Multiply 2 Digit by 2 Digit Numbers

Key Concepts

• Use partial products
• Use the standard algorithm

What are the 2-digit numbers?  

10 to 99 numbers are the 2-digit numbers. 

• The largest 2-digit number is 99. 
• The smallest 2-digit number is 10.  

Use partial products 

What is meant by the partial products? 

The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place. 

For instance, 25 x 32 would become (20 x 30) + (20 x 2) + (5 x 30) + (5 x 2). 

Example 1: 

46 persons can sit in one compartment of the train. How many persons can sit in 52 such compartments? 

Solution: 

Use an area model to find the partial products for 46 x 52. 

2,392 persons can sit in 52 compartments.  

Example 2: 

Ria bought a camera. A camera costs $32. Find the cost of 29 such cameras? 

Solution: 

Use an area model to find the partial products for 29 x 32. 

29 cameras costs $928. 

Use the standard algorithm  

Standard algorithm

The standard algorithm in math strategies is where you line up the places and complete the problem starting on the right side with the ones, then the tens place adding in any number is carried. 

2 Digit Multiplication Steps 

Example 1: Multiply 45 x 36 

Step 1: Multiply the ones on the bottom by the ones on the top. 

Step 2: Put the ones in the ones place and regroup the tens above the tens place. 

Step 3: Multiply the bottom ones by the top tens. 

Step 4: Add the tens you regrouped in step 2. 

Step 5: Write down the answer to step 4 next to the ones. 

Step 6: You now will be multiplying with the tens column. Write a 0 in the ones column. 

Step 7: Multiply the tens on the bottom by the ones on the top. 

Step 8: Put the tens next to the 0 from step 6 and regroup the hundreds by placing them above the tens column. 

Step 9: Multiply the tens on the bottom by the tens on the top 

Step 10: Add the regrouped amount from step 8 

Step 11: Write down the answer to step 10  

Step 12: Add the two numbers 

Example 2: 

Example 3:  

Example 4: 

Charmin took her 54 students to the aquarium. Admission for each student was $67. What was the total amount of money needed for the field trip? 

Solution: 

Step 1: Multiply by the ones. 

Step 2: Multiply by the tens. 

Step 3: Add the partial products. 

 $3, 618 needed for the field trip. 

Example 5: 

Kelvin has jewelry company. He ordered 63 boxes of glass beads. There were 47 beads in each box. How many glass beads did he order? 

Solution: 

Step 1: Multiply by the ones. 

Step 2: Multiply by the tens. 

Step 3: Add the partial products 

Kelvin ordered 2961 beads.

Exercise

• Use the partial products to find the product. Draw an area model as needed.
• 23 x 44
• 12 x 35
• Fill the missing numbers using an algorithm model.

• Fill the missing numbers.

• Use partial products to find the product.

• Use an algorithm to find the product.

• Use an algorithm to find the product. Estimate to check if your answer is reasonable.

• John sold 36 cookbooks. One book cost is $27 each. How much did he make?
• An adult human has 32 teeth. If there are 83 adults in a room, how many teeth is that in all?
• Each of the 15 people who visited a pop-up store bought 23 bars of handmade soap. How many bars of soap did they buy in all?
• 28 children can ride a carousel at a time. If the carousel made 19 trips and was filled to capacity each time, how many children did it carry in all?

Concept Map

What have we learned

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