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We can divide three-digit and four-digit numbers by a one-digit number using efficient written methods

Year 5 Unit 15

What we are learning:

We can use the method we started in year 4 to divide a three-digit number by a one-digit number.
For example, if we have 767 ÷ 3 we set it out like this:

We start by dividing with multiples of 100. We know that 3 x 100 = 300, 3 x 200 = 600 and 3 x 300 = 900, so 3 will go into 767 200 times. We put the 200 into the hundreds column like this and take the 600 away from our dividend.

Having divided with multiples of 100 we can now use multiples of 10. We know that 3 x 50 is 150 which works and that3 x 60 is 180 which is too big. We insert the 50 or 5 tens into the tens column and take the 150 away from the
dividend that is left like this:

Finally we can divide the 17 by 3 and complete the division to leave a remainder of 2

The answer (quotient) is therefore 255 remainder 2
If we want to divide a four-digit number by a one-digit number we use a similar method, except that we have to divide using multiples of 1000 first.
For example, if we want to divide 7856 by 5 we set it out like this:

We start dividing with multiples of 1000. We know that 5 x 1000 is 5000 and 5 x 2000 is 10,000. We only have 7856 so we can only use 5 x 1000 and insert the 5000 into the thousands column like this and then take it away from the dividend to see what we have left to divide:

We now have 2856 to divide by 5 so we use multiples of 100. We know that 5 x 300 = 1500, 5 x 400 = 2000, and 5 x 500 = 2500. 5 x 600 is 3000 which is too big so we put the 500 into the quotient in the hundreds column, insert the 2500 and take it away from the remaining dividend to see what we have left to divide.

We now have 356 to divide by 5 using multiples of 10. We know that 5 x 60 is 300 and 5 x 70 is 350 so we put the 70 into the tens column of the quotient insert the 350 and take it away from the remaining dividend like this:

Finally we can divide the remaining 6 by 5 and take away:

The answer, or quotient for the division is therefore 1,571 remainder 1




Good questions to ask:

Can you explain what the following are: divisor, dividend, quotient, and remainder?
Pick a number in the division calculation on the page that you have finished together and ask Where does this number come from? What part does it play in the calculation? This will get your child to explain part of the process
to you to ensure s/he understands all parts of it.

If your child:

Can’t explain what s/he is doing and gets confused part way through the process
Work on a simpler calculation to re-establish the method.
Go back to the beginning of the calculation and talk through each stage together. Long division is one of the calculations with the most stages in it, so it is not surprising that children get confused sometimes. By talking it
through you will quickly see whether they understand what they are doing.

If you get into difficulty on this Unit, revisit Year 4 Unit 12 for a reminder about division

Extension Activity

Please use this activity when you think your child understands the unit of work. It will deepen and extend your child’s understanding of this unit.


Extension activity (PDF)

Extension activity answers (PDF)