Video: Arranging Integers in Descending Order

Order the following from greatest to least: 6, 18, −10, 1, |−16|.

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Video Transcript

Order the following from greatest to least: six, 18, negative 10, one, and the absolute value of negative 16.

What does it mean to order numbers from greatest to least? This means you’re gonna order your numbers left to right, where the largest numbers on the left and as you go to the right the numbers become smaller and smaller and smaller until your final number on the right is your smallest number.

So essentially, you’re listing your numbers left to right or just to smallest. It’s also important to understand the absolute value sign. The absolute value sign actually makes numbers positive, so the negative 16 is really a positive 16. So let’s go ahead and relist our numbers.

We have six, 18, negative 10, one, and the absolute value of negative 16 is truly 16. Let’s go ahead and list these on a number line to help us visualize what we’re actually doing.

As you go to the right on a number line, numbers become larger. As you go to the left, numbers become smaller. So as you can see here, 18 is our largest number and negative 10 is our smallest number. So if we’re going to list our numbers from greatest to least, our greatest number is 18, so this is the number we should begin with.

Now we must move left on the number line, so our numbers become smaller and smaller until we’re at our smallest number of negative 10, so the next number we should list is 16.

Although 16 is the correct value, they asked us to order the following numbers: six, 18, negative 10, one, and the absolute value of negative 16. So instead of writing 16, let’s write the absolute value of negative 16 instead.

Now we keep moving down the number line to the left, so our next number will be six, then one, and now finally our last number, our smallest number, is negative 10.

So here we have our numbers in order from greatest to least, where 18 is our largest number, the greatest number, and negative 10 is our smallest number, the least number. So our final answer is 18, then the absolute value of negative 16, then six, then one, and the negative 10.