Question

The variables a through h all represent different numbers. Mentally find numbers that make each equation true

3/5 x 5/3 = a3 5 ⋅ 5 3 = a
7 x b = 17 ⋅ b = 1
c x d = 1c ⋅ d = 1
-6 + 6 = e- 6 + 6 = e
11 + f = 011 + f = 0
g + h = 0g + h = 0

Answer 1

To solve for variables a through h, the reciprocals multiply to 1, a pair of numbers add to 0, and some have straightforward answers such as e = 0 when summing -6 and 6.

Step-by-step explanation:

The students question involves finding values for variables a through h that satisfy a set of equations. Let's go through each of the equations in the question step-by-step:

• 3/5 x 5/3 = a: This is a multiplication of reciprocals, which will always equal 1. So, a = 1.
• 7 x b = 17: To find b, we divide 17 by 7, which is approximately 2.4286.
• c x d = 1: This suggests that c and d are reciprocal numbers. An example pair could be 2 and 1/2, so c=2, d=1/2.
• -6 + 6 = e: Adding -6 and 6 gives us 0, so e = 0.
• 11 + f = 0: Solving for f would result in f = -11.
• g + h = 0: If g and h must add to 0, we can choose any number for g and the opposite for h. An example is g=5, h=-5.