Mathematics, 27.09.2019 02:00 gamingisfun

The sum of two rational numbers will always be
an irrational number.
an integer.
a rational number.
a whole number.

Answers: 1

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Answer from: pretti78

I think that the sum will always be a rational number
let's prove that

any rational number can be represented as a/b where a and b are integers and b≠0

and an integer is the counting numbers plus their negatives and 0
so like -4,-3,-2,-1,0,1,2,3,4

so, 2 rational numbers can be represented as

a/b and c/d (where a,b,c,d are all integers and b≠0 and d≠0)

their sum is
a/b+c/d=
ad/bd+bc/bd=
(ad+bc)/bd

to prove that the sum will always be a rational number, we must prove that
1. the numerator and denomenator will be integers
2. that the denomenator does not equal 0

alright
1.
we started with that they are all integers
ab+bc=?
if we multiply any 2 integers, we get an integer
like 3*4=12 or -3*4=-12 or -3*-4=12, etc
even 0*4=0, that's an integer
the sum of any 2 integers is an integer
lik 4+3=7, 3+(-4)=-1, 3+0=3, etc
so we have established that the numerator is an integer

now the denomenator
that is just a product of 2 integers so it is an integer

2. we originally defined that b≠0 and d≠0 so we're good

therfor, the sum of any 2 rational numbers will always be a rational number is the correct answer

Answer from: Quest

the statemwnt is the company makes small and large snow cone cups.

large=it holds more then the small

small=it holds less then the large

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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