Division of Whole Numbers I Teacher’s Quality Grant

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?

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

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 ? 20 - 4 = 16 - 4 = 12 - 4 = 8 – 4 = 4 – 4 = 0 We subtracted 4 five consecutive times, thus: 20 ÷ 4 = 5

20 ÷ 4 = 5 Terminology Dividend: The number being divided 20 ÷ 4 = 5 Dividend: The number being divided Divisor: The number that will divide the dividend equally Quotient: The result of the division

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

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 = ?

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

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

Using an Array

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?

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

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

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.

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

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 ―

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?

Final Division Problem (cont) Is there feedback about the final problem? Discuss your solutions