How to Divide Decimals
Hi, and welcome to this video on dividing decimals. Dividing decimals may not seem like the most useful tool, but it can actually come in handy for several situations in everyday life.
Now, you may be wondering when dividing decimals would ever be useful. Well, let’s say you had $26.84 in your bank account and you wanted to buy gas for your car without going over your budget. Each gallon costs $3.69 and you’d like to tell the attendant how many gallons to put in your car. How many gallons of gas should you ask for?
Or say you are constructing a house, and need pieces of wood that are 4.85 feet long. The local store sells large beams of wood that are 28 feet long. At the store, you wonder: how many pieces of wood can you cut out of each beam?
Having the ability to divide numbers with decimals would help you in these situations.
Let’s start with a basic example. Say you wanted to divide 4.5 by .5
Your first step would be to write out the problem as you would any other long division problem. It should look like this:
When solving this problem, it would be significantly easier to work with whole numbers instead of numbers with decimals.
The simplest way to accomplish this is by multiplying each number in the expression by 10. As a general rule, every time you multiply a number by 10, you are essentially moving the decimal point over one place to the right. If we multiply .5 by 10, we move the decimal point over one place to the right, giving us 5, and if we multiply 4.5 by 10, we move the decimal over one place to the right, giving us 45. Your new expression would look like this:
Now, you would solve 45 divided by 5 as you normally would. Since this is a relatively straightforward problem, we don’t need to go through the steps of long division. 5 times 9 is 45, so we know that 5 goes into 45 nine times, making 9 our final and correct answer.
You may be wondering if we need to do something to modify this answer – after all, we did change both numbers in our expression. How can the answer be correct for our original expression? However, if you pull out your calculator, you will see that dividing 4.5 by .5, our original expression, also yields 9, just like dividing 45 by 5.
Let’s try a more complicated example: we’ll divide 15.75 by 3.5. When you write out the expression, it should look like this:
As mentioned above, the first step is to multiply each number by 10 in order to turn these numbers with decimals into whole numbers. Starting with 3.5, we multiply it by 10 and move the decimal over one place over to the right, giving us 35. However, if we look at the other number in our expression, 15.75, we notice that multiplying it by 10 once does not suffice – that would give us 157.5 – which is still not a whole number. What do we do then, in this instance?
Remember a key rule in dividing numbers with decimals – you need to do the same thing to both numbers in the expression. To make 15.75 a whole number, we need to multiply it by 10 twice, or, you could say, we need to multiply it by 100. That in effect moves the decimal place over two places to the right, giving us 1575.
As we mentioned, we need to do the same thing to both numbers, so now we multiply 3.5 by 10 twice (or 100). We move the decimal over two places to the right, and add a zero to fill the empty place, giving us 350. Now our expression should look like this:
The problem is now long division. 350 does not go into 1, 15, or 157, so we need to guess how many times it goes into 1575. 350 goes into one thousand around three times, so four would be a good estimate for the number of times it goes into 1575. Let’s do some quick multiplication to double check:
4 times zero is zero, 4 times 5 is 20, write down the zero and carry the 2. 4 times 3 is 12, add the 2 which gives us 1400 – which is the best fit we’re going to get into 1575. Write 4 above the last 5 in 1575 and let’s put our 1400 underneath 1575. We subtract the two, leaving us with 175.
350 does not go into 175, so we place a decimal after 1575, add a zero, and bring it down to the 175. Be sure to add a decimal after the 4 on the top as well.
Now we divide 1750 by 350 with some trial and error. Given that we saw before that 350 times 4 was 1400, we can see that 350 times 5 is going to give us exactly 1750, which means that we add a 5 right after the decimal we placed next to the 4. This gives us a final answer of 4.5
While dividing decimals may have seemed daunting at first, remember that it is essentially the same as regular long division. Don’t forget the strategy we discussed in order to turn our numbers with decimals into whole numbers: multiply both numbers in the expression by a multiple of ten to move the decimal point over as many times as necessary. Treat both numbers the exact same way and you’ll be sure to end of up with the correct answer.
I hope this video was helpful for you! See you next time!