204k views
1 vote
C = 12d for d
mathhhhhhhhhhhhhhhh

User Sean
by
8.0k points

1 Answer

3 votes

Answer:

d = c/12

Explanation:

You want to solve c = 12d for d.

Division property

The division property of equality tells you that an equation remains true if both sides of it are divided by the same (non-zero) number.

Here, we can divide both sides of the equation by 12 to find d:

c = 12d

c/12 = (12d)/12 . . . . . . divide both sides by 12

c/12 = (12/12)d . . . . . . rearrange factors

c/12 = 1·d . . . . . . . . . . a number times its inverse is 1

c/12 = d . . . . . . . . . . . 1 times d is d

d = c/12 . . . . . . . . . . . symmetric property of equality

__

Additional comment

You know this already. If a whole pizza is 12 slices, then 1 slice is 1/12 of the pizza.

We use various properties of equality, of operations, and of numbers to ensure that the algebra makes logical sense. These tell us a number multiplied by its inverse is 1 (12/12 = 1), and 1 times anything does not change the value (1d = d). We can write the sides of an equality in either order and it is still the same equality: a = b ⇔ b = a. We also know that division is the same as multiplying by the reciprocal: (12÷12) = 12(1/12), and that factors can be multiplied in any order: (12d)(1/12) = (12)(1/12)d = (12/12)d.

The main rule is that whatever you do to one side of the equation must also be done to the other side (÷12 here).

<95141404393>

User Maxime
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories