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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.

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.

Chris,

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.

George