Division of Whole Numbers I Teacher’s Quality Grant.
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Transcript of Division of Whole Numbers I Teacher’s Quality Grant.
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
5Division = 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 = 0We subtracted 4 five consecutive times, thus:20 ÷ 4 = 5
Terminology
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 Solution12 ÷ 3 = 4
12=3 X 4
What is Division?
When you divide, you partition in equal-sized groups
Using an Array
Use the Multiplication Table
0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81
How can one calculate 20 ÷ 4 using a the multiplication table?
Multiplication Table (cont.) 0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81
1. Find the row that corresponds to the divisor2. Follow the row until you find the dividend
Divisor
Dividend
Multiplication Table (cont.)
0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81
3. Identify the column number where the dividend is located at4. That column number is the quotient
Divisor
DividendQuotient
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.
Division Facts (cont.)
• Multiplying and dividing by 2 Multiplication/Division Inverse Table of 2
0 X 2 = 0 ÷ 2 = 01 X 2 = 2 ÷ 2 = 12 X 2 = 4 ÷ 2 = 23 X 2 = 6 ÷ 2 = 34 X 2 = 8 ÷ 2 = 45 X 2 = 10 ÷ 2 = 56 X 2 = 12 ÷ 2 = 67 X 2 = 14 ÷ 2 = 78 X 2 = 16 ÷ 2 = 89 X 2 = 18 ÷ 2 = 9
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.
36―
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
