PRACTICE 22
Today we start LONG DIVISION. In Math, long division is the
common way for putting numbers we are not commonly
familiar with into groups. Sometimes things work out and
everything fits into the groups you have perfectly and
sometimes they don’t and you have some leftovers (in long
division we call leftovers, remainders). Long division breaks
down a division problem into a series of easier steps.
To begin we must first identify the 6 steps to long division
÷ Divide
x Multiply
- Subtract
> Compare
Bring Down
Repeat
We can remember the steps with this silly sentence
Did
Mom
See
Cats
Biting
Rats
÷ Divide
x Multiply
- Subtract
> Compare
Bring Down
Repeat
Now let’s practice some easy questions.
Example: 48 ÷ 3
This questions goes beyond our multiplication facts for 3’s. The
highest facts we are supposed to know is 3 x 12 = 36. So this is
clearly a long division problem.
We can’t solve it like this. We need to set it up using a DIVISION
BOX.
DIVISION BOX means “÷” sign
48 ÷ 3
turns into
3
4
8
Before you begin solving the problem draw lines to separate the
digits inside the division box. This will help you see the number
inside the division box in easier to handle parts.
3
4
8
Next, write the steps on the left.
÷
x
>
3
4
8
We begin with ÷
Ask yourself: Can the outside number (3) fit inside the first inside
number (4) – YES it can. So put a circle in the space on top of
the division box, above the 4. We will be putting our first answer
in that circle.
÷
x
>
3
4
8
Move on to x
Ask yourself: Is there a number times (x) 3 that equals to 4 – NO
there is not.
Ask yourself: What number times (x) 3 comes closest to 4,
WITHOUT GOING OVER – it’s 1, because 3 x 1 = 3. So put 1 in the
circle and put the answer to 3 x 1 under the 4.
÷
x
>
3
1
4
3
8
Move on to –
Subtract 3 from 4. Put the answer at the very bottom.
÷
x
>
3
1
4
3
8
1
Move on to > (compare)
This step is used to see if your child hasn’t made any mistakes
before moving on.
You are comparing the number outside the division box (3) and
the bottom number (1). The bottom number MUST be less than
the outside number. If it is equal or greater than the outside
number your child made a mistake somewhere and needs to
go back and check their work.
1 IS LESS THAN 3 so I know I didn’t make any mistakes, I can
move on to the next step.
Move on to
This step can only be used if there is another number inside the
division box. If there are no more numbers inside the division
box your child does not have to do any more of the steps. For
this question there IS another number inside the division box,
after the 4 – it’s an 8. You draw the arrow below the eight and
drop it down next to the bottom number.
÷
x
>
3
1
4
3
8
1
8
Move on to
Draw this step next to the 18. Have it point to the space right
after the first circle on top
÷
x
>
3
1
4
3
8
1
8
Start again with ÷
All you have to do for this step is draw a circle where the repeat
arrow ends. That’s it.
÷
x
>
3
1
4
3
8
1
8
Move on to x
Ask yourself: Is there a number times (x) 3 that equals to 18 – YES
3 x 6 = 18. So put 6 in the empty circle and put 18 under 18.
÷
x
>
3
1
4
3
6
8
1
1
8
8
Move on to –
Subtract 18 from 18 – the answer is 0.
÷
x
>
3
1
4
3
6
8
1
1
8
8
0
Move on to > (compare)
Remember you are comparing the outside number (3) and the
bottom number (0). The bottom number MUST be less than the
outside number – IT IS. That means you can more on to the next
step.
Move on to
This step can only be used if there is another number inside the
division box. If there are no more numbers inside the division
box your child does not have to do any more of the steps.
THERE ARE NO MORE NUMBERS INSIDE THE DIVISION BOX AFTER
THE 8. This means you are done with the steps.
ONE LAST THING!
Look at the bottom number. If it is a zero (0) then you have no
leftovers. BUT if the bottom number is any number besides zero
then you have leftovers. In long division leftovers are call the
remainder. You write “R” after the answer on top of the division
box and write the bottom number next to it.
Today we will start simple. We will only do long division questions
like the one above. None of them will have remainders.
Instructions: Answer each question to the best of your abilities.
1. 75 ÷ 5 = ______________
2. 51 ÷ 3 = ______________
3. 78 ÷ 6 = ______________
4. 72 ÷ 4 = ______________
5. 54 ÷ 2 = ______________
6. 98 ÷ 7 = ______________
Instructions: Create fact family sets from the 3 numbers given.
7.
4
12
48
_______________________________
_______________________________
_______________________________
_______________________________
8.
The Answer is ____________________________
9. 96 x 2 = ______________
10. What is the DECIMAL value of the following coins?
*Clipart ETC
The Answer is ____________________________
*Extra Work Never Hurt Anyone*
11. Unity and Neil go to the Bright Future Electronics Store.
Unity buys 4 CDs for $12 each and 8 DVDs for $21 each. Neil
buys 3 video games for $26 each and 6 posters for $3 each.
How much did each person spend at the Bright Future
Electronics Store? What is their COMBINED total?
Unity spent _____________________
Neil spent _____________________
Together, Unity and Neil spent _____________________
12. What is the decimal, fraction, and word form?
The decimal form is _____________________
The fraction form is _____________________
The word form is _____________________
13. Lucille buys 6 turkeys for a huge Thanksgiving dinner she is
hosting for friends and family. Each turkey costs $27. How much
did Lucille spend on the turkeys altogether?
Lucille spent ______________ on all the turkeys.
14. During a sale at her favorite store, Janelle buys 20 plain Tshirts. She decides to keep 5 for herself and give the remaining
T-shirts to her 5 cousins. If each cousin receives the same
number of T-shirts how many T-shirts does each cousin receive?
Each cousin receives ______________ T-shirts.
15. Which table represents the relationship below?
÷ 7 =
Table A
Table C
14
2
7
1
21
3
28
5
35
7
42
6
Table B
Table D
35
5
14
2
56
8
3
21
84
12
35
5
The Answer is Table _________
ANSWERS
Instructions: Answer each question to the best of your abilities.
1. 75 ÷ 5 =
÷
x
>
15
5
1
7
5
5
5
2
2
5
5
0
2. 51 ÷ 3 =
17
÷
x
>
3
1
5
3
7
1
2
2
1
1
0
3. 78 ÷ 6 =
÷
x
>
26
3
2
7
6
6
8
1
1
8
8
0
4. 72 ÷ 4 =
18
÷
x
>
4
1
7
4
3
3
8
2
2
2
0
5. 54 ÷ 2 =
÷
x
>
27
2
2
5
4
7
4
1
1
4
4
0
6. 98 ÷ 7 =
÷
x
>
14
7
1
9
7
4
8
2
2
8
8
0
Instructions: Create fact family sets from the 3 numbers given.
Fact families have 3 numbers written four ways,
either + and – or x and ÷. Add the two small
numbers and you DO NOT get 48, so that tells
you to x and ÷. You need 2 multiplication
problems and 2 division problems.
7.
4
12
4 x 12 = 48
12 x 4 = 48
48 ÷ 4 = 12
48 ÷ 12 = 4
48
8.
How many total stars do you have: 18
How many groups do you have: 6
How many stars in each group: 3
Put it all together in division problem
The Answer is
18 ÷ 6 = 3
9. 96 x 2 =
192
tens
ones
9
6
x
1 9
2
2
+1
10. What is the DECIMAL value of the following coins?
*Clipart ETC
NEVER GUESS!
Break it apart showing the decimal value of
alike coins:
= 0.75
= 0.10
= 0.15
= 0.05
Add the decimals altogether (stack them).
+1
0
0
0
+ 0
1
.
.
.
.
.
+1
7
1
1
0
0
The Answer is
5
0
5
5
5
1 . 0 5
*Extra Work Never Hurt Anyone*
11. Unity and Neil go to the Bright Future Electronics Store.
Unity buys 4 CDs for $12 each and 8 DVDs for $21 each. Neil
buys 3 video games for $26 each and 6 posters for $3 each.
How much did each person spend at the Bright Future
Electronics Store? What is their COMBINED total?
This is a multiple step question.
First, do Unity.
“4 CDs for $12 each”
means
4 x 12 = 48
“8 DVDs for $21 each”
means
8 x 21 = 168
Add the two products (answers to
multiplication) together.
48 + 168 = 216 (how much Unity spent)
Second, do Neil
“3 video games for $26 each”
means
3 x 26 = 78
“6 posters for $3 each”
means
6 x 3 = 18
Add the two products together
78 + 18 = 96 (how much Neil spent)
Third, you are asked to find out how much Unity
and Neil spent together (COMBINED total).
So you add their two sums together
216 + 96 = 312
Unity spent
Neil spent
$216
$96
Together, Unity and Neil spent
$312
12. What is the decimal, fraction, and word form?
The decimal form is
The fraction form is
The word form is
1.95
1 95/100
one and ninety five hundredths
13. Lucille buys 6 turkeys for a huge Thanksgiving dinner she is
hosting for friends and family. Each turkey costs $27. How much
did Lucille spend on the turkeys altogether?
The question wants to know how much all the
turkeys cost.
You have two facts:
6 turkeys
27 dollars for each turkey
The words that describe the numbers (turkeys
and dollars) are different. That means you
choose between x and ÷.
The word “altogether” in the question means x.
tens
ones
2
7
x
1 6
6
2
+4
Lucille spent $162 on all the turkeys.
14. During a sale at her favorite store, Janelle buys 20 plain Tshirts. She decides to keep 5 for herself and give the remaining
T-shirts to her 5 cousins. If each cousin receives the same
number of T-shirts how many T-shirts does each cousin receive?
A multiple step question.
First, subtract 5 from 20 to find out how many Tshirts Janelle is giving to her cousins.
20 - 5 = 15
Second, the phrase “same number” almost
always means divide. So divided 15 (T-shirts
remaining) by 5 (cousins) to get your final
answer.
15 ÷ 5 = 3
Each cousin receives 3 T-shirts.
15. Which table represents the relationship below?
÷ 7 =
Table A
Table C
14
2
7
1
21
3
28
5
35
7
42
6
Table B
Table D
35
5
14
2
56
8
3
21
84
12
35
5
A lot of work needs to be shown here.
You are dividing the triangle numbers by 7 in
order to equal the circle numbers.
Go through each answer possibility SLOWLY –
find the only one that fits the rule.
Table A
14
2
14 ÷ 7 = 2 yes
21
3
21 ÷ 7 = 3 yes
35
7
35 ÷ 7 = 5 NO
Table A cannot be the answer.
Table B
35
5
35 ÷ 7 = 5 yes
56
8
56 ÷ 7 = 8 yes
84
12
84 ÷ 7 = 12 yes
Table B is the answer.
Table C
7
1
7 ÷ 7 = 1 yes
28
5
28 ÷ 7 = 4 NO
42
6
42 ÷ 7 = 6 yes
Table C cannot be the answer.
Table D
14
2
14 ÷ 7 = 2 yes
3
21
3 ÷ 7 = x NO
35
5
35 ÷ 5 = 7 yes
Table D cannot be the answer.
The Answer is Table B