The Mostly Long and Short About Division

Long division troubles some of my students, so here is a short tutorial on how to do it.

Let’s look at 356 ÷ 23. To set this up to do long division, you use the rather descriptive long division symbol,

The number you divide into (356) goes inside the symbol. In this form, it is called the dividend. The other number is called the divisor. To begin long division, starting from the left side of 356, what is the first number that 23 divides into? 35 is the first number and 23 goes into that 1 times. Put the 1 above the 5.

Now multiply the 1 times the 23, put the result under the 35 then subtract. You should get 12,

Now bring down the next digit so that 126 is now showing,

Now repeat the above steps with the 126. How many times does 23 go into 126. You can guess. If after you multiply, you get a number greater than 126, you guessed too high. If after you subtract, you get a number greater than 23, you guessed too low,

Too high,

Too low,

Just right. You are done as there are no more digits to drop down. The answer is 15 with a remainder of 11. If there is no remainder, then you would get a 0 at the bottom.

Now if you did this problem on a calculator, you would get 15.478… . The numbers to the right of the decimal point are the remainder expressed as a decimal number. You can get this answer as well using long division by adding a decimal point to the dividend and adding zeros to the right, as many as required for the accuracy needed. Then just continue the above process,