Question 49134This question is from textbook
: I need help multiplying fractions by negative whole numbers, 2/3(-3)
This question is from textbook
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! Just do 2 things in your head when you do maths:
1. "see" everything
2. take things in stages
OK... point 1 means that  is, fully written, +
Point 2 means we are multiplying + by -. Then (as fractions do) we multiply the numerators and then also the denominators.
+ and - multiply to give -
2 and 3 (the numerators) multiply to give 6
3 and 1 (the denominators) multiply to give 3
So the answer is  which simplifies to -2.
The aim is to just look at and do all this in your head and write  and then -2.
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Now, before you ever multiply fractional terms together, what you should get into the habit of doing is doing any division first, to simplify terms. Since multiplication and division are opposites of each other, it does not matter which order you do these in, for example:
(5*3)/12 --> 15/12 --> 5/4
or
5*(3/12) --> 5*(1/4) --> 5/4
It is always PREFERABLE to divide first, so we keep the numbers as simple as we can when we finally multiply. In the above example we did 5*3 but in the second version we only had to do 5*1.
So, back to the question:
+
we can divide the two 3's, giving:
+
which gives -2, following the same processes in point 2 before.
Hope this helps.
jon
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