Partial Quotients Division Algorithm Lets Learn the Partial

Partial Quotients Division Algorithm

Let’s Learn the Partial Quotients Algorithm for Dividing! Today we are only going to learn how to divide a 3 digit number by a 1 digit number.

Let’s try 244 ÷ 7 We are going to set it up like this: 7 244 To help us, lets make a math box of 7’s multiplication facts! 7 x 1= 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700

We are going to look at our I see a math fact that entire dividend and our is close to 244 math box to find a product without going over! close to our dividend: 7 244 -140 20 104 7 x 1= 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700

Now, we look at our new dividend of 104 and our math box to find a product close to our dividend: 7 244 -140 20 104 -70 10 34 I see a math fact that is close to 104 without going over! 7 x 1= 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700

Again, we look at our new dividend of 34 and our math box to find a product close to our dividend: 7 244 -140 104 -70 34 -28 6 I see a math fact that is close to 34 without going over! However, 14 is quite a bit smaller so we are going to double it (7 x 4 = 28). 7 x 1= 7 20 10 4 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700

Once our dividend is smaller than our divisor we stop! 34 r 6 7 244 -140 104 -70 34 -28 6 20 10 4 Now we are ready to add our partial quotients and report our remainder. We add all three! Then report our quotient with remainder.

7 244 -140 20 104 7 x 1= 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 7 x 20 = 140 7 x 50 = 350 7 x 100 = 700 Let’s review our steps: 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 3. Find the math fact with a product closest to the dividend without going over. 4. Write your quotient to the right of the vertical line. Then subtract.

Let’s Model Another One! Set up the problem & make your math box. 5 322 -250 50 75 Find the product closest to the dividend without going over. Subtract to find the difference. 5 x 1= 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50 5 x 20 = 100 5 x 50 = 250 5 x 100 = 500

Continue until the dividend is smaller than the divisor! 65 r 0 5 322 -250 50 75 -50 25 -25 0 10 Find the product closest to the dividend without going over. Subtract to find the difference. 5 5 x 1= 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50 5 x 20 = 100 5 x 50 = 250 5 x 100 = 500

Try this one using your slate. Use the blank worksheet to help guide you. Follow these steps: 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 3. Find the math fact with a product closest to the dividend without going over. 4. Write your quotient to the right of the vertical line. Then subtract. 4 443 The teacher will be around to assist you. Help Button ~>

110 r 3 4 443 -400 100 43 -40 10 3 4 x 1= 4 4 x 2= 8 4 x 5 = 20 4 x 10 = 40 4 x 20 = 80 4 x 50 = 200 4 x 100 = 400

Let’s try one more! Use the blank worksheet to help guide you. Follow these steps: 1. Set up the problem. 2. Make a math box of simple multiplication facts with the divisor. 3. Find the math fact with a product closest to the dividend without going over. 4. Write your quotient to the right of the vertical line. Then subtract. 8 982 The teacher will be around to assist you. Help Button ~>

122 r 6 8 982 -800 182 -160 20 22 -16 2 6 8 x 1= 8 8 x 2 = 16 8 x 5 = 40 8 x 10 = 80 8 x 20 = 160 8 x 50 = 400 8 x 100 = 800

Homework * You will complete a worksheet with 6 division problems which you will use Partial Quotients to solve.

You did a wonderful job today! We will practice more with partial quotients tomorrow by reviewing first, and then learning how to divide 3 digit and 4 digit numbers by a 2 digit number.