. Therefore, if you multiply 7 by 6, you are in fact multiplying the price of 1 gallon of milk or 5 by 6. In other words, this means that you purchased 6 gallons of water or
6 × 5.

If indeed you did purchase 6 bottles of water and 6 gallons of milk, then the expression will look like this: 6 × (2 + 5)

Putting parentheses ensure that both 2 and 5 will be multiplied by 6. Without the parentheses
or if the problem is 6 × 2 + 5, first you get the cost of buying 6 bottles of water and then add that to the cost of buying 1 gallon of milk. ## Recent Articles 1. ### Operations Research Analyst

Apr 02, 20 12:05 PM

Find out how to become an operations research analyst if you have a math major.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.