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.
Oct 02, 19 04:34 PM
Why multiply before adding? The common sense behind doing multiplication before addition
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Recommended
Scientific Notation Quiz
Graphing Slope Quiz
Adding and Subtracting Matrices Quiz
Factoring Trinomials Quiz
Solving Absolute Value Equations Quiz
Order of Operations Quiz
Types of angles quiz
Oct 02, 19 04:34 PM
Why multiply before adding? The common sense behind doing multiplication before addition