1. Find the additive and multiplicative inverses for each of the following.
(a) 8
(b) 3 1/2
(c) 1/4
I will do one.
b) additive inverse: -3 1/2
multiplicateve inverse = inverse of 7/2 or 2/7
To find the additive inverse of a number, you need to find the number that, when added to the original number, gives you zero. The additive inverse of a number "a" is denoted as "-a".
The multiplicative inverse of a number is the reciprocal of that number. It is denoted as "1/a" or "a^-1" and when multiplied with the original number, gives you the multiplicative identity, which is 1.
Now, let's find the additive and multiplicative inverses for each of the given numbers:
(a) 8:
To find the additive inverse of 8, we need to find a number that, when added to 8, gives us 0. This number is -8. So, the additive inverse of 8 is -8.
To find the multiplicative inverse of 8, we need to find the reciprocal of 8, which is 1/8. So, the multiplicative inverse of 8 is 1/8.
(b) 3 1/2 (or 7/2):
To find the additive inverse of 3 1/2, we need to find a number that, when added to 3 1/2, gives us 0. This number is -3 1/2 (or -7/2). So, the additive inverse of 3 1/2 is -3 1/2 (or -7/2).
To find the multiplicative inverse of 3 1/2, we need to find the reciprocal of 3 1/2. Inverting a fraction means swapping the numerator and denominator. So, the reciprocal of 3 1/2 is 2/7. So, the multiplicative inverse of 3 1/2 is 2/7.
(c) 1/4:
To find the additive inverse of 1/4, we need to find a number that, when added to 1/4, gives us 0. This number is -1/4. So, the additive inverse of 1/4 is -1/4.
To find the multiplicative inverse of 1/4, we need to find the reciprocal of 1/4. Inverting a fraction means swapping the numerator and denominator. So, the reciprocal of 1/4 is 4/1 (or simply 4). So, the multiplicative inverse of 1/4 is 4.
To summarize:
(a) Additive inverse of 8: -8
Multiplicative inverse of 8: 1/8
(b) Additive inverse of 3 1/2 (or 7/2): -3 1/2 (or -7/2)
Multiplicative inverse of 3 1/2 (or 7/2): 2/7
(c) Additive inverse of 1/4: -1/4
Multiplicative inverse of 1/4: 4