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**Dividing Whole Numbers & Decimals**

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**Long division is as simple as memorizing the people in this family.**

Dad Mom Sister Brother Rover

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**Each person represents a step in the long division process.**

3. Subtract Sister 1. Divide 4. Bring down Dad Brother 2. Multiply 5. Repeat or Remainder Mom Rover

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**2 ) 9 4 7 4 Step 1 in Long Division 1. Divide**

Dad Divide 2 into first number in the dividend. How many 2’s will go into 9? Think how many 2’s will fit into 9. Write that number directly above the number you divided into.

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**2 ) 9 4 7 4 8 Step 2 in Long Division 2. Multiply 2 x 4 = 8 Mom**

Multiply the divisor times the first number in the quotient. 2 x 4 = 8 Write your answer directly under the 9 or the number you just divided into.

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**2 ) 9 4 7 4 8 1 Step 3 in Long Division 3. Subtract Sister**

Draw a line under the 8. Write a subtraction sign next to the 8. 1 Subtract 8 from 9. Write your answer directly below the 8.

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**2 ) 9 4 7 4 8 1 4 Step 4 in Long Division 4. Bring down Brother**

Go to the next number in the dividend to the right of the 9. 1 4 Write an arrow under the 4. Bring the 4 down next to the 1.

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**2 ) 9 4 7 4 8 1 4 Step 5 in Long Division 5. Repeat or Remainder Rover**

This is where you decide whether you repeat the 5 steps of division. 1 4 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.

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**2 ) 9 4 7 4 7 8 1 4 Step 1 in Long Division 1. Divide Dad**

Divide 2 into your new number, 14. 1 4 Place your answer directly above the 4 in your quotient.

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**2 ) 9 4 7 4 7 8 1 4 1 4 Step 2 in Long Division 2. Multiply Mom**

Multiply your divisor, 2, with your new number in the quotient, 7. 1 4 1 4 Place your answer directly under the 14.

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**2 ) 9 4 7 4 7 8 1 4 1 4 Step 3 in Long Division 3. Subtract Sister**

Draw a line under the bottom 14. 1 4 Draw a subtraction sign. 1 4 Subtract & place answer under the line.

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**2 ) 9 4 7 4 7 8 1 4 1 4 7 Step 4 in Long Division 4. Bring down**

Brother 2 ) 9 4 7 8 Put an arrow under the next number, 7, in the dividend. 1 4 1 4 Bring the 7 down next to the 0. 7

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Step 5 in Long Division 5. Repeat or Remainder 4 7 2 ) 9 4 7 Rover 8 1 4 If the 2 will divide into your new number, 7, then repeat the steps of division. 1 4 7

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**2 ) 9 4 7 4 7 3 8 1 4 1 4 7 Step 1 in Long Division 1. Divide Dad**

Divide your divisor, 2, into your new number, 7. 1 4 Place your answer in the quotient next to the 7. 1 4 7

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**2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 Step 2 in Long Division 2. Multiply Mom**

Multiply your divisor, 2, by your new number in the quotient, 3. 1 4 7 Place your answer under the number you brought down, 7. 6

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**2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 3 in Long Division 3. Subtract**

Sister 8 1 4 Draw a line under the number 6. 1 4 Place your subtraction sign. 7 Subtract & put your answer directly under the 6. 6 1

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**2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 4 in Long Division 4. Bring down**

Brother 8 1 4 Look at your dividend to see if there are any more numbers to bring down. 1 4 7 If not, move to step 5. 6 1

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**2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 R1 Step 5 in Long Division**

5. Repeat or Remainder 4 7 3 R1 2 ) 9 4 7 8 Rover 1 4 1 4 Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division. 7 6 The number left over, 1, becomes the remainder. 1

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**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)

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Example DMSCB 2 . 5 5 12.5 10 2 5 25

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1 1 . 2 8 Example 2 9 101.52 9 1 1 9 2 5 18 7 2 72

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**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.

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Example 0.3 6.72 One space New problem 03 67.2

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2 2 . 4 DMSCB 3 67.2 6 7 6 1 2 1 2

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Example 2 3.2 2.24 . 7 32 32 x 5 x 8 32 22.4 160 256 22 4 32 x 7 224

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**0.38 13.3 Example 3 SO, our problem becomes 038 into 1330.**

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 becomes 1330 SO, our problem becomes 038 into 1330. 038 is the same as 38.

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3 5 38 38 38 1330 x 5 x 4 114 190 152 38 19 x 3 190 114

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Example 4 2.48 1.3392 248 133.92

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248 248 . 5 4 x 5 x 6 1240 1488 248 133.92 124 0 248 x 4 9 9 2 992 9 92

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**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: … or … Repeating decimals usually have a bar across the repeating portion. 2.3

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7 . 7 5 8 62 .0 56 Terminating decimal 6 56 4 40

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. 8 3 3 5 .0 6 This is a repeating decimal. 4 8 .83 2 18 2 18 2

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