Calculation methods for division

One half equals 0,5. One quarter equals 0,25. These are good to remember, since it’s common to divide things into halves and quarters. But the solution of 456 divided by 3 doesn’t need to be remembered. This can be calculated.

One method of solving the problem is called short division. It works like this: We divide hundreds, tens and ones - all the different place values - by three. Start with the largest place value so we can see if there will be anything to carry over to the next, smaller, place value. In 456, the largest place value is the hundreds: four hundreds. Since we are dividing by three, we use the three times-table.

Three goes into four once, since three times one is three. But three times two is six, and that is more than four. Write “equals one” as the first part of the answer. Three times one is three. And since we’re talking about hundreds, we have used 300 of the 456 we started with.

456 minus 300 is 156. Now let’s divide 156 by 3. The number in the hundreds place value, one, can’t be divided by three. Three times one is three. So it’s too small.

So we move on to include the number in the next place value, the tens, five. Now we have one and five: 15. How many times does three go into 15? Five times. In the answer, write the number five after the number one.

How much is remaining? Three times five is 15, but since we are dealing with the tens place value, we have used 150 of the 156 that was remaining. 156 minus 150 is six. Now let’s divide six by three. Three goes into six two times.

Write the number two after the five in the answer. So 456 divided by three equals 152. Here is another problem: 54 divided by seven. Start with the largest place value, the tens: that’s five. Five goes zero times into seven because seven times one is seven, which is more than five.

Then move on to include the next place value: the ones, four of them. So we have: five and four. How many times does seven go into 54? Seven times. Write “equals seven” as the first part of the answer.

Seven times seven is 49. 54 minus 49 is five. Five remaining. Seven goes zero times into five. So we get a remainder of: five.

In the answer, write: remainder five. 54 divided by seven equals seven, remainder five. Another method of division is long division. To divide 456 by four, this is how that works. Start with the largest place value.

How many times does four go into four? Once. Write “equals one” as the first part of the answer. Four times one is four. Write this under the four hundreds digit in 456.

Now let’s see how many hundreds are remaining. Four minus four is zero. Write zero under the calculation. Now move the tens digit, five, down, and put it next to the zero we just wrote. How many times does four go into five?

Once. Write one after the one in the answer. Four times one is four. Write four under zero-five in the calculation. Remember to keep the numbers lined up in their place value columns!

Then calculate how many tens are remaining. Five minus four is one. Write one below the calculation. Move the ones place value number, six, down, and put it next to the one. How many times does four go into 16?

Four times. Write the number four after the one in the answer. Four times four is 16. Write 16 under 16 in the calculation. Now let’s see if any ones are remaining.

16 minus 16 is zero. Write zero under the calculation. There was no remainder this time. Therefore, 456 divided by four is 114. Now we have gone through two different methods for division.

Pause the video, and test both methods on these problems. 123 divided by three. And 177 divided by four. If you got these answers: 41, and 44 with remainder one, you have probably understood these two calculation methods for division. Great!