Question

If two quantities are equal to the same quantity, then they are ____ to each other: if a = b and b = c, then _____

Answer 1

If two quantities are equal to the same quantity, then they are equal to each other.

Step-by-step explanation:

If two quantities are equal to the same quantity, then they are equal to each other.

For example, if we have the equations a = b and b = c, then we can conclude that a = c.

This is called the transitive property of equality.

Answer 2

If two quantities are equal to the same quantity, then they are equal to each other: if a = b and b = c, then a = c

SOLUTION:

Given that, two quantities are equal two to the same quantity.

Suppose the two quantities be x and y

Now, imagine that, both x and y are equal to a third quantity.

Let the third quantity be z.

Then, according to our assumption x = z and y = z

Then, we can write it as x = and z and z = y ⇒ x = y

Which means the first two quantities are equal.

Now, we are also given that, a = b and b = c, then just like above assumption, here a equals to c i.e. a = c

Hence, If two quantities are equal to the same quantity, then they are equal to each other: if a = b and b = c, then a = c