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

1. How To Use MrV’sTimes Table - For Long Division! Introduction: Long Division – Terms and Concepts Find the Position of the 1stQuotient Digit Division by a 1-Digit Divisor: Divide a 2-Digit Dividendby a 1-Digit Divisor When a Quotient has a Remainder When a Dividend is Past the last Product When a Division has More than One Step When a Quotient has More Than Two Digits Division by Multiple-Digit Divisors Using “Round & Simplify” to EstimateQuotient Digits When a Quotient has an Internal or Ending Zero To move Forward, press Enter, Down Arrow ▼, or Left Mouse Button To go Backward, press the Up Arrow ▲

2. Long Division Terms & Concepts Row 7 from MrV’s Times Table: • Key words: • For this division example,Click to show • The Divisor • The Dividend • The Quotient • The 1stQuotient Digit • The Partial Dividends • The Products to be Subtracted • The Remainder • Click again when done

3. Find the Position of the 1stQuotient Digit “_” is called “underline.” A “partial dividend” is used to find a single quotient digit. • Terms: • Build the Quotientone digit at a time, starting from the left-most position. • How do you find the position of the 1stQuotientDigit? • 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 quotientmay or may not have a remainder)

4. Divide a 2-digit Dividendby a 1-digit Divisor(when one number divides evenly into another) Please notice: Each table cell has aproduct with its two factors below it 1. Find the rowfor the divisor 3. Use the 2ndfactor under the product as the quotient digit 2. Look across the row until you find a product equal to the dividend Prove it! Subtract the product from the dividend to get 0 (no remainder)

5. Ok, try a few even divisions, step by step: 1. Find 1stquotientdigit’s place. 2. Find the row. 3. Find the product. 4. The 2ndfactor is the value. 5. Prove it!

6. When a Quotient has a Remainder(when one number does not divide evenly into another) 1. Find the rowfor the divisor 3. Use the 2ndfactor under the product as the quotient digit 43 2. Look across the row until you see the lastproduct that is less than the dividend 4. Subtract the product from the dividendto get the remainder;Show the remainder with a small r just to the right of the quotient

7. When a Dividend is Past the last Product(there will be a Remainder) 28 3. The quotient digitis the second factor under the product 1. Find the rowfor the divisor 2. Stop at the last product in the row if it is still less than the dividend 4. Subtract the product from the dividendto get the remainder;Show the remainder with a small r just to the right of the quotient

8. Ok, let’s try a few divisions with remainders: 42 40 39 35 1. Find the row and the product. 2. The 2ndfactor is the digit 3. Subtract the product to find the remainder

9. When Division has More Than One Step(for each step, only a partialdividend is used) 4. The 1stquotient digitis the 2ndfactor under the product 5 The 1stquotient digit is 2Subtract product 8 from 8, leaving 0 1. Find the position of the 1st quotient digit 5. Create the 2ndpartial dividend by bringing down the next digit. Use the table to find the product and the 2ndquotient digit. In this case, it’s above the 8,making 8 the 1stpartial dividendThe quotient will be 2 digits long 2. Find the rowfor the divisor Bring down 5, making 05. Ignore any leading 0’s: 5 is the 2ndpartial dividend 5 is right after product 4, so 1 is the 2ndquotient digit. In this case, it’s row 4 3. Stop at the last product that does not exceed the partialdividend (it can be =) 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 In this case 8 is equal to product 8 5 – 4 = 1, which is the remainder

10. Another 2-Digit Quotient Example(You still only need one row from MrV’s Times Table – show work under the division) 1. Find the position of the first quotient digit: 5 does not go into 3, but it will divide into 35 (the 1stpartial dividend) – so the 1stquotient digit goes above the 5 5. Repeat steps 2 and 3 for the last digit in the dividend: 2. Find the value of the first quotient digit, and put it in its place: In MrV’s Table, 0 is exactly on the 0product, so the factor0 is the last quotient digit Subtract 0 from 00, getting 0 Since there is a 0remainder, we are finished Use MrV’s Table, Row 5: 35 exactly matches product35,so the 1stquotient digit is the factor7 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 1 digit, you will need to break the dividend into smaller pieces (call them partial dividends). Subtract 35 from 35, getting 0 Bring down 0: The last partial dividend becomes 00You are now ready to use 0 to find the second quotient digit

11. When a Quotient has More Than Two Digits(You only need one row from MrV’s Times Table – show work under the division) 1. Find the position of the first quotient digit: 7 does not go into 3, but it will divide into 39 – so the first quotient digit has to go right above the 9. 5. Repeat steps 2 and 3 for each remaining digit in the dividend: 2. Find the value of the first quotient digit, and put it in its place: In MrV’s Table, 43 is between products 42 and 47, so 6 is the 2ndquotient digit 39 Subtract 42 from 43, getting 1 Bring down 2: 1 becomes 12 (3rdpartial dividend) Use MrV’s Table, Row 7: 39 is between products 35 and 42,so the first quotient digit is 5 43 In MrV’s Table, 12 is between products 7 and 14,so 1 is the 3rdquotient digit 3. Subtract the product from the dividend. Then bring down the next dividend digit next to the subtraction number Subtract 7 from 12, getting 5 Bring down 8: 5 becomes 58 (4thpartial dividend) 12 In MrV’s Table, 58 is between products 56 and 63,so 8 is the 4thquotient digit Subtract 56 from 58, getting 2 No more digits to bring down! 58 Subtract 35 from 39, getting 4 Bring down 3: 4 becomes 43You are now ready to use 43 as the 2ndpartial dividend to find the second quotient digit 6. If finding the last quotient digit resulted in a non-zero remainder, write it next to the quotient with a small r . 2 is the remainder; write r2at the end of the quotient

12. “Round and Simplify” is used to get an estimatedQuotient digit(The estimated digit may need to be adjusted) 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: 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 1st quotient digit goes above the 9.Let’s call 219 a partial dividend, the number that will have a product subtracted from it. 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. 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 3. “Check the Estimated Digit for Fit: Is it too big, too small, or just right(Fit)?- Multiply the estimated digittimes the real divisor to make a test product: a.) If the test productis > the partial dividend, the estimated digit is too big: Subtract 1 from the estimated digit, and try again.- Otherwise, subtract the test productfrom 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. - 7 times 34 makes 238 as a test product. a.) Since 238 > 219, we need to reduce 7 to 6 and try again 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. Bringing down the 4 makes 154 the new partial dividend. 4. Now let’s finish off this division by finding the 2ndquotient digit and the remainder: Use Round and Simplify on 34 and 154…

13. When the divisor has two digits(You will need a work area, and one row from MrV’s Times Table) 1. Find the position of the first quotient digit: 18 does not go into 1 or 12, but it will divide into 123 – so the 1stquotient digit has to go right above the 3. 15 2. Estimate the value of the first quotient digit: Round both 18 and 123 to 10’s.Shorten 20 and 120 to 2 and 12 Use MrV’s Table: Row 2 at 12 equals 6. 3. Check to see if the estimated quotient digit fits: Multiply 18 times 6, and get 108.This is ok so far, since 108 is < 123. 5. Bring down the next digit from the dividend, and repeat the process 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. 6. For longer dividends, repeat the process until the last digit is processed. It may come out evenly, or a remainder may exist. Round both 18 and 154 to 10’s. Shorten 20 and 150 to 2 and 15. 4. Move the quotient digit and the product to the long division, and subtract: 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. Put 108 under 123 and subtract it. You get 15, which is good… it’s < 18. 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.

14. When a Quotient has an Internal or Ending Zero(You need a work area, and the usual table row) 1. Find the position of the first quotient digit: 31 does not go into 6, but it will divide into 64 – so the 1stquotient digit has to go right above the 4. 2. Estimate the value of the first quotient digit: Round both 31 and 64 to 10’s.Shorten 30 and 60 to 3 and 6 MrV’s Row 3 at 6 gives quotient digit 2 3. Check to see if the estimatedquotient digit fits: 5. Bring down the next digit from the dividend, and repeat the process Multiply 31 times 2, and get 62.This is ok so far, since 62 is < 64. Bring down 0 after the 28, making 280. Round both 31 and 280 to 10’s. Shorten 30 and 280 to 3 and 28. 2 is the right digit because 64 – 62 = 2, which is smaller than 31 Row 3: 28 is right after 27, which makes 9 the 3rdestimatedquotient digit. 31 times 9 is 279, so 8 is the right digit because 280 -279 = 1. 4. Bringing down the next digit may result in a partial dividend that is still smaller than the divisor: Bring down 2 after the 1, making 12. 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. Bring down 8 after the 2, making 28. 28 is still smaller than 31, so put a zero as the 2ndquotient digit, put 00 under 28 and subtract getting 28. 12 is the remainder; Put r12 on the quotient.

15. 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.