### Video Transcript

Use partial sums to find 825 plus
165.

In this question, we need to add
together these two three-digit numbers. But the way they have been written
side by side isn’t very helpful. What would be much more helpful is
if we were to write them on top of each other. If we write both our numbers into a
place-value table like this, then we can see straightaway that it’s very easy to
separate both numbers into the hundreds, tens, and ones. Instead of having the numbers all
in one go, we can add them in parts. This is what the idea of partial
sums means. First, let’s add the hundreds. 825 has eight hundreds and 165 has
one hundred. And 800 plus one more 100 makes a
total of nine hundreds.

Onto the tens, 825 contains two
tens, which is worth 20. And 165 contains six tens or
60. Two tens plus six tens equals eight
tens, just the same as saying 20 plus 60 equals 80. And now let’s find the sum of the
ones. Both our numbers end in a five. And we know that five plus five
equals 10. Now we can’t write the whole of the
number 10 in the ones place because a 10 is made up of one ten and zero ones. So we’re going to have to write the
total of our ones in this way as one ten and a zero in the ones place. You have to remember this extra 10
when it comes to adding our tens.

Now that we found the sum of the
three parts of our numbers, the hundreds, the tens, and the ones, we need to put
them all back together again to find the overall total. If we start with the ones column,
we can see that all the digits are zeros. And so our answer is going to
contain zero ones. If we add the digits in the tens
column, we can see eight tens plus one more ten which equals nine tens. And finally, we’ve only got the
digit nine in the hundreds column. We’ve used partial sums to find
that 825 plus 165 equals 990.