Add the biggest number and the smallest number in this list. 42065, 39180, 85633, and 57636.
In this problem, we need to do two things, and we need to do them accurately in order to get the right answer. The first thing we need to do is to find the biggest and the smallest numbers out of the four numbers that we have in the list. Then, when we’ve done that, we’re told that we have to add them together.
First, let’s try to identify which number is the largest and which number is the smallest. We can use a place value grid to do this. And writing the numbers out vertically can help us to compare them. Here are the five columns that we need, ten-thousands, thousands, hundreds, tens, and ones. So, first of all, we can complete our place value grid by writing in each number, 42065, 39180, 85633, and 57636.
All of our numbers have five digits. And the way we compare them is to start with the digit with the most value first. So, we need to compare all of the digits in the ten-thousands place. The digit with the greatest value is eight. All of the other ten-thousands digits are less than eight, so this number is the biggest number. 85633 is the biggest number out of the four.
Let’s carry on comparing the ten-thousands digits. The smallest digit in the ten-thousands place is three. All of the other numbers are greater than three lots of 10000. And so, we know the smallest number out of our four numbers is 39180. Now that we’ve identified the biggest and the smallest numbers, we need to add them in order to solve the problem.
We can do this using column addition. And so, we’re going to start by adding the ones and work from right to left. Three ones plus zero ones equals three ones. Three 10s plus eight 10s equals 11 10s. 11 10s are the same as one 10 and we can exchange the remaining 10 10s for 100. Now, we can add the digits in the hundreds place. Six 100s plus one 100s equals seven 100s. Remember, we exchanged 100 as well. That takes us to eight 100s.
Five 1000s plus nine 1000s equals 14 1000s. So, we can write the digit four in the thousands column and exchange 10 1000s for one lot of 10000. Finally, eight lots of 10000 plus three lots of 10000 equals 11 10000s, plus the one that we’ve exchanged, 12 lots of 10000s, which is the same as 120000.
We found the answer by first writing all of the numbers vertically. We put them in a place value grid, which helped us to compare each of the columns. We started by comparing the digits in the column with the greatest value. We thought this would be a way to spot the biggest and the smallest numbers.
The number with the largest value of ten-thousands was the largest number. And the number with the smallest value of ten-thousands was the smallest number. We then wrote these two numbers out vertically again. This time so that we could add them using column addition. And so, the total of the biggest and the smallest numbers in the list is 124813.