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Dividing Whole Numbers & Decimals
• Long division is as simple as memorizing the people in this family.
Dad Mom Sister Brother
Rover
• Each person represents a step in the long division process.
Dad
Mom
Sister
Brother
Rover
1. Divide
2. Multiply
3. Subtract
4. Bring down
5. Repeat orRemainder
Step 1 in Long Division
• Divide 2 into first number in the dividend.
2 ) 9 4 7
• Think how many 2’s will fit into 9.
4
How many 2’s will go into 9?
• Write that number directly above the number you divided into.
Dad
1. Divide
Step 2 in Long Division
• Multiply the divisor times the first number in the quotient.
2 ) 9 4 7
• Write your answer directly under the 9 or the number you just divided into.
4
2 x 4 = 8
2. MultiplyMom
8
Step 3 in Long Division
• Draw a line under the 8.
2 ) 9 4 7
• Write a subtraction sign next to the 8.
43. Subtract
8Sister
• Subtract 8 from 9.
• Write your answer directly below the 8.
1
Step 4 in Long Division
• Go to the next number in the dividend to the right of the 9.
2 ) 9 4 7
• Write an arrow under the 4.
44. Bring down
8
• Bring the 4 down next to the 1.
1
Brother
4
Step 5 in Long Division
• This is where you decide whether you repeat the 5 steps of division.
2 ) 9 4 7
• If your divisor can divide into your new number, 14, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.
45. Repeat or Remainder
81 4
Rover
Step 1 in Long Division
• Divide 2 into your new number, 14.
2 ) 9 4 7
• Place your answer directly above the 4 in your quotient.
41. Divide
81 4
Dad
7
Step 2 in Long Division
• Multiply your divisor, 2, with your new number in the quotient, 7.
2 ) 9 4 7
• Place your answer directly under the 14.
42. Multiply
81 4
7Mom
1 4
Step 3 in Long Division
• Draw a line under the bottom 14.
2 ) 9 4 7
• Draw a subtraction sign.
43. Subtract
81 4
7
1 4
Sister
• Subtract & place answer under the line.
0
Step 4 in Long Division
• Put an arrow under the next number, 7, in the dividend.
2 ) 9 4 7
• Bring the 7 down next to the 0.
44. Bring down
81 4
7
1 40
Brother
7
Step 5 in Long Division
• If the 2 will divide into your new number, 7, then repeat the steps of division.
2 ) 9 4 7
45. Repeat or Remainder
81 4
7
1 40 7
Rover
Step 1 in Long Division
• Divide your divisor, 2, into your new number, 7.
2 ) 9 4 7
41. Divide
81 4
7
1 40 7
Dad
• Place your answer in the quotient next to the 7.
3
Step 2 in Long Division
• Multiply your divisor, 2, by your new number in the quotient, 3.
2 ) 9 4 742. Multiply
81 4
7
1 40 7• Place your answer under
the number you brought down, 7.
3Mom
6
Step 3 in Long Division
• Draw a line under the number 6.
2 ) 9 4 7
43. Subtract
81 4
7
1 40 7
• Place your subtraction sign.
3
6
Sister
• Subtract & put your answer directly under the 6. 1
Step 4 in Long Division
• Look at your dividend to see if there are any more numbers to bring down.
2 ) 9 4 744. Bring
down
81 4
7
1 40 7
3
6• If not, move to step 5.
1
Brother
Step 5 in Long Division
• Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division.
2 ) 9 4 7
45. Repeat or Remainder
81 4
7
1 40 7
3
6• The number left over, 1, becomes the remainder. 1
Rover
R1
Dividing a Decimal by a Whole Number
• Place the decimal point in the quotient directly above the decimal point in the dividend.
• Divide as you normally would (DMSBR)
Example
5 12.5. D
MSCB
2
1025
5
250
Example 29 101.52.1
91 1
1
92 5
2
187 2
8
720
Dividing a Decimal by a Decimal
• Move the decimal point in the divisor to the right, until you get to the end of the digits.
• Count how many places you moved that decimal.
• Move the decimal point in the dividend the same number of places to the right that you moved the decimal point in the divisor.
Example
0.3 6.72
One space
03 67.2New problem
3 67.2DMSCB
.2
607
2
61 2
4
1 20
Example 23.2 2.24
32 22.4. 32
x 5160
32x 8
25632
x 7224
7
22 40
Example 30.38 13.3
The decimal must be moved 2 spaces to the right.
When we move this one 2 spaces, we find that we need to add a space. What will we fill it with?
Answer: Fill it in with a 0. 13.3 becomes 1330
SO, our problem becomes 038 into 1330.
038 is the same as 38.
38 133038
x 5190
38x 4152
38x 3114
3
114
190
5
1900
Example 4
2.48 1.3392
248 133.92
248 133.92.
248x 5
1240
248x 6
14885
124 099 2
248x 4992
4
9 920
Terminating and Repeating Decimals
• A terminating decimal is a decimal that stops, or terminates.
• Examples: 1.25 or 0.892
• A repeating decimal is a decimal that has a repeating digit or a repeating group of digits.
• Examples: 1.3333… or .121212121…
• Repeating decimals usually have a bar across the repeating portion.
2.3
6287
566
.0
.
0
7
564
0
0
5
400
Terminating decimal
56 .0. 8
4 82
0
0
3
18
2
0
0
3
182
This is a repeating decimal.
.83
