Lesson Video: Subtraction of Numbers up to 100,000 Mathematics

In this video, we will learn how to use the most appropriate strategy to subtract numbers with up to five digits.

11:19

Video Transcript

Subtraction of Numbers up to 100,000

In this video, we’re going to learn how to use the most appropriate strategy to subtract numbers with up to five digits.

These children are working on a project about South American volcanoes. They’ve found out that the highest active volcano on Earth is Ojos del Salado, which means salty eyes. It measures 22,615 feet. And the Sierra Nevada Mountain range, which also lies in Argentina and Chile, measures 20,102 feet. They want to find the difference in height between these two volcanoes, so they need to calculate 22,615 subtract 20,102. How could they calculate the answer? Let’s take a closer look at how they calculated their answers.

We could start with 22,615 and subtract 20,000, which leaves us with 2,615. Then we could subtract 100 from 2,615, which would leave us with 2,515. There are no 10s in 20,102; we’ve already subtracted the 1000s and the 100s. So, all that’s left is to subtract the ones. 2,515 subtract two equals 2,513.

Another way to find the difference would be to use column subtraction. Five ones take away two ones leaves us with three ones. One 10 take away no 10s leaves us with one 10. Six 100s take away 100 leaves us with five 100s. There’s nothing to subtract from our two 1000s, which leaves us with two 1000s. Now, we know that two take away two is zero. So, there’s nothing left in the 10 thousands column. So, the difference between 22,615 and 20,102 is 2,513.

It doesn’t matter which strategy we use to find the answer as long as we can work efficiently and accurately. And we can check if the answers are accurate by adding together 20,102 and 2,513. We know that two plus three is five. Zero 10s and one 10 gives us one 10. 100 and five 100s gives us six 100s. We’ve got two 1000s and two in the 10 thousands place 20,102 plus 2,513 is 22,615. We can check our subtraction calculations using addition.

So, we’ve learned that we can use any strategy to subtract and still reach the same result. And we can check our subtraction calculations using addition. Let’s try some questions now where we can think about the most appropriate strategy to use to subtract.

Complete the following: 87,652 subtract 1,550.

There are lots of strategies we could use to calculate 87,652 take away 1,550. Let’s try to subtract mentally. We’re starting with 87,652, and we’re going to subtract 1,550. We could start by subtracting the 1000 in 1,550. 1000 less than 87,000 is 86,000. The thousands digit has decreased by one. 87,652 subtract 1,000 is 86,652. Next, we could subtract the 100s. The hundreds digit in 1,550 is a five, which is worth 500. 86,652 subtract 500 is 86,152. Our hundreds digit has decreased by five because we subtracted 500.

So, we subtracted the thousands, the hundreds. Now, let’s subtract our tens. There are five 10s in 1,550. 86,152 subtract 50 is 86,102. Our tens digit has decreased by five. We had five 10s. Now, we’ve got no 10s. We subtracted the thousands, the hundreds, and the tens. And there are no ones in 1,550, so we don’t have to subtract any ones. 87,652 take away 1,550 is 86,102.

81,252 take away 21,439 equals what.

In this question, we have to choose an appropriate way to calculate 81,252 subtract 21,439. These are both five-digit numbers. It’s quite a tricky calculation to do mentally, so we could subtract using the standard written method or column subtraction. We’re starting with the number 81,252 which we’ve modeled using place value counters, and we need to subtract 21,439. So, let’s start by subtracting the ones.

We’ve got two ones, and we need to subtract nine. So, we’re going to need to regroup. We need to take one of our 10s and exchange it for 10 ones. Now, we’ve got 12 ones, and we can subtract nine. We know that 12 take away nine is three. Now, we can subtract in the tens column. We’ve got four 10s, and we need to take away three. Four 10s take away three 10s leaves us with one 10. We’re going to need to regroup again. We’ve only got two 100s, and we need to subtract four. So, we can take one of our thousands, which is our only 1000 and exchange it for 10 100s. Now, we’ve got 12 100s, and we can subtract four. 12 take away four leaves us with eight 100s.

We’re going to need to regroup again. We’ve got no 1000s, and we need to take away one. So, we can take one of our 10 1000s and exchange it for 10 1000s. Now, we’ve got 10 1000s. We can subtract our one. And we know that 10 take away one is nine. Now, what we need to do is subtract in the 10 thousands column. We’ve got seven 10 thousands left, and we need to subtract two. We know that seven take away two is five. So, 81,252 subtract 21,439 equals 59,813.

Because we were subtracting a five-digit number from a five-digit number, we decided to use the standard written method or column subtraction. And we had to do quite a lot of regrouping. So, we used the place value table and counters to help us keep track. 81,252 take away 21,439 equals 59,813.

35,736 subtract 35,000 equals what.

This is quite an easy subtraction to work out mentally. The number we’re subtracting from is 35,736. We could break this number apart into an amount of thousands. And we know 35,736 has 35 1000s, and the hundreds part of the number is 736. If we subtract 35,000, we’re just left with 736. We used our knowledge of place value to partition our number into an amount of thousands and hundreds. Then, we just subtracted our 35,000. 35,736 take away 35,000 equals 736.

What have we learned in this video? We’ve learned that we can select the most appropriate strategy to subtract. We’ve learned that sometimes a mental strategy is the most appropriate to use, and sometimes it’s more efficient or easier to use a written method.

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