WE need to complete the following operation of rational numbers:
(7/2) times (-2) and this quantity minus the quantity (3/2) times (-1)
so, as with all operations with numbers we need to perform the Multiplications BEFORE we perform any Addition or Subtraction.
We have two products (multiplications) to perform:
first one: (7/2) times (-2)
with product of fractions, we first multiply their sings (positive times negative will render a negative). Then we multily numerator times numerator, and denominator times denominator separately. In our case: 7 times 2, which gives 14 in the new numerator, and then 2 times 1 (notice no denominator for the second number (-2) is in fact a one), which gives 2.
Then first produc is : (7/2) * (-2) = -14/2 = -7
Now for the second product:
(3/2) times (-1) . We wrok similarly and get:
Sign = positive times negative = negative
3 times 1 = 3
2 times 1 = 2
that gives the fraction: 3/2
Completed product gives: (3/2) times (-1) = -3/2
And finally, we combine these two values with the subtraction (minus symbol) that separated them:
-7 - (-3/2) = - 7 + (3/2)
Notice that subtracting a negative 3/2 is the same as adding 3/2
then we express -7 in fraction form with denominator 2, as -14/2 (so we can perform the combinationof the two numbers)
-14/2 + 3/2 = -11/2