Understanding long division as repeated subtraction

Understanding long division as repeated subtraction

Many children find the traditional long division method far to complex to understand. Below are two different ways for you to help your children understand long division. The first method uses repeated subtraction and the second is a grid method.

Question: 765÷12

12x10=120 765-120=645 12x10-120 645-120=525 12x10=120 525-120=405 12x10=120 305-120=285 12x10-120 185-120=165 12x10=120 165-120=45

You now know that 12x60=720
765-720=45
How many 12’s in 45?
12x3=36 remainder 9
60+3=36 remainder 9
Answer: 765÷12=63 r9

Grid method for division which can be used if you know you tables well.

Question: 765÷12
Start by partitioning 765 as in the grid below:

÷	700	60	5
12

First box needs 700÷12, this is quite had to work out so lets make it easier:

÷	720	40	5
12	60

720÷12=60 (because 72÷12=6)
The second box needs 40÷12=3 remainder 4:

÷	720	40	5
12	60	3

The remainder(4) is added to the last box - see grid below:

÷	720	40	5 9
12	60	3	0 r9

Now all you need to do is add.
60+3+0=63 r9Answer: 765÷12=63 r9

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How to Do Long Division

Steps 1: Find a simple example to start with: If there are six mushrooms in a 250 gram pack how much does each mushroom weigh? (We must divide 250 by 6.)

Steps 2: Set up the equation. Place the dividend (number being divided) under the tableau, the divisor (number doing the division) to the left outside, and the quotient (answer) will eventually go on top.

Steps 3: Perform the division. (Note: there is an error in the picture at the first step.)

Ask yourself how many times 6 goes evenly into 2. (Write a 0 below the 2.) It doesn't because 6 is greater than 2, so draw a line below that and write a 0 above the 2.
Add the next digit to 2 to get 25 (write this below the line), and ask yourself how many times 6 goes evenly into 25: 4 times 6 equals 24.
Write 24 below 25. Above the 5 of the 250 write 4 to indicate the number of times 6 goes into the number at this position.
Subtract 24 from 25. Draw another horizontal line and place the difference below the line (1). Since 1 is too small for 6 bring down the final zero of 250. This makes 10.
Ask yourself how many times 6 goes into 10: 6 times 1 equals 6. Only one 6 will go evenly into 10, so write a 1 above the 0 of 250.
Draw a vertical line down the page after the 0 of the 250 (see photo). This helps us with the location of the decimal point. (If you prefer you can just write a decimal point.)
Subtract 6 from 10 to get 4. Add a 0 the 4 and you will have 40.
Ask yourself how many times 6 goes into 40. 6*6 = 36, so write 36 under the 40, and write a 6 up and to the right of 250.
Subtract 36 from 40 to get 4. If you continue the process you can see that you are adding an infinite amount of 6's. So the quotient (answer) is 41.6666666666666...

More books about long division for kids

Mathimagination Series: Book A, beginning multiplication and division; Book B, operations with whole numbers; Book C, number theory, sets and number bases; Book D, fractions; Book E, decimals and percent

Decimals and Percentages With Pre- And Post-Tests: Place Value, Addition, Subtraction, Multiplication, Division

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