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**Division of Whole Numbers I**

Teacher’s Quality Grant

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**Division Basic Problem**

Jill has 4 friends and 20 apples. She needs to distribute the apples equally among her friends. How many apples does each friend receive?

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What is Division? ÷ 20 4 ? 5 Division = Sharing or Grouping a Number in equal parts

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What is Division? Dividing 2 numbers a and b, written as a ÷ b, is actually a repeated subtraction of the number a over b times. Example : 20 ÷ 4 ? = = = 8 – 4 = 4 – 4 = 0 We subtracted 4 five consecutive times, thus: 20 ÷ 4 = 5

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**20 ÷ 4 = 5 Terminology Dividend: The number being divided**

÷ = Dividend: The number being divided Divisor: The number that will divide the dividend equally Quotient: The result of the division

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**Division/Multiplication**

Division is the inverse operation of multiplication Since 4 x 5 = 20 then 20 ÷ 4 = 5 Division fact drill: 36 ÷ 9 = ? Find answer through multiplication: 9 x = 36

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Example We have 12 train enthusiasts. We want to divide them in 3 equal groups so they can ride in the three cars (#2). How many will ride in each car in total? 12 ÷ 3 = ?

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Example Solution 12 ÷ 3 = 4 3 X 4 = 12

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What is Division? When you divide, you partition in equal-sized groups

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Using an Array

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**Use the Multiplication Table**

1 2 3 4 5 6 7 8 9 10 12 14 16 18 15 21 24 27 20 28 32 36 25 30 35 40 45 42 48 54 49 56 63 64 72 81 How can one calculate 20 ÷ 4 using a the multiplication table?

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**Multiplication Table (cont.)**

Dividend 1 2 3 4 5 6 7 8 9 10 12 14 16 18 15 21 24 27 20 28 32 36 25 30 35 40 45 42 48 54 49 56 63 64 72 81 Divisor Find the row that corresponds to the divisor Follow the row until you find the dividend

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**Multiplication Table (cont.)**

Quotient Dividend 1 2 3 4 5 6 7 8 9 10 12 14 16 18 15 21 24 27 20 28 32 36 25 30 35 40 45 42 48 54 49 56 63 64 72 81 Divisor Identify the column number where the dividend is located at That column number is the quotient

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**Division Facts Dividing by 0**

Numbers cannot be divided by 0 because it is impossible to make 0 groups of a number. Dividing by 1 Any number divided by 1 equals that number. If you divide by 1 you have one group and so everything is in that group.

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**Multiplication/Division Inverse Table of 2**

Division Facts (cont.) Multiplying and dividing by 2 Multiplication/Division Inverse Table of 2 X 2 = ÷ 1 4 3 6 8 5 10 12 7 14 16 9 18

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Division Facts (cont.) Dividing is separating a number into several equal groups. When we divide 6 by 3 we are separating 6 into 3 equal groups of 2. There are two common ways to write the sign for division. The number 6 divided by 3 could be written as or 6 ÷ 3. 3 6 ―

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**Final Division Problem**

Judith wants to divide a collection of pencils into groups of 8. Judith has 64 pencils. How many groups will be created?

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**Final Division Problem (cont)**

Is there feedback about the final problem? Discuss your solutions

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