# The sum of three consecutive odd numbers is -21, how do you find the smallest number?

Feb 11, 2016

$- 5$

#### Explanation:

First things first, we have to analyze the question for clues. The question is: the sum of three consecutive odd numbers is -21, how do you find the smallest number?

Let's take it apart. SUM means addition. So we'll be adding $3$ numbers together.

CONSECUTIVE mans that the numbers come right after each other, like $3 , 4 , 5$.

ODD. Okay, that mans that the numbers have to be odd. So the list would go more like $3 , 5 , 7$.

The negative in $\textcolor{red}{-} 21$ says that the numbers will be negative, because you cannot add positive numbers to get a negative number, so it has to be caused by negative values.

I think we have all the information now, so let's put it together. I'm going to start by putting in the numbers in order, starting at $- 1$ and going on from there, skipping the even numbers. So we start out with $\left(- 1\right) + \left(- 3\right) + \left(- 5\right) =$... $- 9$. So that didn't work. Let's try with $\left(- 3\right) + \left(- 5\right) + \left(- 7\right)$. This equals... $- 15$. Let's try another one. $\left(- 5\right) + \left(- 7\right) + \left(- 9\right)$. This equals... $\textcolor{red}{- 21}$! We got it! Let's just double check that it meets all the requirements, just to make sure.

Is it $3$ consecutive odd numbers that add up to $- 21$? Yep, yep, yep, and yep. We're good to go!

So, which is the smallest number out of $- 5 , - 7 , - 9$? Well, the smallest is the number closest to zero on a numberline, and out of all three, $- 5$ is the closest to $0$. Great job!