Video: Long Division and Partial Quotients

Partial Quotient Video Script
Partial Quotient Method for solving division problems. Let’s review some terms before we begin. Here is a division sign. In the division sign is the dividend or the number we are dividing up. Outside of the division sign is the divisor or the number we are dividing by. Above the division sign is the quotient or answer. So how many times the divisor goes into the dividend.
We can use partial quotients to make long division fast and easier. Let’s see how to do that. 4 divided by 64. Remember 64 is the dividend or number we’re dividing up and 4 is the divisor or number we’re dividing by. We want to know how many times 4 goes into 64. For this example we will put the partial quotient above the division sign. Later you will see a different method on where to put it.
The first partial quotient we can start with is 10. 10 is an easy number to work with when multiplying. We multiply the divisor 4 by 10.  10 x 4 is 40. So we put the 10 as the partial quotient above the division sign and 40 below to subtract from the dividend. 64-40 = 24. We now ask ourselves how many times does 4 go into 24. If we know our math facts, we know that 4 x 6 = 24, so 4 goes into 24 6 times. We put 6 above the 10, and subtract 24 from 24 to get 0. Now we add the partial quotients together to find the whole quotient. 10 + 6 = 16. So, 4 divided by 64 is 16. Partial quotients helped up find the answer.
Here is another long division problem. 8 divided by 208. How many times does 8 go into 208? We can use partial quotients. What should we start with? We can start with 10. 8 x 10 = what? 80. We put the partial quotient 10 above the division sign, and the answer 80 below to subtract from the dividend 208. 208-80 = 128. We can put 80 into 128, so we can use the partial quotient of 10 again. Put 10 above the 10 in the answer space, and subtract 80 from 128. 128-80= 48. We can’t use 10 again because it is larger than 80, so now we need to recall our math facts. What times 8 is 48 or close to 48? 8 x 6 = 48. So the 6 goes above the 10 in the answer space and we subtract 48 from 48. 48-48=0 so we are done. Now we need to add the partial quotients together to get our answer. 10 + 10 + 6 = 26. So 8 divided by 208 is 26.
There is an even shorter way to find the answer instead of using 10’s. Estimating using larger numbers is a short cut to find the answer. How many 8’s go into 208? If we know 8x10 is 80, what if we did 8x20? 8x20=160. 160 is closer to 208. Let’s multiply 8x30. 8x30=240. That’s larger than 208, so that won’t work. But we can use 8x20. We put the partial quotient 20 above the answer space. We line the tens place up with the dividend’s ten place. Now we subtract. 208-160=48. Again we think to our math facts. What times 8 equals 48. 6. So the 6 goes above the 20 in the ones place. Add the partial quotients. 20+6=26. We got the same answer as before, we just did 1 less step. Estimating can help us find the answer in less steps.
Even when we divide, it’s important to line up place values. The dividend and the quotient’s place value line up. The ones place, the tens place and the hundreds place. So instead of having to put 20, we can just write 2 in the tens place which means 2 tens or 20. Then we can find the number in the ones place.
A different way to write out the partial quotients is to the right of the problem, then put the final quotient above the division sign. Like this. We are still working through the problem the same way, we are just writing the partial quotients in a different place. Our answer stays the same. Either strategy will help you in finding the final quotient.
Review Time: Divide using partial quotients. Pause the video to solve 15 divided by 195 using partial quotients. Press play to check your answer. 15 divided by 195 is 13. 15x10=150. Subtract and put the partial quotient to the right. 195-150=45. How many times does 15 go into 45? 15x3=45. Subtract and put the partial quotient to the right. Add the partial quotients. 10 + 3 = 13 so 15 divided by 195 equals 13.