SOLUTION: I have figured on my calculator that 10/33 * -5 * -11/24 = 25/36, but I can't figure out how to explain my answer?

Question 537112: I have figured on my calculator that 10/33 * -5 * -11/24 = 25/36, but I can't figure out how to explain my answer?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The problem is
All the rules and procedures of arithmetic and algebra were invented so that the calculations would make sense in real life. If everything was properly explained (and the reasonings were remembered) you would not need to memorize any seemingly arbitrary rules or procedures.
Soon after negative numbers were invented (to serve perceived needs), the meaning of multiplication was extended to negative numbers. At that point it was decided that the only way it could make sense was to say that to multiply two numbers, you multiply the absolute values and give it a minus sign if the factors have different signs. If the factors have the same sign, you give it a plus sign, but it is usually omitted. As a result there is no doubt that your product will be positive and the plus sign in front of it does not need to be written.
After that, it's a question of multiplying fractions, and you must know that to multiply fractions you make another fraction with the product of the numerators for a numerator and the product of the denominators for a denominator. It is often useful to leave the multiplication indicated for a while, until you figure out if and how it can be simplified. I would calculate it like this:

Do you see how I could simplify? I paired factors that were multiplying everything in the numerator and in the denominator into a fraction that equals one, so that multiplying by it does nothing.
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