**Product of Additive Inverse and Multiplicative Inverse of (-3)/7**

To find the product of the additive inverse and multiplicative inverse of the rational number (-3)/7, we first need to understand what these terms mean.

**Additive Inverse:**
The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. In other words, the additive inverse of a number "a" is denoted as "-a" and satisfies the equation a + (-a) = 0.

**Multiplicative Inverse:**
The multiplicative inverse of a number is the number that, when multiplied by the original number, gives a product of one. In other words, the multiplicative inverse of a number "a" is denoted as 1/a and satisfies the equation a * (1/a) = 1.

Now, let's find the additive inverse and multiplicative inverse of (-3)/7.

**Finding the Additive Inverse:**
The additive inverse of (-3)/7 is the number that, when added to (-3)/7, will give a sum of zero. Therefore, the additive inverse of (-3)/7 is (3)/7. We can verify this by adding (-3)/7 and (3)/7:
(-3)/7 + (3)/7 = 0/7 = 0

**Finding the Multiplicative Inverse:**
The multiplicative inverse of (-3)/7 is the number that, when multiplied by (-3)/7, will give a product of one. Therefore, the multiplicative inverse of (-3)/7 is (-7)/3. We can verify this by multiplying (-3)/7 and (-7)/3:
(-3)/7 * (-7)/3 = 21/21 = 1

**Finding the Product:**
To find the product of the additive inverse and multiplicative inverse of (-3)/7, we multiply (3)/7 and (-7)/3:
(3)/7 * (-7)/3 = -21/21 = -1

Therefore, the product of the additive inverse and multiplicative inverse of (-3)/7 is -1.

Explanation:-
In Additive inverse we have to add something to the number that gives us zero. So simplest way of finding is that use a (-) sign if there is no such sign and if there is (-) sign then just remove it.

In Multiplicative inverse we have to multiply something with the given number that gives us 1. So simplest way of finding it is that reverse the number. Don't remove any (-) sign or add it , just reverse the number.

So,
Additive inverse of -3/7 is 3/7 .
Multiplicative inverse of -3/7 is -7/3 .

Hope you have well understood.