CONFIDENTIAL 1

Today our topic of discussion will be: Multiply 2-4 digit by 2 digit

Good Afternoon!

Let’s Warm up:.

1) (2 x 6) x 3 =

3) Estimate 5 x 73.

2) (8 x 2) x 6 =

Find the product:

573X 3

4)

CONFIDENTIAL 2

REVIEWLet’s discuss what we did in the last session.

ASSOCIATIVE PROPERTY of Multiplication:

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 2 x (3 x 4) = 2 x 12 = 24 (2 x 3) x 4 = 6 x 4 =24

Associative Property of Multiplication can be used to multiply the three factors. The grouping of the numbers does not affect the

answer.

Multiplication is an operation on two numbers to find a product. Like 3 x 4 = 12.

CONFIDENTIAL 3

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

REVIEW

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.

CONFIDENTIAL 4

REVIEW

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.

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.

CONFIDENTIAL 5

REVIEW

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.

Overestimate: It is estimate greater than the exact answer.Underestimate: It is estimate less than the exact

answer.

CONFIDENTIAL 6

REVIEW

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:

CONFIDENTIAL 7

Let’s start now

Find 20 x 23.

Multiply by the multiples of 10.

For this we can break apart the factors and then add the parts.

3 blocks

20 blocks

20 blocks

20 blocks

20 x 2020 x 3

Hence a total of 460 blocks.

CONFIDENTIAL 8

Find 20 x 23.We can do it in the other way

also.

23 can also be written in the Expanded Form as: 20 + 3.

Now, we multiply each part by 20.

20X 20

400

20X 3

60

Hence, 400 + 60 = 460

CONFIDENTIAL 9

Now, we will see the multiplication of any 2-digit numbers.Find 16 x 19

We will first use models to find the solution:

Use one factor as width and the other factor as the length. The order does not

matter.

Count the blocks.

16 blocks

19

bloc

ks

The product is 304.

CONFIDENTIAL 10

DISTRIBUTIVE PROPERTY of Multiplication:To multiply a sum by a number, You can multiply each addend

by the number and add the product.

EXAMPLE:

3 x (9 + 7) = (3 x 9) + (3 x 7) = 27 + 21 =

48

Here we look at one more property of multiplication.

CONFIDENTIAL 11

Find 236 x 46

We now see the other way of multiplication.

We multiply numbers by first lining up the digits in the following manner:

236X 461416

23

Multiply by the ones.

STEP 1:

Regroup Whereve

r necessar

y.

CONFIDENTIAL 12

STEP 2:

Multiply by the tens.

Regroup Whereve

r necessar

y.236

X 461416

23

9440

12

CONFIDENTIAL 13

236X 461416

23

+9440

12

10856

STEP 3:

Then, add the products.

Hence, 236 x 46 = 10,856

CONFIDENTIAL 14

Some multiplication problems involves multisteps.

By MULTISTEP we mean those problems consisting of multiplications at more than one

step.Solve: Ronny can read 6 pages in hour. He reads 4 hours in one

day. How many pages does he reads in 12 days?

Here, we see that we have to fine the solution in 2 steps.

First step would be to find the number of pages that Ronny reads in 1 day. Second step would be to find the number of pages that Ronny reads in 12 days.

So, we move stepwise.

CONFIDENTIAL 15

STEP 1:

STEP 2:

The number of pages that Ronny reads is 1 day will be:= 6 x 4 = 24 pages

Now, we calculate the number of pages that Ronny reads is 12 days will be:

= 12 x 24 = 288 pages.

Hence, we see that Ronny reads 288 pages in 12 days.

CONFIDENTIAL 16

Estimating Products:

Estimate: 36 x 54

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

While estimating products, we round each factor.36 x 54.

40 x 50 =2,000

Round to the

nearest tens.

Hence, the estimated value of 40 x 50 is 2,000.

Round to the

nearest tens.

CONFIDENTIAL 17

Estimate to the Nearest Hundred or Thousand

Estimate: 48 x 278

48 x 278.

50 x 300 =15,000

Round to the nearest Hundreds.

Hence, the estimated value of 40 x 300 is 15,000.

Round to the

nearest tens.

Estimate: 62,964 x 329

CONFIDENTIAL 18

BREAK

CONFIDENTIAL 19

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puzzle

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CONFIDENTIAL 20

Assessment

Multiply:

1) 20 x 37 = 2) 32 x 50 =

Using the Distributive Property of Multiplication, find the product:

3) 5 x (6 + 7) = 4) 5 x (6 + 7) =

CONFIDENTIAL 21

5) 742X 37

Find the values of the following.

6) 935X 33

CONFIDENTIAL 22

7) Vivian teaches 16 students in one hour. She teaches for 3 hours each day. How many students does she teach in 23

days?

CONFIDENTIAL 23

8) 45 x 320

Estimate:

9) 683 x 7,629

CONFIDENTIAL 24

10) Lisa has 4 boxes of chocolates. Each box has 35 chocolates. How many chocolates does she have in all?

CONFIDENTIAL 25

Very Good!Let's Review

Find 20 x 23.32 can also be written in the Expanded Form as: 20 + 3.Now, we multiply each part by 20.

20X 20

400

20X 3

60Hence, 400 + 60 = 460

We saw the multiplication of 2-digit numbers with the help of models.

We saw the other way of multiplication also.

CONFIDENTIAL 26

DISTRIBUTIVE PROPERTY of Multiplication:To multiply a sum by a number, You can multiply each addend by the

number and add the product.EXAMPLE:

3 x (9 + 7) = (3 x 9) + (3 x 7) = 27 + 21 =

48

Find 236 x 46

We saw more ways of multiplication.

We multiply numbers by first lining up the digits in the following manner:

236X 461416

23Multiply by the ones.

Regroup Whereve

r necessar

y.

STEP 1:

CONFIDENTIAL 27

STEP 2:

Regroup Whereve

r necessar

y.236

X 461416

23

9440

12

Multiply by the tens.

236X 461416

23

+9440

12

10856

STEP 3:

Then, add the products.

Hence, 236 x 46 = 10,856

CONFIDENTIAL 28

By MULTISTEP we mean those problems consisting of multiplications at more than one step.

Estimate: 36 x 54

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

While estimating products, we round each factor.

36 x 54.

40 x 50 =2,000

Round to the

nearest tens.

Hence, the estimated value of 40 x 50 is 2,000.

Round to the

nearest tens.

CONFIDENTIAL 29

You have done a nice job.See you in the next session.