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product of 18 and 7 plus 5?

I'm trying to help my daughter with math and having troble with the best way to help her so she understands it.

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2 Answers

The problem asks for the product of 18 and 7 plus 5, you do order of operations (P.E.M.D.O.S.). So slots 1 and two would be 18 and 7. Then you add 5 to the product of 18*7. Which is 131.
The statement "the product of 18 and 7 plus 5" should be seen as 18*7+5.
Apply P.E.M.D.O.S.; there is only multiplication and addition
multiply first 18*7 = 126
then add 5 to 126 = 131
If the wording was different you would 7+5 first, but the wording simply says "product of 18 and 7 plus 5." In this statement the operation (multiplication) is defined, the joining "and" then links 18 and 7, leaving 5 as an additional operation.
If the wording was 18 times the sum of 7 and 5 then George would be correct, the operation that joins two numbers is 7 and 5 to sum them, then you multiply 18 to the sum of 7 and 5 (12).
Long story short the problem should be read as 18*7+5, apply PEMDOS and get the answer of 131.


The problem here is interpret the words into something you can calculate. The phrase "18 and 7 plus 5" means that you are to add 7 and 5 before multiplying by 18. An easy mistake is think it means to add 18 and 7, then add 5 to the result.

The key to interpeting the phrase correctly is to look at the whole phrase "product of 18 and 7 plus 5". The convention is that the phrase "product of ?1 and ?2" means to multiply ?1 by ?2. In this case, ?1 is just a number, 18. But in the ?2 slot is the phrase "7 plus 5".

The convention is to execute the inner phrase before the outer one. Thus, the steps are:

1. Add 7 to 5, for 12.

2. Multiply 18 times 12, for 216.

If your daughter is given the problem is the shorthand of mathematics, it would be "what is 18*(7+5)". To evaluate this expression, you still work from inner to outer: add 7 and 5 before multiplying by 18.

That is the key to much mathematical manipulation: work from the innermost expression out.