Multiply 3 Digit by 2 Digit Numbers

Key Concepts

• Use partial products
• Use the standard algorithm

What are the 3-digit numbers? 

100 to 999 are the 3-digit numbers. 

100 is the smallest 3-digit number. 

999 is the largest 3-digit number. 

How to multiply a 3-digit number with a 2-digit number? 

1. Multiply by the number in the ones place. 

2. Put a zero below in the ones place. 

3. Multiply by the number in the tens place. 

4. Add them up. 

For example, 324 × 46 

Use partial products 

Example 1: 

In an auditorium, there are 493 rows with 14 seats in each row. How many seats are available? 

Solution:  

Multiply 493 × 14 

6, 902 seats are available. 

Example 2: 

Lenin bought a school bag. A bag cost is $ 236. Find the cost of 47 such bags?  

Solution: 

Multiply 236 × 47 

47 bags cost $11,092. 

Use the standard algorithm  

Example 1: 

Charmin took her 735 students to the cricket stadium. Admission for each student was $24. What was the total amount of money needed? 

Solution: 

Step 1: To use the standard algorithm, first multiply by the ones, regroup as needed. 

4 × 5 ones= 20 ones or 2 tens 

4 × 3 tens = 12 tens  

12 tens + 2 tens = 14 tens. 

14 tens = 1 hundred 4 tens. 

4 × 7 hundred = 28 hundreds. 

28 hundred + 1 hundred = 29 hundred. 

Step 2: Multiply by the tens regroup as needed.  

20 × 5 ones =100 ones 

20 × 3 tens = 60 tens or 6 hundred. 

20 × 7 hundreds = 140 hundreds or 14 thousand. 

 Step 3: Add to get the final product 

$17, 640 amount was needed. 

Example 2: 

Robert ordered 134 boxes of magnetics. There were 35 magnetic balls in each box. How many magnetic balls did he order? 

Solution: 

Step 1: To use the standard algorithm, first multiply by the ones, regroup as needed. 

5 × 4 ones= 20 ones or 2 tens 

5 × 3 tens = 15 tens  

15 tens + 2 tens = 17 tens. 

17 tens = 1 hundred 7 tens. 

5 × 1 hundred = 5 hundreds. 

5 hundred + 1 hundred = 6 hundred. 

Step 2: Multiply by the tens regroup as needed.  

30 × 4 ones =120 ones 

30 × 3 tens = 90 tens or 9 hundred. 

30 × 1 hundreds = 30 hundreds or 3 thousand. 

3 thousand +1 thousand = 4 thousands. 

Step 3: Add to get the final product.

Step 3: Add to get the final product. 

He ordered 4,690 magnetic balls.

Exercise

• Find each product. Estimate to check your answer is reasonable.

a.       3 1 5                                                 b.       4 9 6

          × 7 7                                                            × 1  6

          _________                                                         _________

          _________                                                         _________

• Use partial products to find the product.

a.     8 6 7                                                 b.       5 4 8

         × 6 3                                                            × 8  6

         _________                                                         _________

         _________                                                         _________

• Use standard algorithm model to find the product.

a.     9 9 1                                                 b.       5 4 0

                  × 4 4                                                            × 5  1

                  _________                                                         _________

                  _________                                                         _________

• Determine the missing digit in the following multiplication.

a.     3 8 2

         × __ 4              

         _________

         16,808

         _________

• Determine the missing digit in the following multiplication.

• Find the product. Estimate to check for reasonableness.

         a.     3 7 2

                  × 4 3

                  _________

                  _________           

• Last month bakery sold 345 boxes of cupcakes. Each box has 15 cupcakes. How many cakes did the store sell in the last month? Find 15 x 345.
• Sally shoots an arrow 130 yards. Flame shoots her arrow 12 times as far. How far did  Flame’s arrow go
• Mother bought 35 large packets of spearmint bubble gum. If each packet contains pieces, how many pieces are there altogether?
• Laura sells home-made pizza sauce. If she uses 19 tomatoes to make one jar of sauce, how  many tomatoes do she need to make 115 jars?

What have we learned

• Understand 3 digit numbers.
• Understand partial products.
• Multiplying 3-digit number by 2 digit numbers through partial product model.
• Identify the partial products.
• Multiplying 3-digit number by 2 digit numbers through standard algorithm model.

Concept Map