Sure! Here are some exercises to practice the inverse and identity properties:
1. For each of the following numbers, determine its inverse:
a) 5
b) -3
c) 1/4
d) 0
e) -6
2. Find the multiplicative or additive identity for each of the following operations:
a) Addition
b) Subtraction
c) Multiplication
d) Division
3. Simplify the following expressions using the inverse and identity properties:
a) 7 + (-7)
b) 5 - 0
c) 3 * (1/3)
d) 2 / 1
4. Determine if the given numbers are inverse of each other:
a) 4 and -4
b) 7 and -7
c) 0.5 and -2
d) -3 and -1/3
5. Write the inverse property for addition and multiplication.
Solutions:
1.
a) The inverse of 5 is -5.
b) The inverse of -3 is 3.
c) The inverse of 1/4 is 4.
d) The inverse of 0 does not exist, as the concept of division by zero is undefined.
e) The inverse of -6 is 1/6.
2.
a) The additive identity for addition is 0.
b) The additive identity for subtraction is 0.
c) The multiplicative identity for multiplication is 1.
d) The multiplicative identity for division is 1.
3.
a) 7 + (-7) = 0 (using the inverse property of addition)
b) 5 - 0 = 5 (using the identity property of subtraction)
c) 3 * (1/3) = 1 (using the inverse property of multiplication)
d) 2 / 1 = 2 (using the identity property of division)
4.
a) Yes, 4 and -4 are inverses of each other.
b) Yes, 7 and -7 are inverses of each other.
c) No, 0.5 and -2 are not inverses of each other.
d) No, -3 and -1/3 are not inverses of each other.
5.
The inverse property of addition states: For any number a, its inverse (additive inverse) exists and is equal to -a.
The inverse property of multiplication states: For any non-zero number a, its inverse (multiplicative inverse or reciprocal) exists and is equal to 1/a.
Inverse and identity properties practice
2 answers
I just need the answer for number 2
−310⋅ =1
−310⋅ =1