1. Today we will review the Chapter:
Good Afternoon!
Today we will review the Chapter:
Whole Numbers – Multiplying & Dividing
Let’s Warm up:.
1) 6 x 4 =
2) 11 x 3 =
3) 8 x 5 =
4) 7 x 6 =
CONFIDENTIAL

2. Multiplication by a whole number is REPEATED ADDITION
Let's Review Factors & Multiples
Factor: Number that is multiplied to give a product.
Product: Number that is obtained by multiplying numbers.
Multiplication by a whole number is REPEATED ADDITION
CONFIDENTIAL

3. There are several properties of multiplication.
1) COMMUTATIVE PROPERTY:
We can change the order of the factors and the product stays the same.
EXAMPLE: 4 x 3 = 12
3 x 4 = 12
2) IDENTITY PROPERTY:
We can multiply a number by 1 and the product is the number.
EXAMPLE: x 1 = 3
3) ZERO PROPERTY:
We can multiply a number by 0 and the product is zero.
EXAMPLE: x 0 = 0
CONFIDENTIAL

4. Complete each problem using the
COMMUTATIVE PROPERTY.
"Change the Order" x
6 x 3 =
2 x 5 = x
CONFIDENTIAL

5. Complete each problem using the
IDENTITY PROPERTY.
6 x 1 =
5 x 1 =
CONFIDENTIAL

6. Complete each problem using the
ZERO PROPERTY.
0 x 3 =
6 x 0 =
CONFIDENTIAL

7. Patterns to Multiply by 2, 10, 100 etc.
We learnt about the following terms:
Multiple: It is the product of a number and any whole number.
Even numbers: Whole numbers that are divisible by 2 are even numbers.
Odd numbers: Whole numbers that are not divisible by 2 are odd numbers.
Prime numbers: Numbers whose factors are only 1 and the number itself are prime numbers.
Composite numbers: All the non-prime numbers except 0 and 1, are Composite Numbers.
CONFIDENTIAL

8. Use a Known Fact Double a Known Fact
We can multiply by the means of Skip Counting also.
By Skip Counting we mean that we can find the multiples of any number by hopping equal steps on the number line. 2 2 2
Here the numbers are taking 3 jumps each of 2 steps. 1 2 3 4 5 6
There are other strategies that can be used for multiplication.
Find 7 x 3.
Find 8 x 6.
Use a Known Fact
Double a Known Fact
7 groups of 3 = 7 groups of 2 plus 7
8 groups of 6 = 4 groups of groups of 6
7 x 3 = 7 x 2 + 7
= = 21
8 x 6 = (4 x 6 ) + (4 x 6)
= = 48
CONFIDENTIAL

9. We looked into the Multiplication Table and its patterns now:
In the table, the pattern of the square numbers are shown within the yellow squares. x 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 15 21 27 30 33 36 28 32 40 44 48 25 35 45 50 55 60 42 54 66 72 49 56 63 70 77 84 64 80 88 96 81 90 99
108
100
110
120
121
132
144
CONFIDENTIAL

10. Find the products of the following:
1) 3 x 4 =
2) 7 x 2 =
3) 9 x 9 =
4) 5 x 5 =
CONFIDENTIAL

11. Multiply 2-4 digit by 1 digit
Multiplication is an operation on two numbers to find a product. Like 3 x 4 = 12.
ASSOCIATIVE PROPERTY:
While multiplying, we can change the grouping of the factors and the product stays the same.
EXAMPLE: x (3 x 4) = (2 x 3) x 4
You can use pattern of factors and products to multiply mentally.
3 x 2 = 6
3 x 20 = 60
3 x 200 = 600
3 x 2,000 = 6,000
CONFIDENTIAL

12. We multiply numbers by first lining up the digits.
STEP 1:
First multiply 6 with 6 to obtain 36.
Regroup 36 as 3 tens and 6 ones. 3
236
X 6 6
STEP 2:
Again, multiply 6 with 3 at the tens place to obtain 18.
Then, add 3 and 18 to obtain 21.
Regroup 21 as 2 hundreds and 1 tens. 23
236
X 6 16
CONFIDENTIAL

13. By Estimate, we mean an answer that is close to the exact answer.
STEP 3:
Then, multiply 6 with 2 at the hundreds place to obtain 12.
Then, 2 and 12 to obtain 14.
Hence, the result. 23
236
X 6
1416
By Estimate, we mean an answer that is close to the exact answer.
Estimate 6 x 44.
While estimating products, we round the greater factor.
6 x 44.
Round to the nearest tens.
6 x 40 =240
CONFIDENTIAL

14. Overestimate: It is estimate greater than the exact answer.
Underestimate: It is estimate less than the exact answer.
We also use the Distributive Property to multiply.
Multiply: 5 x 3,839
Split 3,839 into 4 parts: 3,
Then multiply each part by 5:
5 x 3,000 =15,000
5 x 800 = 4,000
5 x 30 = 150
5 x 9 = 45
Then finally add each part:
15, , = 19,195
CONFIDENTIAL

15. Estimate the products of the given problems:
1) 6 x 44
2) 7 x 48
CONFIDENTIAL

16. Multiply using the Distributive Property :
1) 6 x 694
2) 2 x 7,295
CONFIDENTIAL

17. Multiply 2-3 digit by 2 digit
Example: To find 21 x 45
STEP 1:
STEP 2:
STEP 3:
Multiply by the ones. Regroup if necessary.
Multiply by the tens. Regroup if necessary.
Add the products. 1 45 45 45
X 21
X 21
X 21 45 45 45
900
+900
945
Use a zero to show that you are multiplying by tens.
You can use the Distributive Property to break apart the factors: (1 x 45) + (20 x 25)
CONFIDENTIAL

18. Multiply 2-3 digit by 2 digit
Your Turn! Find 19 x 67
CONFIDENTIAL

19. Let us take a break!
CONFIDENTIAL

20. Let us see how fast you are on this one!
Jig-Saw puzzle
Let us see how fast you are on this one!
CONFIDENTIAL

21. Patterns to Divide and Division facts
Division: An operation on two numbers that tells how many groups or how many in each group.
Dividend: A number to be divided.
Divisor: The number by which the dividend is divided.
Quotient: The result of division.
CONFIDENTIAL

22. Patterns to Divide and Division facts
Use Models
STEP 1:
Total
Number of Groups
Number in Each Group 10 5
Find how many groups of 5 are in 10 counters.
10 ÷ 2 = 5
10 divided by 2 equals 5
STEP 2:
Total
Number of Groups
Number in Each Group 10 2
Find how many counters are in each group if you put 10 counters in 2 equal groups
10 ÷ 5 = 2
10 divided by 5 equals 2
CONFIDENTIAL

23. Patterns to Divide and Division facts
Your Turn!
Use models to find
how many are in each group: 12÷6
35 has how many groups of 5?
CONFIDENTIAL

24. Patterns to Divide and Division facts
Use a related multiplication fact to help you divide
32 ÷ 8 = 4
Think:
_ x 8 = 32
4 x 8 = 32
Use a Number Line 2 2 2
6 ÷ 2 = 3
There are 3 jumps from 6 to 0 1 2 3 4 5 6
Multiplication and division are inverse operations.
CONFIDENTIAL

25. Dividing with Remainders
Remainder The number less than the divisor that remains after division is completed.
31 ÷ 6 = 5 R1.
1 is the remainder.
CONFIDENTIAL

26. Division by 1-digit divisors
You can use models to divide (Example: 57 ÷ 4)
STEP 1:
Show 57 as 5 tens and 7 ones. Draw rectangles to show 4 groups.
STEP 2:
Place an equal number of tens in each group.
Regroup 1 ten and 7 ones as 17 ones.
CONFIDENTIAL

27. Division by 1-digit divisors
You can use models to divide (Example: 57 ÷ 4)
STEP 3:
Place an equal number of ones in each group.
There will be 1 one left. This is the remainder.
CONFIDENTIAL

28. Division by 1-digit divisors
Your Turn! Use models to divide 136 ÷ 4
CONFIDENTIAL

29. Division by 1-digit divisors
Find: 148 ÷ 3
STEP 1:
STEP 2:
Estimate to place the first digit.
Divide the tens.
Think:
3 x 4 tens = 12 tens
3 x 5 tens = 15 tens
3 148
Think:
3 1hundred
Not enough hundreds to divide
3 148
Think:
3 14 tens
5 tens are too high.
So use 4 tens.
Enough tens to divide x 4
3 148
The first digit is in the tens place.
3 148
-12
Multiply 3 x 4 2
Subtract 14 – 12
Compare: 2 < 3
CONFIDENTIAL

30. Division by 1-digit divisors
Find: 148 ÷ 3
STEP 3:
STEP 4:
Bring down the ones and divide.
Check the answer. 49
Multiply the quotient by the divisor.
3 148
-12 49
Quotient 28
x 3
divisor
-27
Multiply 3 x 9
147 1
Subtract 28 – 27
Compare: 1 < 3
Then add the remainder.
remainder
148
dividend
The amount left over is the remainder.
148 ÷ 3 = 49 R1
CONFIDENTIAL

31. Division by 1-digit divisors
Your Turn! Find: 935 ÷ 8
CONFIDENTIAL

32. Division by 2-digit divisors
Use Models to find: 115 ÷ 12
Show 115 using place-value models.
Regroup the hundreds as tens.
STEP 1:
STEP 2:
Regroup the tens as needed.
CONFIDENTIAL

33. Division by 2-digit divisors
Use Models to find: 115 ÷ 12
STEP 3:
Form 12 groups.
Regroup more tens.
Count the number of ones in each group.
There are 9 ones in each group.
Count the number of ones left.
There are 7 ones left (the remainder).
CONFIDENTIAL

34. Division by 2-digit divisors
Find: 184 ÷ 13 1
1 ten in each group
13 184
-13
13 tens used 5
5 tens left 14
13 184
-13
Bring down 4 ones.
54 ones in all. 54
14R2
13 184
-13 54
52 ones used.
-52 2
The 2 left is the remainder.
CONFIDENTIAL

35. Division by 2-digit divisors
Your Turn! Find: 3,470 ÷ 55
CONFIDENTIAL

36. Word problems
A team wants to sell 240 books to raise money. If there are 15 players, what is the number of books each player must sell?
CONFIDENTIAL

37. Word problems
Skate laces are available in boxes of 20 pairs for $30 or boxes of 100 pairs for $120. Which is the better buy? Why?
CONFIDENTIAL

38. Assessment Find the product with the help of model. 1) 2 x 2 =
CONFIDENTIAL

39. Assessment
Find the product: 3)
573 4)
924
X 3
X 17
CONFIDENTIAL

40. Assessment
Divide.
6) 3,572 ÷ 77
5) 1,323 ÷ 4
CONFIDENTIAL

41. Assessment Solve. What number am I?
7) I am a number between 10 and 20. If you divide either 61 or 73 by me, the remainder is 1.
8) I am a number between 10 and 20. If you divide either 45 or 56 by me, the remainder is 1.
CONFIDENTIAL

42. Assessment
9) There is $180 to build 12 booths. How much money is there fro each booth?
10) There are 5,000 cups for lemonade at the carnival. The lemonade will be served at 12 tables. How many cups are on each table? How many cups are left over?
CONFIDENTIAL

43. Good Job!
CONFIDENTIAL