What is 725 divided by 29?
We know this is a division question by the way that the question has been laid out. We’re being asked to find how many 29s are in 725.
Remember, when we use this method of division, we look at each digit from left to right. And we keep dividing by this number here, which we call the divisor. But notice that, in this question, we’re dividing by a two-digit number, 29. And so we can’t ask how many 29s are in seven. It’s too small.
So we need to look at the first two digits instead. How many 29s are in 72? Can we make 72? How close can we get to 72 if we can’t make 72 itself? We know there’s definitely one lot of 29 and 72, but are there two lots? What is 29 multiplied by two?
Here’s where we can use facts we already know to help us. 29 is only one away from 30. And we know that 30 lots of two equals 60. So 29 twos is one less lot of two. So we can take away two to give us the answer 58. 29 multiplied by two equals 58. So there are two lots of 29 in 58. So we know there are definitely two lots of 29 in 72, but are there three lots?
Well, we can see that if we add 20 to 58, it becomes 78, which is already too large. So we can only fit two lots of 29 into 72. So let’s write the number two at the top.
We said that two lots of 29 equals 58. And now let’s subtract 58 from 72 to find out what the remainder is. How much do we have left? Well, the difference between 72 and 58, or the remainder, is 14. We need to keep dividing. How many 29s are in 14?
Well, 14 is too small. We need to add another digit like before to help us keep dividing by 29. So let’s bring the five digit down to give us 145. How many 29s are in 145?
Well, the 29 times table is not something that we’ll have memorised. So we need to use known facts again to help us. Are there any multiplications where we multiply by 29 that we could use to help us? What about 29 times 10? Multiplying by 10 is always quite quick to do. How close can we get to 145?
When we multiply by 10, the digits shift one place to the left, as a 29 lots of 10 is 290. This is too large. We want to get as close to 145 as possible. But can we see something interesting about the numbers 290 and 145?
145 is half of 290. And so the number of 29s in 145 must be half the number of 29s in 290. Instead of 10 29s, there must be five 29s in 145. And so we can write the answer 145 divided by 29 equals five at the top.
Just to end neatly, let’s take away five lots of 29 or 145 to show that there’s no remainder. 145 take away 145 leaves us with zero. There’s nothing left over to divide.
So how did we find our answer? We knew that the way the calculation had been written we had to use long division, which is a little bit like short division. But we need to think a little bit more carefully in this case because we were dividing by a two-digit number.
We didn’t know our 29 times table off by heart. So to help us divide by 29, we used known facts to help us. We used things we already knew to help us find things we didn’t. And each time, we subtracted the multiple of 29 to find out how much we had left. And so what is 725 divided by 29? The answer is 25.