1

Math 50

1.4 – Dividing Whole Numbers; Solving Equations

2

Natural numbers: ______________________

Whole numbers: ______________________

3

Natural numbers: ______________________

Whole numbers: ______________________

1, 2, 3, 4, 5, 6, …

4

Natural numbers: ______________________

Whole numbers: ______________________

1, 2, 3, 4, 5, 6, …

0, 1, 2, 3, 4, 5, 6, …

5

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

6

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

7

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

8

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

9

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

10

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

11

Here’s a division sentence:

Other ways to write the same division sentence:

How to divide

12

Ex 1.Divide: Ex 2.Divide:

How to divide

13

What does division mean?In math, it means separating into equal parts.

Division problems come in two main flavors.

When to divide

14

1. If a deck of 52 cards are divided between 13 players, how many cards does each player get?

(Imagine dealing out the cards, and each player would end up with 4 cards.)

When to divide

15

2. How many bags of 5 oranges could be made from a box of 40 oranges?

(Imagine making each bag of 5 oranges until you run out of oranges)

When to divide

16

Ex 3.How many 15-cent stamps can you buy with $10?(Imagine buying each 15-cent stamp until you run out of money.)

When to divide

17

Ex 4.Suppose Roger’s annual salary is $42552, and he gets paid monthly. What is his monthly salary?(Imagine “dealing out” the $42552 into each of the 12 months.)

When to divide

18

Note: We can check our answers using ____________________ (which is the “inverse” of division).

That is, take your answer and multiply it by the ____________. Then add the ______________.

19

Note: We can check our answers using ____________________ (which is the “inverse” of division).

That is, take your answer and multiply it by the ____________. Then add the ______________.

multiplication

20

Note: We can check our answers using ____________________ (which is the “inverse” of division).

That is, take your answer and multiply it by the ____________. Then add the ______________.

multiplication

divisor

21

Note: We can check our answers using ____________________ (which is the “inverse” of division).

That is, take your answer and multiply it by the ____________. Then add the ______________.

multiplication

divisor remainder

22

(that is, division is not _______________________)

(that is, division is not _______________________)

3. ____(here is any number)

4. ____

Some things to know about division

23

(that is, division is not _______________________)

(that is, division is not _______________________)

3. ____(here is any number)

4. ____

Some things to know about division

commutative

24

(that is, division is not _______________________)

(that is, division is not _______________________)

3. ____(here is any number)

4. ____

Some things to know about division

associative

commutative

25

(that is, division is not _______________________)

(that is, division is not _______________________)

3. ____(here is any number)

4. ____

Some things to know about division

𝒏

associative

commutative

26

(that is, division is not _______________________)

(that is, division is not _______________________)

3. ____(here is any number)

4. ____

Some things to know about division

𝟎

𝒏

associative

commutative

27

5. is ______________ (here )

6. is ___________________

7. ____ (here )

Some things to know about division

28

5. is ______________ (here )

6. is ___________________

7. ____ (here )

Some things to know about division

undefined

29

5. is ______________ (here )

6. is ___________________

7. ____ (here )

Some things to know about division

indeterminate

undefined

30

5. is ______________ (here )

6. is ___________________

7. ____ (here )

Some things to know about division

𝟏

indeterminate

undefined

31

When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________

Divisibility rules

32

When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________

Divisibility rules

When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

33

When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________

Divisibility rules

When the sum of the digits is divisible by 3

When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

34

When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________

Divisibility rules

When it ends in 0 or 5

When the sum of the digits is divisible by 3

When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

35

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

36

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

37

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

38

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 3+0=3 6+8+0+9=23 3+8+9+4=24 5+8+3+9+0=25 8+4+3+7+1=23 4+5+7+4+8+9+2+0+5=44Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

39

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 3+0=3 6+8+0+9=23 3+8+9+4=24 5+8+3+9+0=25 8+4+3+7+1=23 4+5+7+4+8+9+2+0+5=44Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

div. by 3

div. by 3

40

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 3+0=3 6+8+0+9=23 3+8+9+4=24 5+8+3+9+0=25 8+4+3+7+1=23 4+5+7+4+8+9+2+0+5=44Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

div. by 3

div. by 3

41

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 3+0=3 6+8+0+9=23 3+8+9+4=24 5+8+3+9+0=25 8+4+3+7+1=23 4+5+7+4+8+9+2+0+5=44Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

div. by 3

div. by 3

42

Ex 5.Circle the numbers that are divisible by 2:30 3894 84371 6809 58390 457489205 Ex 6.Now circle the numbers that are divisible by 3:30 3894 84371 6809 58390 457489205 3+0=3 6+8+0+9=23 3+8+9+4=24 5+8+3+9+0=25 8+4+3+7+1=23 4+5+7+4+8+9+2+0+5=44Ex 7.Now circle the numbers that are divisible by 5:30 3894 84371 6809 58390 457489205

div. by 3

div. by 3

43

Sometimes it is helpful to write unknown quantities as variables, like , , , etc.

Ex 8.Solve and check. Ex 9.Solve and check. Ex 10.The area of a rectangular room is 150 square feet, and the length of one side is 15 feet. What is the width of the room?

Solving equations