Video: Solving Word Problems by Subtracting Two Decimal Numbers from an Integer

If the total amount of cheese a trader has is 48 kg, and he sold 5.62 kg in the first day and 17.825 kg in the day after, find how many kilograms he has left rounded to the nearest hundredth.

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Video Transcript

If the total amount of cheese a trader has is 48 kilograms, and he sold 5.62 kilograms in the first day and 17.825 kilograms in the day after, find how many kilograms he has left rounded to the nearest hundredth.

This problem is one long sentence. So it might look complicated. Just like the cheese, let’s break it up into smaller chunks to try to understand it. The total amount of cheese that the trader begins with we’re told is 48 kilograms. We’re then told that he sells 5.62 kilograms the first day. So this amount here is the amount of cheese that’s left after the first day. We’re then told that the trader sells 17.825 kilograms the day after. So we can see that this amount here is now the amount he has left. And so our problem is asking us to calculate this amount.

How can we find the answer? Well, there are two ways of doing this. The first is to start with 48, then subtract one of the numbers, then subtract the other number. So we could find the answer by subtracting twice. Our second method could be to add the two amounts we need to subtract to find out the total amount we need to subtract and then just take away this total figure from 48. In this method, we only subtract once. Let’s use our second method to find the answer. So step one is to add the two amounts of cheese that the trader sells on both days. What is 17.825 kilograms plus 5.62 kilograms?

Let’s use column addition to find the answer. First of all, we write both numbers on top of each other. Notice, how the decimal points are in line with each other. By doing this, we make sure that all the ones digits are in the ones place. All the tenths digits are in the tenths place and so on. Also notice that our second number 5.62 doesn’t have any digits in the thousandth column. So as a placeholder we could write a zero in there. Make sure our decimal point is in the answer. And let’s add each column.

Five thousandths plus zero thousandths is five thousandths. Two hundredths plus two hundredths is four hundredths. Eight tenths plus six tenths is 14 tenths. We need to exchange 10 of those and put them in the ones column. Seven ones plus five ones is 12 plus the one underneath is 13. So we can write three ones and exchange 10 ones into the ten column. One ten plus another one ten underneath is two tens. And so the total amount of cheese that the trader sells over the two days is 23.445 kilograms. So step two is to take the total amount of cheese that the trader has to begin with and to subtract the total amount that he sells, 48 subtract 23.445.

Let’s use vertical subtraction. Again, we write both numbers on top of each other. We can write in a decimal point and some zeros as placeholders because 48.000 is still the same as 48. We need to do some exchanging before we begin. We can take one of our ones. So we’ve now got seven ones and exchange it for 10 tenths. So we now have 10 tenths. We can then take one of our tenths, so we now have nine tenths, and exchange it for 10 hundredths. We now have 10 hundredths. Finally, we can take one of our hundredths, so we now have nine hundredths, and exchange it for 10 thousandths. So we now have 10 in the thousandths column.

By doing this we can now subtract each of the columns. Make sure we write the decimal point before you begin. 10 thousandths subtract 5 thousandths is 5 thousandths. Nine hundredths subtract 4 hundredths is 5 hundredths. Nine tenths subtract four tenths is five tenths. Seven ones take away three ones is four ones. And finally, four tens take away two tens is two tens. And so the answer is 24.555. And so we can say that the trader has 24.555 kilograms left.

But there’s one final part to our problem. We need to round this number to the nearest hundredth. 24.555 comes exactly in the middle between 24.55 and 24.56. What is the nearest hundredth we should round to? Should we round a number up or down? Because the number of thousandth is five and the number 24.555 is exactly in the middle, we’re going to round it upwards. We always round numbers that are in the middle upwards. And so rounded to the nearest hundredth, the trader will have 24.56 kilograms of cheese left.

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