The product should be found first, and then the ratio. Then the subtraction should be changed
to negative addition, and finally the additions should be done. This gives us
6 × 8 − 14/2 + 3 = 48 − 14/2 + 3
= 48 − 7 + 3
= 48 + (−7)+ 3
= 41 + 3
= 44
Question 5-7
How can we change the expression in Question 5-6 to indicate that the subtraction should be
done first, then the multiplication, then the division, and finally the last addition? What will
the result be then?
Answer 5-7
We should place an opening parenthesis to the left of the 8 and a closing parenthesis to the
right of the 14, like this:
6 × (8 − 14)/2 + 3Now we’ve isolated the subtraction problem so it must be done first. We don’t need to change
it to negative addition in this case, because there’s no risk of ambiguity with the subtraction
part alone inside the parentheses. We proceed like this:
6 × (8 − 14)/2 + 3 = 6 × (−6)/2+ 3
=−36/2+ 3
=− 18 + 3
=− 15
Question 5-8
What does the commutative law tell us about the product of two integers? What does the
associative law tell us about the product of three integers? What do these laws, taken together,
allow us to do?
Answer 5-8
The commutative law tells us that when we multiply two integers, we can do it in either order
and the product will be the same. If a and b are integers, then
ab=baThe associative law says that we can group a product of three integers in a certain order by
twos either way, and the result will always be the same. If a, b, and c are integers, then
(ab)c=a(bc)Taken together, the commutative and associative laws allow us to arrange and group a product
of integers in any possible way, and the result will always be the same.
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