Use Partial Quotients

Division using partial quotients is a slight deviation from the regular method of division. Here, after multiplying the divisor with any number, usually 5, 10 , 2 or 1, the number is subtracted from the dividend or a part of it. Note that the number multiplied by the divisor is as close to the dividend as possible. The quotient we obtain as a result of this is a partial quotient. We repeat the operation until the remainder is lesser than the divisor. Finally, all the partial quotients are added to get the final quotient.

Let’s take the following example where 168 is divided by 14 to understand the concept of partial quotients. Initially, 14 is multiplied by 10 which gives us 140. 140 is deducted from 168 to get 28.

Next, 14 is multiplied by 2 to give us 28. Deducting 28 from 28 gives us 0.

The numbers 10 and 2 are the partial quotients here and adding the both gives us the final quotient. So, 10 plus 2 gives us 12.

An area model is a  tool that can be used to express what division looks like using geometric shapes. Let’s take the same example and see what it looks like in an area model.

In this model here the entire area of the rectangle is the dividend. The width of the rectangle is the divisor, and the sum of the partial quotients will give us the length. Each of the rectangles within the larger rectangle gives us the area of each partial quotient. 

Let’s take another example where 471 is divided by 35. In this case, we will try to reduce the entire number by multiplying 35 by 10, which gives us 350. The result of 471 minus 350 gives us 121. The partial quotient is 10. Next, to reduce 121 further we multiply 35 by 2 giving us 70. After subtracting 70 from 121 we get 51.

Finally we multiply 35 with 1 to to reduce 51 to 16. So, the numbers we have taken to multiply with 35 to reduce 471 to 16 are 10, 2 and these are your partial quotients. We get the final quotient by adding the partial quotients together.

We get the final quotient as 10 + 2 + 1 = 13 and the remainder is 16.