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

## product of 18 and 7 plus 5?

# 2 Answers

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