Download 07.Long.Division.Notes

Name _________________________________________________________________ Class ____ Long Division Notes
Long division is not bad at all ... once you get the hang of it! At first, though, it's going to seem
like a LOT of steps and stuff to keep track of. But, each step is easy math. You just need to get
used to what to do at each step. Sometimes, students find long division confusing. This is
because you'll be doing Division, Multiplication and Subtraction all in the same problem. (The
DMS loop!  ) But, believe me, if you take your time, you WILL be able to get this! One
warning: If you are not good at your times tables, this is NOT going to be fun for you at all.
The one thing that makes long division really hard is not knowing your times tables very well.
So, if this is you, make it your goal to learn your times tables this week!
I. Vocabulary
A. Dividend – the number you are dividing into
B. Divisor – the number you are dividing by
C. Quotient - the answer to the division problem
II. Steps For Long Division
A. Write the problem using the division bracket (dividend is inside; divisor is outside)
B. Look at the first digit on the left side of the divided and see if the divisor will go into it. If not, keep moving over
one digit to the right in the dividend until you have a number the divisor will go into
C. Put a little arrow head ^ above the digit in the dividend where your quotient will begin (this helps keep things
lined up correctly)
D. Decide how many times the divisor goes into the part of the dividend you are using (this is the divide step)
E. Put the answer above the digit in the dividend you are using and multiply it by the divisor (this is the multiply step)
F. Write the product under the part of the dividend you are using and subtract (this is the subtract step)
G. Be sure your difference is smaller than the divisor (If it is larger than the divisor, stop! The number you wrote in
the quotient is too small. Erase and use a larger digit in the quotient.)
H. Bring down the next digit in the dividend and repeat the DMS loop until you have nothing left to bring down.
I.
You can always check to see if your quotient is correct by multiplying the quotient by the divisor. If it equals the
dividend, your answer is correct. Remember that multiplication and division are opposites of each other – they
“undo” each other. That’s why this way of checking your answer works.
LET’S DO A PRACTICE PROBLEM TOGETHER!
1,348 ÷ 4
Now take out your own notebook paper for more practice!
a. 1,623 ÷ 3
b. 195,282 ÷ 6
c. 572 ÷ 11
d. 3,888 ÷ 36
e. 1,215 ÷ 45
)
III. Writing Remainders
When we are given a long division problem to do, it will not always work out to a whole number. Sometimes there
will be numbers left over. These are known as remainders. There are three general ways to deal with remainders.
One note to remember: When checking your answers, you multiply the divisor by the quotient. ADD the remainder!
A. Writing Remainders With An “r”
1. Divide as usual.
2. When there are no digits left to bring down and you have something other than
zero left over, this is the remainder.
3. After the quotient, write the letter r and put the number left over after it.
PRACTICE – Do all of these problems on your own notebook paper!
1. 1,361 ÷ 3
2. 152,923 ÷ 6
5.
1,564 ÷ 13
6. 654 ÷ 25
9.
58,445 ÷ 15
3. 21,098 ÷ 10
7. 32,857 ÷ 50
4. 789 ÷ 12
8. 195 ÷ 2
10. 7,349,024 ÷ 20
B. Writing Remainders As A Fraction
1. Divide as usual.
2. When there are no digits left to bring down and you have something
other than zero left over, this is the remainder.
3. After the quotient, write a fraction with the remainder as the numerator
and the divisor as the denominator
4. Be sure to reduce the fraction if possible
PRACTICE – Do all of these problems on your own notebook paper!
11. 4,135 ÷ 9
12. 7,705 ÷ 8
13. 329 ÷ 5
14. 658,947 ÷ 2
15. 16,926 ÷ 30
19. 2,277,096 ÷ 99
16. 7,396 ÷ 21
17. 6,722 ÷ 64
18. 78 ÷ 25
20. 8,691 ÷ 82
C. Writing Remainders As A Decimal
1.
Divide as usual.
2. When there are no digits left to bring down and you have something other than
zero left over, this is the remainder.
3. Recall that every number has a decimal point in it. Invisible decimals are hiding
on the end (right side).
4. Also recall that you may add as many zeroes as you want to the end of a decimal
without changing its value.
5. Make the decimal point visible at the end of the dividend.
6. Write a decimal point straight above it in the quotient (fill the decimal point with
helium and let it float).
7. Add a zero after the decimal point and bring it down next to the remainder.
8. Continue dividing as usual (DMS loop).
9. You may keep adding zeroes and continue to divide as many times as you need to
do. **Special Note: Some numbers will never divide evenly.
PRACTICE – Do all of these problems on your own notebook paper!
21. 15 ÷ 6
22. 437 ÷ 2
23. 1,874 ÷ 4
24. 95,871 ÷ 10
25. 2,717 ÷ 44