Waht will the sign of answer if we multiply 38 negative integers and 98 positive integers ?
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What will be the sign of the product if we multiply 39 negative integers and 98 positive integers?
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Jack Blake
Answered May 16, 2020
Question: What will be the sign of the product if we multiply 39 negative integers and 98 positive integers?
Negative and Minus and Positive and Plus used interchangeably throughout.
Provided the equation is straightforward, assuming no brackets or other operators are involved, (i.e. only a set of figures with + or - signs), then, in many ways, the minuses decide the outcome: this includes equal numbers of (+ and -)
Minuses: Equal to or in excess of the no. of pluses ( - >= + ) the outcome is minus.
Pluses: Those “in excess” of the no. of minuses ( + <= - ) equate to ONE plus.
In the question we have: 39 Negatives and 98 Positives
39 Negatives and 39 Positives if multiplied (+) x (-) = (-) yield a net negative.
59 Positives remain. (+) x (+) = (+) and yield (equate to) only one positive (odd or even numbers of positives stay positive).
Any positive matched with a negative will yield a negative (+) x (-) = (- )
Importantly two negatives yield a positive, three yield a negative and so on.
Hence the answer to your question is the net result will be negative ( - )
Note, if the question gave one extra (-) then the result will be reversed (-) x (-) = (+)
END of Question.
Further reading if you wish.
Basic Rules Summary:
Apply to the whole of a simple equation.
Apply section by section for equations with brackets and/or other operators.
(+) x (+) …. = (+)
(+) x (-) …. = (-)
(-) x (+) …. = (-)
(-) x (-) …. = (+) Important to note
Note: -a /-b = -(a) /-(b) = (-a) /(-b) = a/b = (a)/(b).
Negatives in odd numbers will result in a negative (-)
Negatives in equal numbers will result in a positive (+)
Positives in equal or odd numbers will result in a positive (+)
A mix of Positive and Negative numbers (all able to affect each other) will be decided by sign of the quantity of negative numbers.
In the mix, an odd number of negatives gives (-). An even number gives (+).
The rules apply within brackets subject to the avtiond of any operators
If qualifying brackets or other operators are involved. Carry out the bracket or operator sections individually to progress the answer in sections.
Operators (such as brackets) define priority (sequences) for calculation. There are many different operators (including brackets) for different “levels” of maths.
Once you are clear what a given operator requests you to do, the plus-minus rules must be applied to sections as defined by brackets or other operators.
Also, the rule will be applied to “sections” of the equation, one at a time.
The plus-minus rules then take second place to any brackets or other operators.
Priority of Basic Rules. Using the rules without any other clarification, (eg brackets or more advanced operators), the basic order of priority is:
(Exponentials or Roots) then (Multiply or Divide) then (Add or Subtract).
For advance maths this list may not be exhaustive,
To Stress At a basic it is important to understand the use of brackets to clarify and define important sections of an equation. These sections be resolve before other operations.. i.e. “Solve” or expand the sections individually, slowly unravelling the entire equation in accordance with ALL the rules.
If you will be working a lot with complex equations it would be beneficial to source a text book you find ok to read, if possible a brief reference book to remind you of … ) .
Answer:
-3724 will be the answer.