Question

if a and b are two positive integer such that a=bq+r . where q and r are unique integers . if b greater than a. find value of q

Answer 1

Answer:

$-\frac{r}{b}$< q <$1-\frac{r}{b}$

Step-by-step explanation:

First we need to analyze the problem in order to build our equations.

If "a" and "b" are two POSITIVE integers, this means that:

$a>0$

$b>0$

Now, our condition is that:

$a=bq+r$

"q" and "r" being unique integers, also called constant numbers.

Our last condition is that "b" is greater than "a", meaning:

$b>a$

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With this information we can conclude that if:

$b>a$  

and

$a>0$

$b>0$

then,

$b>a>0$

Replacing a on the inequation:

$b>bq+r>0\\ b>bq+r\\ b-bq>r\\ b(1-q)>r\\ 1-q>\frac{r}{b}\\-q>\frac{r}{b}-1\\ q<1-\frac{r}{b}$

On the other side:

$bq+r>0\\ bq>-r\\ q>-\frac{r}{b}$

In conclusion, "q" is dependent on "r" and "b".

Answer 2

Answer:

HII! In the above image is the ANSWER

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