Question

the product of two rational numbers is -12/35.If one of them is 3/5,find the absolute value of the difference of two rational numbers.

Answer 1

Concept:

Absolute value of the difference of two numbers is the positive numerical value of the subtraction.

Now replace the unknown quantity by a variable and form a mathematical equation, on solving which we can find the required value or result.

Given:

The product of two rational numbers is -12/35 and one rational number is 3/5.

Find:

The absolute value of the difference of the two rational numbers.

Solution:

Let the second rational number be = x

First one given is = 3/5

The product of them is = -12/35

According to condition,

(3/5)*x = -12/35

3x/5 = -12/35

3x = (-12/35)*5, multiplying 7 with both sides

3x = -12/7

x = -12/(7*3)

x = -4/7

The other rational number is -4/7

The difference between rational numbers = -4/7-3/5

                                                                      = (-4*5-3*7)/35

                                                                      = (-20-35)/35

                                                                      = -55/35

                                                                      = -11/7

So the absolute value of it = 11/7

Hence the absolute value of the difference of the given two rational numbers is 11/7.

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Answer 2

the absolute value of the difference of two rational numbers is  $\frac{1}{35}$.

Step-by-step explanation:

Given:

The product of two rational numbers is $\frac{-12}{35}$.

One of them is $\frac{3}{5}$.

To Find:

The absolute value of the difference of two rational number.

Solution:

Let the two rational numbers  are p and q.

As given,The product of two rational numbers is is $\frac{-12}{35}$.

$p\times q =\frac{-12}{35}$     ------- equation no.01.

As given,One of them is $\frac{3}{5}$.

$p=\frac{3}{5}$

Putting the value of p in the  equation no.01. We get.

$\frac{3}{5} \times q =\frac{-12}{35}$

$q=\frac{-12\times 5}{35\times3}$

  $=\frac{-60}{105}$

   $=\frac{-4}{7}$

The absolute value of p $=|\frac{3}{5} |=\frac{3}{5}$

The absolute value of q $=|\frac{-4}{7} |=\frac{4}{7}$

The absolute value of the difference of two rational numbers $=p-q$$=\frac{3}{5} -\frac{4}{7} \\=\frac{21-20}{35} \\=\frac{1}{35}$

     Thus,the absolute value of the difference of two rational numbers is  $\frac{1}{35}$.

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