Decimals
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KeyStage 2 Upper

Long division - divide decimals by 1 digit number

Lesson

Dividing decimals

We've seen how we can divide whole numbers using long division, and how we set our work out going down the page. We show each step, so that we can see what we've allocated, or shared, and what we have left.

With decimals, it's exactly the same process! The only difference is that our digits may be in columns with tenths, hundredths etc., rather than units, tens and hundreds. Let's see how we can solve them, first by thinking about what our answer might be.

In Video 1, we start with a simple example, dividing by $2$2. This allows us to think about estimating our answer, since dividing by $2$2 is the same as finding half of a number.

Dividing decimals with long division

Next we'll work through the same problem, using long division. Again, we'll divide our decimal by $2$2, so that we can focus on the process, without worrying about different times tables. By using this approach, you can work through the process, and get the hang of it.

Here's Video 2, showing you how we solve the problem, using long division. Writing our answers and workings under the correct place needs to be done, just like when we add or subtract decimals.

Dividing a decimal by a larger number

Okay, now we're ready to tackle a problem where we know the distance travelled over $9$9 days, but need to work out what the average for $1$1 day would be. Using long division means we can do just that. Let's work through that problem in Video 3. 

Did you know?

You could also solve the problem in Video 2 using whole numbers. By writing $65.09$65.09 km in metres, you have a whole number! Why not try this, and see if you can compare your answer in metres to the one in kilometres from Video 2.

 

Worked Examples

Question 1

We want to find $71.2\div4$71.2÷​4

  1. Choose the most reasonable estimate for $71.2\div4$71.2÷​4

    $18$18

    A

    $180$180

    B

    $1.8$1.8

    C

    $0.18$0.18

    D
  2. Complete the long division to find $71.2\div4$71.2÷​4

      $\editable{}$ $\editable{}$ $.$. $\editable{}$
    $4$4   $7$7 $1$1 $.$. $2$2
      $\editable{}$  
      $\editable{}$ $\editable{}$  
      $\editable{}$ $\editable{}$  
      $\editable{}$   $\editable{}$
      $\editable{}$   $\editable{}$
      $\editable{}$

Question 2

We want to find $9.92\div8$9.92÷​8

  1. Choose the most reasonable estimate for $9.92\div8$9.92÷​8

    $10$10

    A

    $0.01$0.01

    B

    $1$1

    C

    $0.1$0.1

    D
  2. Complete the long division to find $9.92\div8$9.92÷​8

      $\editable{}$ $.$. $\editable{}$ $\editable{}$
    $8$8   $9$9 $.$. $9$9 $2$2
      $\editable{}$  
      $\editable{}$   $\editable{}$  
      $\editable{}$   $\editable{}$  
      $\editable{}$ $\editable{}$
      $\editable{}$ $\editable{}$
      $\editable{}$

Question 3

We want to find $38.72\div8$38.72÷​8

  1. Choose the most reasonable estimate for $38.72\div8$38.72÷​8

    $50$50

    A

    $0.05$0.05

    B

    $0.5$0.5

    C

    $5$5

    D
  2. Complete the long division to find $38.72\div8$38.72÷​8

        $\editable{}$ $.$. $\editable{}$ $\editable{}$