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:
- 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.
Related topics
Square 1 to 20 : Chart, Table, Perfect Squares and Examples
Square 1 to 20 When you multiply a number by itself, the result is called a square. And when you’re preparing for exams, you need to have a foundation for algebra and quick mental math because you get a really short time to do your exam. Therefore, learning the squares from one to twenty is […]
Square 1 to 40 : Table, Perfect Squares, Chart and Examples
Square 1 to 40 When you multiply a number by itself, the resulting number is a square, and if you are someone who is either appearing in a competitive exam or just wants to do well in math in school, knowing square 1 to 40 is a really important skill. But manually multiplying every time, […]
Square Root : Definition, Formula, Methods and Types Explained
Square Root Square roots are one of those seemingly daunting maths topics that appear in many different situations, from algebra to geometry. Yet the concepts behind them aren’t as hard to grasp. It makes handling numbers far easier if you know the concept well. Let us understand how to find the square roots of a number […]
Cubes 1 to 20 : Chart, Table, Memory Tricks and Examples
Most students don’t struggle much with smaller cubes like 2³ or 3³. Those usually come quickly. The hesitation starts with numbers like 11³ or 17³. Or when someone suddenly asks, what is 20 cubed? That pause is not a memory problem. It’s about the lack of proper understanding and hence confidence. Naturally, learning cubes 1 […]
Other topics
Comments: