Multiplication of 3-Digit Numbers By Regrouping
1. Find the product of 231 and 3.
![finding the difference of numbers using the model method](/images/notes/P3_Whole_Numbers_Multiplication_model_1.png)
Step 1: Multiply the ones by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_1_table_step1.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_1_step1.png)
1 ones × 3
= 3 ones
Step 2: Multiply the tens by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_1_table_step2.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_1_step2.png)
3 tens × 3
= 9 tens
Step 3: Multiply the hundreds by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_1_table_step3.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_1_step3.png)
2 hundreds × 3
= 6 hundreds
So, the product of 231 and 3 is 693.
2. What is 135 × 3 ?
Step 1a: Multiply the ones by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_2_table_step1a.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_2_step1.png)
5 ones × 3 = 15 ones
Step 1b: Regroup the ones.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_2_table_step1b.png)
15 ones = 1 ten 5 ones
Step 2a: Multiply the tens by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_2_table_step2a.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_2_step2.png)
3 tens × 3 = 9 tens
Add the tens.
9 tens + 1 ten = 10 tens
Step 2b: Regroup the tens.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_2_table_step2b.png)
10 tens = 1 hundred 0 tens
Step 3: Multiply the hundreds by 3.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_2_table_step3.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_2_step3.png)
1 hundred × 3 = 3 hundreds
Add the hundreds.
3 hundreds + 1 hundred = 4 hundreds
So, 135 × 3 = 405.
3. Rayan has 2 packs of 877 cards each. How many cards does he have in all?
![](/images/notes/P3_Whole_Numbers_Multiplication_model_2.png)
Step 1a: Multiply the ones by 2.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step1a.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_3_step1.png)
7 ones × 2 = 14 ones
Step 1b: Regroup the ones.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step1b.png)
14 ones = 1 ten 4 ones
Step 2a: Multiply the tens by 2.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step2a.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_3_step2.png)
7 tens × 2 = 14 tens
Add the tens.
14 tens + 1 ten = 15 tens
Step 2b: Regroup the tens.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step2b.png)
15 tens = 1 hundred 5 tens
Step 3a: Multiply the hundreds by 2.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step3a.png)
![step-by-step subtraction](/images/notes/P3_Whole_Numbers_Multiplication_3_step3.png)
8 hundreds × 2
= 16 hundreds
Add the hundreds.
16 hundreds + 1 hundred
= 17 hundreds
Step 3b: Regroup the hundreds.
![step-by-step multiplication](/images/notes/P3_Whole_Numbers_Multiplication_3_table_step3b.png)
17 hundreds
= 1 thousand 7 hundreds
= 1 thousand 7 hundreds
Rayan has 1754 cards in all.