# INVERSE PROPERTY OF MULTIPLICATION WORKSHEET

Problem 1 :

Verify whether 0.4 and 5/2 are multiplicative inverse to each other.

Problem 2 :

If m and n are multiplicative inverse to each other, solve for m in terms of n.

Problem 3 :

If (k + 12) and 1/5 are multiplicative inverse to each other, find the value of k.

Problem 4 :

If (3 - x) and 1/3 are multiplicative inverse to each other, find the value of x.

Problem 5 :

If p + q  =  5/2, p and q are multiplicative inverses, find the value of p.

Problem 1 :

Verify whether 0.4 and 5/2 are multiplicative inverse to each other.

Solution :

If 0.4 and 5/2 are multiplicative inverse to each other, their product has to be 1.

0.4 x (5/2)  =  (4/10) x (5/2)

=  (2/5) X (5/2)

=  1

Because the product is 1, 0.4 and 5/2 are multiplicative inverse to each other.

Problem 2 :

If m and n are multiplicative inverse to each other, solve for m in terms of n.

Solution :

Because m and n are multiplicative inverse to each other, their product is 1.

mn  =  1

Solve for m : Divide each side by n.

m  =  1/n

Problem 3 :

If (k + 12) and 1/5 are multiplicative inverse to each other, find the value of k.

Solution :

Because (k + 12) and 1/5 are multiplicative inverse to each other, their product is 1.

(k + 12) ⋅ 1/5  =  1

(k + 12) / 5  =  1

Multiply each side by 5.

k + 12  =  5

Subtract 12 from each side.

k  =  -7

Problem 4 :

If (3 - x) and 1/3 are multiplicative inverse to each other, find the value of x.

Solution :

Because (3 - x) and 1/3 are multiplicative inverse to each other, their product is 1.

(3 - x) ⋅ 1/3  =  1

(3 - x) / 3  =  1

Multiply each side by 3.

3 - x  =  3

Subtract 3 from each side.

-x  =  0

x  =  0

Problem 5 :

If p + q  =  5/2, p and q are multiplicative inverses, find the value of p.

Solution :

p + q  =  5/2

Subtract p from each side.

q  =  5/2 - p

q  =  5/2 - 2p/2

q  =  (5 - 2p)/2

Because p and q are multiplicative inverses, their product is 1.

pq  =  1

Substitute (5 - 2p)/2 for q.

p ⋅ (5 - 2p)/2  =  1

[p(5 - 2p)] / 2  =  1

Multiply each side by 2.

5p - 2p2  =  2

Subtract 2 from each side.

5p - 2p2 - 2  =  0

-2p2 + 5p - 2  =  0

Multiply each side by -1.

2p2 - 5p + 2  =  0

Solve for p by factoring.

2p2 - p - 4p + 2  =  0

p(2p - 1) - 2(2p - 1) = 0

(2p - 1)(p - 2)  =  0

2p - 1  =  0  or  p - 2  =  0

p  =  1/2  or  p  =  2

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