How To Use MrV’s Times Table - For Long Division!

1. Introduction:a. Long Division – Terms and Conceptsb. Find the Position of the 1st Quotient Digit

2. Division by a 1-Digit Divisor:a. Divide a 2-Digit Dividend by a 1-Digit Divisorb. When a Quotient has a Remainderc. When a Dividend is Past the last Productd. When a Division has More than One Stepe. When a Quotient has More Than Two Digits

3. Division by Multiple-Digit Divisorsa. Using “Round & Simplify” to Estimate Quotient Digitsb. When a Quotient has an Internal or Ending Zero

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• Key words:

• For this division example,Click to show– The Divisor– The Dividend– The Quotient– The 1st Quotient Digit– The Partial Dividends– The Products to be Subtracted– The Remainder

• Click again when done

Long Division Terms & Concepts

QuotientDividendDivisor

Row 7 from MrV’s Times Table:

• Terms:

• Build the Quotient one digit at a time, starting from the left-most position.

• How do you find the position of the 1st Quotient Digit?• Critical skill: Putting the first quotient digit in the correct position

(underlining the 1st digit position is recommended, but it’s not required. Don’t use red )

• Bonus: You will know exactly how many digits will be in the quotient(the quotient may or may not have a remainder)

Find the Position of the 1st Quotient DigitQuotientDividendDivisor

482? 7

355?? ?4

1233??? ??3

668822???? ??1

66885402?????

“_” is called “underline.”A “partial dividend” is used to find a single quotient digit.

1. Find the rowfor the divisor

2. Look across the row until you find a product equal to the dividend

3. Use the 2nd factor under the product as the quotient digit

_567

Divide a 2-digit Dividend by a 1-digit Divisor(when one number divides evenly into another)

8

560

Prove it! Subtract the product from the dividend to get 0 (no remainder)

Please notice:Each table cell has a product with its two factors below it

5408

Ok, try a few even divisions, step by step:

4007284280

8729720

6366360

1. Find 1st quotient digit’s place. 2. Find the row. 3. Find the product. 4. The 2nd factor is the value. 5. Prove it!

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??

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1. Find the rowfor the divisor

2. Look across the row until you see the last product that is less than the dividend

3. Use the 2nd factor under the product as the quotient digit438

When a Quotient has a Remainder(when one number does not divide evenly into another)

403

4. Subtract the product from the dividend to get the remainder;Show the remainder with a small r just to the right of the quotient

5

3r

43

1. Find the rowfor the divisor

2. Stop at the last product in the row if it is still less than the dividend

3. The quotient digitis the second factor under the product

283When a Dividend is Past the last Product

(there will be a Remainder)

271

4. Subtract the product from the dividend to get the remainder;Show the remainder with a small r just to the right of the quotient

28

9

1r

28425

r

Ok, let’s try a few divisions with remainders:

40239

394

r

363

83359

r

278

55407

r

355

42

39

40

1. Find the row and the product. 2. The 2nd factor is the digit 3. Subtract the product to find the remainder

35

2. Find the rowfor the divisor

3. Stop at the last product that does not exceed the partial dividend (it can be =)

4. The 1st quotient digit is the 2nd factor under the product

854When Division has More Than One Step

(for each step, only a partial dividend is used)

80

6. Subtract the product from the dividend to get the remainder;Show the remainder with a small r just to the right of the quotient

5

2

1r

541

1

In this case, it’s row 4

In this case 8 is equal to product 8

The 1st quotient digit is 2Subtract product 8 from 8, leaving 0

5. Create the 2nd partial dividend by bringing down the next digit. Use the table to find the product and the 2nd quotient digit.

1. Find the position of the 1st quotient digit

In this case, it’s above the 8,making 8 the 1st partial dividendThe quotient will be 2 digits long

Bring down 5, making 05. Ignore any leading 0’s: 5 is the 2nd partial dividend5 is right after product 4, so 1 is the 2nd quotient digit.

5 – 4 = 1, which is the remainder

3505???

1. Find the position of the first quotient digit:

2. Find the value of the first quotient digit, and put it in its place:

3. Subtract the product from the dividend. Then bring down the next dividend digit next to the subtraction number

Another 2-Digit Quotient Example(You still only need one row from MrV’s Times Table – show work under the division)

35

00

_ 5. Repeat steps 2 and 3 for the last digit in the dividend:7

00

5 does not go into 3, but it will divide into 35 (the 1st partial dividend) – so the 1st quotient digit goes above the 5

Use MrV’s Table, Row 5:35 exactly matches product 35,so the 1st quotient digit is the factor 7

Subtract 35 from 35, getting 0Bring down 0: The last partial dividend becomes 00You are now ready to use 0 to find the second quotient digit

In MrV’s Table, 0 is exactly on the 0 product,so the factor 0 is the last quotient digitSubtract 0 from 00, getting 0Since there is a 0 remainder, we are finished

0

When a quotient has more than 1 digit, you will need to break the dividend into smaller pieces (call them partial dividends).

????,?328,397

1. Find the position of the first quotient digit:

2. Find the value of the first quotient digit, and put it in its place:

3. Subtract the product from the dividend. Then bring down the next dividend digit next to the subtraction number

When a Quotient has More Than Two Digits(You only need one row from MrV’s Times Table – show work under the division)

35

241

_ 5. Repeat steps 2 and 3 for each remaining digit in the dividend:

6. If finding the last quotient digit resulted in a non-zero remainder, write it next to the quotient with a small r .

2r

,5

43

7 does not go into 3, but it will divide into 39 – so the first quotient digit has to go right above the 9.

Use MrV’s Table, Row 7:39 is between products 35 and 42,so the first quotient digit is 5

Subtract 35 from 39, getting 4Bring down 3: 4 becomes 43You are now ready to use 43 as the 2nd partial dividend to find the second quotient digit

In MrV’s Table, 43 is between products 42 and 47,so 6 is the 2nd quotient digit

In MrV’s Table, 58 is between products 56 and 63,so 8 is the 4th quotient digit

In MrV’s Table, 12 is between products 7 and 14,so 1 is the 3rd quotient digit

Subtract 42 from 43, getting 1Bring down 2: 1 becomes 12 (3rd partial dividend)

2

6

7

1

58

8

562

2 is the remainder; write r2 at the end of the quotient

39

43

58

12Subtract 7 from 12, getting 5Bring down 8: 5 becomes 58 (4th partial dividend)

Subtract 56 from 58, getting 2No more digits to bring down!

When divisors are longer than 1 digit, MrV’s Table can’t be used without doing some work area computations: The “Round and Simplify” technique is used to get an estimated digit by using MrV’s Table. “Check for Fit” uses multiplications to see if the estimated digit should be used , or be adjusted. For example:

2. Round the divisor so that the leading digit is followed by all 0’s, and round the partial dividend to the same position… Then shorten both to simplify. Now you can use MrV’s Table to find the estimated quotient digit.

219434

“Round and Simplify” is used to get an estimated Quotient digit(The estimated digit may need to be adjusted)

20415

3. “Check the Estimated Digit for Fit: Is it too big, too small, or just right(Fit)?- Multiply the estimated digit times the real divisor to make a test product: a.) If the test product is > the partial dividend, the estimated digit is too big: Subtract 1 from the estimated digit, and try again.- Otherwise, subtract the test product from the partial dividend:b.) If that number is < or = the real divisor, the estimated digit is just right!c.) But if that number is > the real divisor, the digit is too small: Subtract 1 from the estimated digit and try again.

7223

22030

21934

1. Find the place for the first quotient digit:34 does not go into 2 or 21, but it will divide into 219 – so the 1 st quotient digit goes above the 9.Let’s call 219 a partial dividend, the number that will have a product subtracted from it.

34 rounds down to 30, and rounding 219 to the 10’s digit rounds up to 220. (show work!)Shorten to Simplify: Remove the matching right-hand zeroes from both to make a 1 digit divisor.Row 3 with product 22 yields 7 as the estimated digit

- 7 times 34 makes 238 as a test product. a.) Since 238 > 219, we need to reduce 7 to 6 and try again

382743

2

042643

2

b.) 6 times 34 makes 204 as a test product. Since 204 < 219 and 219 – 204 = 15, 6 is just right: Use it as the exact quotient digit.

6

Bringing down the 4 makes 154 the new partial dividend.

413618

701543

2

361443

1

5153

15030

15434

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ok15204219

bigtoo170154

ok18136154

4. Now let’s finish off this division by finding the 2nd quotient digit and the remainder: Use Round and Simplify on 34 and 154…

4 18r

????123418

1. Find the position of the first quotient digit:

_

2. Estimate the value of the first quotient digit:

3. Check to see if the estimated quotient digit fits:

When the divisor has two digits(You will need a work area, and one row from MrV’s Times Table)

108

4. Move the quotient digit and the product to the long division, and subtract:

14410

6

1086814

5. Bring down the next digit from the dividend, and repeat the process

6. For longer dividends, repeat the process until the last digit is processed. It may come out evenly, or a remainder may exist.

212

20120

81312

1

updown

digitstFind

10r8

154

18 does not go into 1 or 12, but it will divide into 123 – so the 1st quotient digit has to go right above the 3.

Round both 18 and 123 to 10’s.Shorten 20 and 120 to 2 and 12Use MrV’s Table: Row 2 at 12 equals 6.

Multiply 18 times 6, and get 108.This is ok so far, since 108 is < 123.6 is good, maybe 7 is better…But 18•7 = 126, which exceeds 123,so 6 is the best fit. Put 6 in the quotient Bring down 4 after the 15, making 154.

Put 8 above the 4 in 1234.Put 144 under 154 and subtract it.You get a remainder of 10; put it with the quotient.

In MrV’s Table, Row 2: 15 is between 14 and 16.We already have 18x7=126, so do 18x8=144.144 is closer to 154, so 8 is the right digit.

215

20150

81415

2

updown

digitndFind

1448816

1267815

Put 108 under 123 and subtract it.You get 15, which is good… it’s < 18.

Round both 18 and 154 to 10’s.Shorten 20 and 150 to 2 and 15.

15

1. Find the position of the first quotient digit:

2. Estimate the value of the first quotient digit:

3. Check to see if the estimated quotient digit fits:

When a Quotient has an Internal or Ending Zero(You need a work area, and the usual table row)

4. Bringing down the next digit may result in a partial dividend that is still smaller than the divisor:

62213

5. Bring down the next digit from the dividend, and repeat the process

31 does not go into 6, but it will divide into 64 – so the 1st quotient digit has to go right above the 4.

Round both 31 and 64 to 10’s.Shorten 30 and 60 to 3 and 6MrV’s Row 3 at 6 gives quotient digit 2

Multiply 31 times 2, and get 62.This is ok so far, since 62 is < 64.

2 is the right digit because 64 – 62 = 2, which is smaller than 31

Bring down 8 after the 2, making 28.

Bring down 0 after the 28, making 280.

Bring down 2 after the 1, making 12.

Row 3: 28 is right after 27, which makes 9 the 3rd estimated quotient digit. 31 times 9 is 279,so 8 is the right digit because 280 -279 = 1.

279913

28 is still smaller than 31, so put a zero as the 2nd quotient digit, put 00 under 28 and subtract getting 28.

Round both 31 and 280 to 10’s.Shorten 30 and 280 to 3 and 28.

????,?802,6431

62

0028

,_ 12r2

28

0

0

927

9

12

0

0012

12 is still smaller than 31, so put a zero as the 4th (and last) quotient digit, put 00 under 12 and subtract getting 12.12 is the remainder; Put r12 on the quotient.

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Summary• Using MrV’s Times Table for Long Division gives students an

excellent practice tool for understanding and performing the process of doing Long Division, one digit at a time.

• If a student can do single digit multiplication and division in his/her head, using MrV’s table may become unnecessary.

• Work areas are still needed when Round and Simplify needs to be done for multiple-digit divisors.