1. How To Use Times Table - For Long Division!
Introduction:
Long Division – Terms and Concepts
Find the Position of the 1st Quotient Digit
Division by a 1-Digit Divisor:
Divide a 2-Digit Dividend by 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
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 the Times Table:
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

3. Find the Position of the 1st Quotient Digit
“_” is called “underline.”
A “partial dividend” is used to find a single quotient digit.
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 (underline the 1st digit position)

4. Divide a 2-digit Dividend by a 1-digit Divisor (when one number divides evenly into another)
Please notice:
Each table cell has a product with its two factors below it
1. Find the row for the divisor
3. Use the 2nd factor 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 1st quotient digit’s place Find the row Find the product The 2nd factor 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 row for the divisor
3. Use the 2nd factor under the product as the quotient digit 43
2. Look across the row until you see the last product that is less than the dividend
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

7. When a Dividend is Past the last Product (there will be a Remainder)28
3. The quotient digit is the second factor under the product
1. Find the row for 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 dividend to 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 The 2nd factor is the digit 3. Subtract the product to find the remainder

9. When Division has More Than One Step
4. The 1st quotient digit is the 2nd factor under the product 5
The 1st quotient digit is 2 Subtract product 8 from 8, leaving 0
1. Find the position of the 1st quotient digit
5. Create the 2nd partial dividend by bringing down the next digit. Use the table to find the product and the 2nd quotient digit.
In this case, it’s above the 8, making 8 the 1st partial dividend The quotient will be 2 digits long
2. Find the row for the divisor
In this case, it’s row 4
Bring down 5, making 05. Ignore any leading 0’s: 5 is the 2nd partial dividend
5 is right after product 4, so 1 is the 2nd quotient digit.
3. Stop at the last product that does not exceed the partial dividend (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 the Times Table)
1. Find the position of the first quotient digit:
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
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 the Table, 0 is exactly on the 0 product,
so the factor 0 is the last quotient digit
Subtract 0 from 00, getting 0
Since there is a 0 remainder, we are finished
Use the Table, Row 5:
35 exactly matches product 35, so the 1st quotient digit is the factor 7
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 00 You are now ready to use 0 to find the second quotient digit

11. When a Quotient has More Than Two Digits
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 the Table, 43 is between products 42 and 47,
so 6 is the 2nd quotient digit 39
Use the Table, Row 7:
Subtract 42 from 43, getting 1
Bring down 2: 1 becomes 12 (3rd partial dividend)
39 is between products 35 and 42, so the first quotient digit is 5 43
In the Table, 12 is between products 7 and 14, so 1 is the 3rd quotient 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 (4th partial dividend) 12
In the Table, 58 is between products 56 and 63, so 8 is the 4th quotient digit 58
Subtract 56 from 58, getting 2
No more digits to bring down!
Subtract 35 from 39, getting 4
Bring down 3: 4 becomes 43 You are now ready to use 43 as the 2nd partial 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 r2 at the end of the quotient

12. Ok, let’s try a few on our own:

13. Ok, let’s try a few on our own:

14. Ok, let’s try a few on our own:

15. Ok, let’s try a few on our own:

16. Ok, let’s try a few on our own: