Rational Numbers?

Question

3 (4/9) (-4) (6/4)

5 (3/4) (-4) (-2)


I really want to know how to do these problems I just don't want the answers I want an explaintion of the overall material as well

Answer 1

When multiplying rational fractions, you multiply all the numerators together (the top numbers) and you multiply all the denominators together. When a denominator is absent, it is a 1.

for example 5 is the same as 5/1

(five divided by 1 is still 5)

the first one is
numerators: 3*4*(-4)*6 = -288
denominators: 1*9*1*4 = 36
Answer = -288/36

It is normally good practice to reduce a rational fraction to relatively prime numbers (in other words, you eliminate common factors).
For example, one does not leave an answer as 12/24, but reduces it all the way to 6/12, 3/6, 1/2.

12/24 is the same as 1/2 but 1/2 looks simpler (and more useful).

-288/ 36
both are divisible by 4
-72/9
both are divisible by 9
-8/1
which is the same as -8.
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You can save time by cancelling a number that is present both in the numerator and the denominator of the same multiplication (even if the numbers are not in the same fraction). For example, you have a 4 in the numerator of the second factor (4/9) and a 4 in the denominator of the last factor (6/4). Cancel the 4's to get:
3 (1/9) (-4) (6/1)

Next, you can simplify a common factor: you have a 3 in the numerator of the first factor (3) and a 9 -- which is 3*3 -- in the denominator of the second factor. The three above cancels one of the threes below:
(1) (1/3) (-4) (6)

Do the same with the 6 (which is 2*3) and the 3:
(1) (1/1) (-4) (2) = (-4) (2) = -8
as we had found the long way.

Answer 2

#2 = 30

Answer 3

Certainly. But the price of fuel is bound to go up as well.