SOLUTION: My homework says "Show that the number is a rationsl by righting it in a/b form. Then give the multiplication inverse and the additive inverse of the number" how would you do that?

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Question 260829: My homework says "Show that the number is a rationsl by righting it in a/b form. Then give the multiplication inverse and the additive inverse of the number" how would you do that?
1. -4/7
2. 8 2/5
3. -1 1/2
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the product of a number and it's multiplicative inverse is equal to 1.

see http://www.mathwords.com/m/multiplicative_inverse_of_a_number.htm

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

see http://www.mathwords.com/a/additive_inverse_number.htm

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.


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
If this is true then you should throw out your book.
My homework says "Show that the number is a rational by righting it in a/b form.
Righting means to fix something that is wrong.
Writing is to put down on paper.