Whole number division resulting in decimal quotient

Dividing three digit numbers

When you divide numbers in the hundreds, which we call three digit numbers, sometimes you'll find there is no remainder, and you can divide equally. An example of this is $624\div6$624÷​6, where we can break our problem into smaller problems. Here, we might solve $600\div6=100$600÷​6=100 and then $24\div6=4$24÷​6=4, which means we know that $624\div6=104$624÷​6=104.

We could also write this number as $104.0$104.0 if we need to express it as a decimal. What do we do though, when we end up with remainders? Let's find out.

Division with remainders

In our earlier example, we had the problem $624\div6=104$624÷​6=104.

Imagine we were putting $624$624 watermelons into$6$6 crates. We could put $104$104 watermelons into each crate. But if we had $627$627 watermelons, we will have $3$3 left over. You might write this as $104r3,$104r3, or $104\frac{3}{6}$10436​. This is known as division with remainder. Now we will look at how to write an answer like this by expressing it as a decimal.

It's a good chance to refresh your memory on how to convert fractions to decimals too. Those $3$3 leftover watermelons represent half, or $\frac{1}{2}$12​, so we express this as $0.5$0.5 in decimal form. In the next video we'll explore this further. We can use visual examples to help us imagine dividing or sharing into groups.

Short division

When we use short division, we use a mathematical expression to represent our division or sharing. When we work through our problem, we think of the place value of each digit. So, $824$824 has $8$8 hundreds, $2$2 tens and $4$4 units. Working through our problem, from left to right, we use regrouping of any remainders, until we get to the end. For our remainder at the end, we need to change our fraction to a decimal. In this next video, we look at how to do that. Money is a great help for us since we can use the facts that $1$1 dollar has $100$100 cents. This can help us when we are working with hundredths!

One problem, many ways

Is there one method you find easier? While we've looked at some ways to solve these problems, you could also use long division to solve division with a remainder expressed as a decimal. Perhaps you could try one problem a few different ways, to see which you prefer.

Practice questions

Question 1

QUESTION 2

QUESTION 3

We have looked at some division problems with numbers in the hundreds, where a decimal answer is needed. Now we can look at problems that have numbers in the thousands, and solve them using many of the same processes.

In Video 1, you can see we have a remainder, which we write as a fraction. So, if we are solving $2303$2303 divided by $4$4, we would express our remainder as $\frac{3}{4}$34​. Next, we find an equivalent fraction in tenths or hundredths, and then we can express that as a decimal. This process is what we do each time we have a remainder to write as a decimal.

In our second video, we look at short division, which is just another way to solve our division problem. In our example, we can't share our units out evenly, so we see just how important our zero place holder is. We can then look at our remainder as a fraction, and use an equivalent fraction in hundredths, which then allows us to write our remainder as a decimal.

Practice Questions

Question 4

QUESTION 5

QUESTION 6

Dividing with remainders

When we divide numbers, we are essentially sharing. Sometimes we can share equally so that there are no remainders. Other times, we do have remainders, and need to express our answer as a decimal. We have looked at how to solve division problems that result in decimal answers when we divide by a one-digit number.

Strategies to help us

Now let's imagine you are dividing by a two-digit number, such as $315\div25$315÷​25. We know that $100$100 is $4\times25$4×25 so $300$300 is $3$3 groups of $4\times25$4×25, or $12$12 groups of $25$25. There is still $15$15 left though, and we can't make a group of $25$25 from $15$15. We can, however, express $\frac{15}{25}$1525​ as a decimal.

In our third video, we work through an example like this, as well as using the strategy of dividing by $10$10, to help when we need to divide by $20$20. Dividing by $10$10 is something we use often, and a great strategy to help us here.

Short Division

Solving by short division uses some of these same approaches, but we also use place value to help us. When we share, we start with the highest value digit, and move to the right. When we run out of whole numbers, we simply keep going with tenths, hundredths etc. Let's see how we can share  $$540$540 among $25$25people, using short division. If you feel up to it, you could even solve the same problem using long division of two digit numbers!

 

Practice questions

Question 7

QUESTION 8

QUESTION 9

Using things we know

Just like dividing numbers in the hundreds that result in a decimal answer, we have strategies that can help us multiply larger numbers as well. The first video uses two strategies to solve $2750\div20$2750÷​20. First, we solve $2750\div10$2750÷​10, and then we can take half of our answer, using partitioning to solve the rest of our problem, breaking it into smaller problems.

Let's take a look at how we do this.

How many groups of?

We can also partition our number, and find out how many groups of our divisor we have. If we are dividing by $25$25, we can look at our thousands and hundreds, and find out how many groups of $25$25 we have. This then helps us solve our division problem, with any remainder left at the end, which we change to decimals. The next video shows you how we can take this approach.

Short division

Finally, we solve $2750\div20$2750÷​20 again, but this time using short division. By remembering place value, we can divide each digit, working from left to right. Instead of thinking we can't share any further, we move from units to tenths, and find we can!

 

Practice Questions

Question 10

QUESTION 11

QUESTION 12