Arrays and Partial Products

Key Concepts

• Use of array for finding product
• Use of area model for finding product

4. 4 Arrays and partial products

 

What is meant by array? 

An arrangement of objects, pictures, or numbers in rows and columns is called an array. 

The below image is an example for an array. 

What are partial products?  

A product obtained by multiplying a multiplicand by one digit of a multiplier having more than one digit. 

The multiplication below is an example for multiplication through a partial product. 

4. 4.1 Finding products through array models 

Example1: 

There are 13 rows of birds with 24 birds in each row. How many birds are there? 

Use an array to find 13 x 24. 

Solution: 

Step1: Separate each factor into tens and ones. 

Step2: Color each section in a different color. 

Step3: Multiply 10 x 20 = 200 

Step4: Multiply 3 x 20 = 60 

Step5: Multiply 4 x 10 = 40 

Step6: Multiply 3 x 4 = 12 

Step7: Partial products 12,60,40, 200 

Step8: Now add the products. 

             12+60+40+200=312 

 312 birds are there in 13 rows. 

Example2:  

12 rows of cars 13 cars per row. How many cars are there in the parking area? 

Solution: 

Step1: Separate each factor into tens and ones.  

Step2: Color each section in a different color.  

Step3: Multiply 10 x 10 = 100 

Step4: Multiply 2 x 10 = 20 

Step5: Multiply 3 x 10 = 30 

Step6: Multiply 3 x 2 = 6 

 Step7: Partial products 6,20,30,100 

Step8: Now add the products. 

              6+20+30+100=156 

12 x 13 = 156 is close to 10 x 10 =100. The answer is reasonable. 

4.4.2 Finding products through partial products 

Example1: 

An auditorium has 61 rows. Each row has 12 seats. How many seats are there in the auditorium? 

Solution: 

Step1: Multiply 2 one’s x 1 ones. 

Step2: Multiply 2 one’s x 6 tens. 

Step3: Multiply 1 tens x 1 ones.  

Step4: Multiply 1 tens x 6 tens. 

Step5: Add the partial products.
An auditorium has 732 chairs. 

Example2:  

A library has 13 rows. Each row has 25 books. How many books are there in the library? 

Solution: 

Multiply 13 x 27.

Step1: Multiply 7 one’s “×” 3 ones.   

Step2: Multiply 7 one’s  1 ten.

Step3: Multiply 7 one’s  1 ten.      

Step3: Multiply 7 one’s  1 ten.

Step3: Multiply 7 one’s  1 ten.

351 books are there in a library.

Exercise:

1. Use the array drawn on a grid to find each product.

2. Use the array drawn on a grid to find each product.
13 x 14.

3. Find the product of 34 x 45 using partial products strategy.

4. A tire factory produces 48 tires a day. How many tires will the factory produce in 60 days? Use array model for finding the product.

5. 47 books are to be arranged equally on shelves. If 78 books are arranged on each shelf, how many shelves will be needed? Explain which strategy was used.

6. Find the missing factors for the following:
23 x ______ =230
45 x 45 = _________.
36 x 20= __________.
43 x 32 = ________.

7. Find the product of 67 x 42 using partial product model.

8. Find the product of 43 x 64 using partial product model.

9. Match the following:

10. Find the product of 23 x57. Solve this problem using the array strategy.

Concept map

What have we learned:

• Understand an array and partial products.
• Understand how to find the products through array model.
• Understand how to find the products through partial products.
• Identify the partial products.