Look at the expression 76 take away 39. Choose a strategy and solve the expression. Hint: you can use the vertical column method.
In this problem, we’re given an expression, 76 take away 39. And we’re told to solve it by choosing a strategy. What are some of the strategies we could use? We could sketch a number line, start with 76 and count back 39. Another strategy is that we could partition 39 into 30 and nine and subtract each part separately.
We could even recognise that 39 is near to 40 and use this to help by subtracting 40, and then adjusting our answer. These are just some of the strategies that we could choose. And each one, if we use them accurately, will give us the correct answer. But as part of our problem, we’re given a hint. So, let’s take the hint and use the vertical column method as it suggests.
This method is called the vertical method because the numbers are written vertically, or on top of each other. This helps us to see the place value of each digit. The 10s are on top of each other. And the ones are on top of each other. And we start by looking at the ones column.
In the ones column, we can see that we need to work out six take away nine. What are six ones subtract nine ones? Well, we can’t do this. Because the number of ones we want to take away is greater than the number of ones we already have. Is it possible?
Well, it is possible because we have to remember we’re subtracting nine from a much larger number, 76. And we can subtract nine ones from 76. We just have to rearrange it a little. So, what can we do? Well, we can take one of the 10s from the tens column and exchange it for 10 ones. Instead of seven 10s, we now have six 10s. And let’s exchange it for 10 ones. Instead of six ones, we’ve now have got 16 ones. 60 and 16 is exactly the same number as 76. We’ve just partitioned it differently by exchanging one ten for 10 ones.
So, now we have enough ones to take away nine ones. 16 take away nine. 16 take away nine equals seven. Now we subtract the tens column. What are six 10s take away three 10s? Remember, we’re starting with six 10s because we’ve already exchanged one ten for 10 ones. Six 10s take away three 10s leaves us with three 10s. And so, by using the vertical column method, we found that 76 take away 39 equals 37. There is a second part to this problem.
Check your answer using the inverse operation. Remember, the inverse means the opposite. Which addition expression shows the opposite calculation you need to carry out?
What this second part of the problem is reminding us is that we can always work backwards to check our answers. In our original calculation, we started with 76. We subtracted 39. And we were left with an answer of 37. So, to check our answer, we need to move in the opposite direction.
Start with 37. Add 39 because we’re moving in the opposite direction. And if we calculated our first answer correctly, we should find that the answer to the addition is 76. And so, the addition expression we need to use is 37 plus 39. And we can use vertical addition this time to add those two numbers together and see that we do get 76. And so, our original calculation must have been correct.