Decimals
NZ Level 5
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Divide 4 digit number by 1 digit number resulting in decimal answer
Lesson

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 first 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!

Remember!

We use the same process, but we may need to think about how many times we can share larger numbers. Solving with a calculator first, and then working out our answer ourselves is a great way to see we are on the right track.

 

Examples

Question 1

We want to find $715\div22$715÷​22.

  1. Choose the most reasonable estimate for $715\div22$715÷​22.

    Between $3$3 and $4$4.

    A

    Less than $20$20.

    B

    Greater than $50$50.

    C

    Between $30$30 and $40$40.

    D

    Between $3$3 and $4$4.

    A

    Less than $20$20.

    B

    Greater than $50$50.

    C

    Between $30$30 and $40$40.

    D
  2. Fill in the multiplication table for $22$22.

    $1$1 $22$22
    $2$2 $\editable{}$
    $3$3 $\editable{}$
    $4$4 $\editable{}$
    $5$5 $110$110
    $6$6 $\editable{}$
    $7$7 $154$154
    $8$8 $\editable{}$
    $9$9 $\editable{}$
    $10$10 $\editable{}$
  3. Complete the short division to find $715\div22$715÷​22.

        $\editable{}$