The Forgiving Method of Long Division in 5th Grade Math

In fourth and fifth grade, students typically begin to work on long division and often rely on their parents to help with their math homework. The trouble is that math help isn't as easy as it used to be. Take, for example, long division. It's always been tough for many people, relying on a superb recall of multiplication facts and a good instinctual number sense. Many teachers and math books are using a new technique known as the Forgiving Method of Long Division for 5th grade division.

It takes longer than the old way of dividing, but you need to know it to help your child. So let's walk through the process.


Examine the Problem

Brother and sister doing math homework with markers at table
Hero Images / Getty Images

This problem asks for you to find how many times 718 is divisible by 5. In this example, 718 is known as the dividend and 5 is the divisor. In the old days, we'd simply divide each digit of the dividend by 5, starting with 7 and then bringing down the next number (1) after subtracting. The Forgiving Method of Division asks students to look at the dividend as a whole and guesstimate how many times the divisor would go into it.


Make a Reasonable Estimate

It always helps to begin estimating with numbers ending in zero. This is because most children know that you simply need to multiply the divisor by the first digit and add the correct number of zeros. Here, using 100 makes the most sense, as 200 x 5 is 1000, which is larger than 718. Write the estimated number to the side.


Perform the Multiplication and Subtraction

Multiply the estimate by the divisor (100 X 5) and make sure the result (product) is less than the dividend. If it is, subtract the product from the dividend. If not, make another guess and perform the multiplication again.


Look at the Difference

Take a look at the number that's left after subtracting, also known as the difference. Make another reasonable estimate of how many times the divisor will go into the difference. Sticking with numbers that end in zero, in this example, we know that our guess needs to be more than 20 because 5 x 20 is only 100, so we'll try 30.


Multiply and Subtract Again

Again, multiply your guess by the divisor and subtract it from what you have left. If it's too much, you'll have to erase and take another guess. Continue to do this until the difference you end up with is less than the divisor. In the example problem, this number is 3. That's the remainder.


Add All the Estimates

Line up all the numbers used so that the place values match and add them together.


Transfer the Sum

The sum (the answer you got when you added all the guesses together) can be transferred to the top of the division problem, along with remainder. This is the answer, using the Forgiving Method of Division.

Was this page helpful?