confidential1 today our topic of discussion will be: multiply 2-4 digit by 2 digit good afternoon!...
DESCRIPTION
CONFIDENTIAL3 You can use pattern of factors and products to multiply mentally. 3 x 2 = 6 3 x 20 = 60 3 x 200 = x 2,000 = 6,000 REVIEW We multiply numbers by first lining up the digits. 236 X 6 First multiply 6 with 6 to obtain STEP 1: Regroup 36 as 3 tens and 6 ones.TRANSCRIPT
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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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.