What is the answer to (+5)(-4)(+3)(-2)(+1)? Are there any tips or tricks to doing these kinds of problems?
Since the multiplication is commutative and associative, you can group the factors of multiplication (the numbers) as you wish, but you need to consider the following rules:
- the multiplication of two positive factors gives a positive result
- the multiplication of two negative factors gives a positive result
- the multiplication of bne negative factor and one positive factor gives a negative result
Since there exists two negative factors and three positive factors, the result will be positive.
Group the terms in this way, such that:
`[(+1)(+3)(+5)]*[(-2)(-4)] = 15*8 = 120`
Hence, evaluating the result of the given multiplication, yields `[(+1)(+3)(+5)]*[(-2)(-4)] = 120` .
Answer is 120.
If you know the rules
then solving this is easy.
Count the number of negative signs.
If the number of negative signs is even, then the answer will be positive.
If the number of negative signs is odd, then the answer will be negative.
Assuming this, then you can just multiply (in this case) 5! or 5*4*3*2*1, which equals 120, and the fact that there are 2negative signs means that the answer will be positive.
Answer = 120
You need to know that:
Ignoring signs, just multiply all the numbers out:
5 x 4 x 3 x 2 x 1 = 120 (Side note: this is also called 5!)
In the original we have two negative numbers and three positive numbers. Keep in mind that order does not matter for multiplication and that two negative numbers multiplied together gives a positive number. So a (neg x neg) x pos x pos x pos
..which is all equal to a positive number.
so the answer is equal to positive 120
just multiply the numbers
`-60xx-2=120 ` (because negative times negative = positive )
so the result is 120
Trick: Any number mulitplied by a +1 is itself, so you can basically ignore this.
Multiplication is a function that order does not matter in, so you can group how you like. I would group the negatives and positives like so:
Answer : 120