Question

A student is learning about positive and negative numbers with manipulatives. Each black cube represents + 1 , and each white cube represents − 1 . If there are currently 15 black cubes on the student's desk, how many white cubes must the student add to the desk for the combined value of the cubes to represent 0 ?

Answer 1

15 white cubes

Explanation:

Given

`White\ Cubes = -1`

`Black\ Cubes = +1`

`Number\ of\ Black\ Cubes = 15`

Required

Determine the number of white cubes needed to represent 0

To solve this question, we make use of the following equation.

`Black\ Cubes +White\ Cubes = 0`

If there are 15 black cubes, the the 15 black cubes is worth: +1 * 15

Substitute +1 * 15 for the Black Cubes

`+1 * 15 +White\ Cubes =0`

`+15 +White\ Cubes =0`

Collect Like Terms

`White\ Cubes = 0 - 15`

`White\ Cubes = - 15`

Recall that 1 white cube is worth -1

So, the number of white cubes is:

`Number = (-15)/(-1)`

`Number = 15`

Hence, the student needs 15 white cubes