today we will review the chapter:

CONFIDENTIAL 1

Today we will review the Chapter:Whole Numbers – Multiplying & Dividing

Good Afternoon!

Let’s Warm up:.

1) 6 x 4 = 2) 11 x 3 =

3) 8 x 5 = 4) 7 x 6 =

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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

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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 = 122) IDENTITY PROPERTY:We can multiply a number by 1 and the product is the

number. EXAMPLE: 3 x 1 = 3

3) ZERO PROPERTY:We can multiply a number by 0 and the product is

zero. EXAMPLE: 7 x 0 = 0

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Complete each problem using the COMMUTATIVE PROPERTY.

"Change the Order"

6 x 3 = x

2 x 5 = x

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Complete each problem using the IDENTITY PROPERTY.

6 x 1 =

5 x 1 =

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Complete each problem using the ZERO PROPERTY.

0 x 3 =

6 x 0 =

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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.

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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.

0 1 2 3 4 5 6

2 2 2

There are other strategies that can be used for multiplication.Find 7 x 3.

Use a Known Fact

7 groups of 3 = 7 groups of 2 plus 7 7 x 3 = 7 x 2 +

7 = 14 + 7 = 21

Here the numbers are

taking 3 jumps each of

2 steps.

Double a Known Fact

Find 8 x 6.

8 x 6 = (4 x 6 ) + (4 x 6)

= 24 + 24 = 48

8 groups of 6 = 4 groups of 6 + 4 groups of 6

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We looked into the Multiplication Table and its patterns now:

x 0 1 2 3 4 5 6 7 8 9 10 11 12

0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9 10 11 12

2 0 2 4 6 8 10 12 14 16 18 20 22 24

3 0 3 6 9 12 15 18 21 24 27 30 33 36

4 0 4 8 12 16 20 24 28 32 36 40 44 48

5 0 5 10 15 20 25 30 35 40 45 50 55 60

6 0 6 12 18 24 30 36 42 48 54 60 66 72

7 0 7 14 21 28 35 42 49 56 63 70 77 84

8 0 8 16 24 32 40 48 56 64 72 80 88 96

9 0 9 18 27 36 45 54 63 72 81 90 99 108

10 0 10 20 30 40 50 60 70 80 90 100 110 120

11 0 11 22 33 44 55 66 77 88 99 110 121 132

12 0 12 24 36 48 60 72 84 96 108 120 132 144

In the table, the pattern of the square numbers are shown within the yellow

squares.

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Find the products of the following:

1) 3 x 4 = 2) 7 x 2 =

3) 9 x 9 = 4) 5 x 5 =

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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: 2 x (3 x 4) = (2 x 3) x 4

Multiply 2-4 digit by 1 digit

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

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We multiply numbers by first lining up the digits.

236X 6

First multiply 6 with 6 to obtain 36.

6

3

STEP 1:

Regroup 36 as 3

tens and 6 ones.

236X 6

Again, multiply 6 with 3 at the tens place to obtain 18.

Then, add 3 and 18 to obtain 21.

16

23

STEP 2:

Regroup 21 as 2

hundreds and 1 tens.

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236X 6

Then, multiply 6 with 2 at the hundreds place to obtain 12.

Then, 2 and 12 to obtain 14.

1416

23

STEP 3:

Hence, the

result.

Estimate 6 x 44.

By Estimate, we mean an answer that is close to the exact answer.

While estimating products, we round the greater factor.

6 x 44.

6 x 40 =240

Round to the

nearest tens.

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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.

Split 3,839 into 4 parts:3,000 + 800 + 30 + 9

5 x 3,000 =15,0005 x 800 = 4,000

5 x 30 = 1505 x 9 = 45

Then finally add each part:15,000 + 4,000 + 150 + 45 =

19,195

Multiply: 5 x 3,839

Then multiply each part by 5:

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Estimate the products of the given problems:

1) 6 x 44 2) 7 x 48

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Multiply using the Distributive Property :

1) 6 x 694 2) 2 x 7,295

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Multiply 2-3 digit by 2 digit

45X 21

Multiply by the ones. Regroup if

necessary.

45

STEP 1:

Example: To find 21 x 45

45X 21

Multiply by the tens. Regroup if necessary.

45

STEP 2:

900

45X 21

Add the products.

45

STEP 3:

+900945

1

You can use the Distributive Property to

break apart the factors: (1 x 45) + (20

x 25)

Use a zero to show that you are multiplying

by tens.

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Multiply 2-3 digit by 2 digit

Your Turn! Find 19 x 67

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Let us take a break!

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Jig-Saw puzzle

• http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/snowman1.html

Let us see how fast you are on this one!

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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.

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Patterns to Divide and Division facts

• Use Models

Find how many groups of 5 are in 10

counters.

STEP 1:

Find how many counters are in each group if you put 10

counters in 2 equal groups

STEP 2:

Total Number of Groups

Number in Each Group

10 5

10 ÷ 2 = 510 divided by 2 equals 5

Total Number of Groups

Number in Each Group

10 2

10 ÷ 5 = 210 divided by 5 equals 2

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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?

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Patterns to Divide and Division facts

0 1 2 3 4 5 6

2 2 2

Use a related multiplication fact to help you divide32 ÷ 8 = 4

Think:_ x 8 = 324 x 8 = 32

Use a Number Line

6 ÷ 2 = 3There are 3 jumps from 6 to 0

Multiplication and division are inverse operations.

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Dividing with Remainders

• Remainder The number less than the divisor that remains after division is completed.– 31 ÷ 6 = 5 R1. – 1 is the remainder.

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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.

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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.

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Division by 1-digit divisors

• Your Turn! Use models to divide 136 ÷ 4

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Division by 1-digit divisors

• Find: 148 ÷ 3

STEP 1:

Estimate to place the first digit.3 148 Think: 3 1hundred

Not enough hundreds to divide

3 148 Think: 3 14 tensEnough tens to divide

3 148x

The first digit is in the tens place.

STEP 2:

Divide the tens.Think:

3 x 4 tens = 12 tens3 x 5 tens = 15 tens

5 tens are too high.So use 4 tens.

3 1484

-122

Multiply 3 x 4Subtract 14 – 12Compare: 2 < 3

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Division by 1-digit divisors

• Find: 148 ÷ 3

STEP 3:

Bring down the ones and divide.

STEP 4:

3 14849-

1228-27

1Multiply 3 x 9Subtract 28 – 27Compare: 1 < 3

The amount left over is the remainder.

Check the answer.Multiply the quotient by the divisor. 49

x 3147Then add the

remainder.+ 1

148

148 ÷ 3 = 49 R1

Quotientdivisor

remainderdividend

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Division by 1-digit divisors

• Your Turn! Find: 935 ÷ 8

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Division by 2-digit divisors

• Use Models to find: 115 ÷ 12

STEP 1: Show 115 using place-value models.Regroup the hundreds as tens.

STEP 2: Regroup the tens as needed.

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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).

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Division by 2-digit divisors

• Find: 184 ÷ 13

13 1841

-135

13 tens used5 tens left

1 ten in each group

13 184 14

-1354

Bring down 4 ones.54 ones in all.

13 184 14R2-13

54 52 ones used.-522 The 2 left is the remainder.

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Division by 2-digit divisors

• Your Turn! Find: 3,470 ÷ 55

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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?

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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?

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Assessment

Find the product with the help of model.

1) 2 x 2 =

2) 7 x 3 =

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Assessment

Find the product:

573X 3

924X 17

3) 4)

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Assessment

Divide.

5) 1,323 ÷ 4 6) 3,572 ÷ 77

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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.

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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?

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Good Job!