Reciprocal of a fraction:
The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. For example, the reciprocal of the fraction a/b is b/a.

Sum of fractions:
The sum of two fractions is obtained by finding a common denominator and adding the numerators. For example, the sum of the fractions a/b and c/d is (ad + bc)/bd.

Dividing the reciprocal of the sum:
To divide the reciprocal of a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. For example, to divide the reciprocal of a/b by c/d, we multiply (a/b) * (d/c).

Given fractions:
The given fractions are -4/5 and 2/5.

Reciprocal of the sum:
To find the reciprocal of the sum of -4/5 and 2/5, we first need to find the sum of these fractions and then take the reciprocal of the sum.

Sum of fractions:
The sum of -4/5 and 2/5 is (-4 + 2)/5 = -2/5.

Reciprocal of the sum:
The reciprocal of -2/5 is obtained by interchanging the numerator and the denominator, which gives us -5/2.

Dividing the reciprocal by the sum:
To divide the reciprocal of the sum (-5/2) by the sum (-2/5), we multiply (-5/2) * (-2/5).

Multiplicative identity:
The multiplicative identity is the number 1. When we multiply any number by 1, the result is the same number. In other words, 1 is the identity element for multiplication.

Verifying the result:
To check if the quotient obtained after dividing the reciprocal of the sum (-5/2) by the sum (-2/5) is the multiplicative identity, we need to multiply the quotient by the sum and see if we get 1 as the result.

(-5/2) * (-2/5) = (5/2) * (2/5) = (5 * 2) / (2 * 5) = 10/10 = 1.

Therefore, the quotient that we obtained is indeed the multiplicative identity 1.

In conclusion, the quotient that we get after dividing the reciprocal of the sum of -4/5 and 2/5 by the sum is the multiplicative identity 1.

False