Question 260829
the product of a number and it's multiplicative inverse is equal to 1.


see <a href = "http://www.mathwords.com/m/multiplicative_inverse_of_a_number.htm" target = "_blank">http://www.mathwords.com/m/multiplicative_inverse_of_a_number.htm</a>


the sum of a number and it's additive inverse is equal to 0.


see <a href = "http://www.mathwords.com/a/additive_inverse_number.htm" target = "_blank">http://www.mathwords.com/a/additive_inverse_number.htm</a>


to find the multiplicative inverse of a number, you take it's reciprocal.


you take it's reciprocal by dividing the number into 1.


to find the additive inverse of a number, you take it's opposite.


to find it's opposite, you reverse the sign.


example:


multiplicative inverse of 5 is 1/5 because 1/5 * 5 = 1


additive inverse of 5 is -5 because 5 + (-5) = 0


problem number 1:


number is -4/7


multiplicative inverse is -7/4 because -(4/7) * (-7/4) = 1


we got that by taking (-4/7) and dividing it into 1 to get:


1/(-4/7)


if we multiply numerator and denominator of that expression by 7/7, we get:


7/-4 = (-7/4)


additive inverse is 4/7 because -(4/7) + (4/7) = 1


problem number 2:


number is 8 + 2/5


convert this number to an improper fraction to get:


40/5 + 2/5 = 42/5


multiplicative inverse is 5/42 because 5/42 * 42/5 = 1


additive inverse is -42/5 because 42/5 + (-42/5) = 0


problem number 3:


-1 1/2 is the same as -1 - 1/2.


convert to improper fraction to get:


-2/2 - 1/2 = -3/2


multiplicative inverse is -2/3 because -(3/2) * (-(2/3) = 1


additive inverse is 2/3 because -2/3 + 2/3 = 0


note:


improper fraction is a fraction in a/b form where the numerator is greater than the denominator.