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Partial Products to Multiply

Key Concepts

  • Multiplication through partial products
  • Multiplication through estimation

Use partial products to multiply by 2-digit numbers  

What is meant by partial products? 

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

Example: 

Find the product of 39 x 15. 

4. 6.1 Multiplication through estimation and partial products. 

Jason donated 16 duffle bags of first aid kits to the American red cross. Each bag contains 12 first aid kits. How many first aid kits did the red cross receive in all? 

Find 12 x 16. 

Solution: 

Draw model for given multiplication. 

Estimate: 12 x 16 is about 10 x 15 =150 

Step1: First, multiply the ones  

Step2: Multiply the tens. 

Example2: 

Ria distributed 27 fruits per one person in an old age home. There are 16 people in an old age home. How many fruits Ria distributed to all? 

Find : 27 x 16.  

Solution:  

Draw area model for 27 x 16. 

Estimate: 16 x 27 is about 15 x 30 = 450 

Step1: First, multiply the ones. 

              20 7 

Step2: Multiply the tens. Add the partial products. 

Ria distributed 452 fruits. 

Example3:  

If there are 23 pages in one drawing book. How many pages are there in 12 drawing books? 

Find 23 x 12. 

Solution: 

Estimate: 23 x 12 is about 20 x 10 = 200. 

Step1: Multiply 23 x 12. 

Step2: Add the partial partial products for the final product. 

12 drawing books has 276 pages.

Exercise:

  1. Estimate the product of 89 X 36.
  2. Estimate the product of 92 X 78.
  3. Find all the partial products. Then add to find the final product draw area model as needed.
    1. 24 x 45
    2. 37 x 68
    3. 38 x 56
  4. Draw area model for the following:
    1. 23 x 64
    2. 67 x 89
    3. 29 x 57
  1. Find the product of 45 x 30 using partial product model.
  2. Estimate, find all the partial products. Then add the final product, draw an area model as needed.
    1. 96 x 23
    2. 36 x 24
    3. 56 x 78
  3. Estimate and find the product of 37 x 23 using partial product model.
  1. Find the product of 26 x 17. Use partial product model.
  1. A cultivator sells 56 packets of oyster mushroom. If each packet contains 22 mushrooms. How many mushrooms did the cultivator sell in all?
  2. If one box contains 45 jelly beans. How many jelly beans do 38 boxes contain?

Concept map:

What have we learned:

  • Understand partial product and estimation.
  • Identify partial products.
  • Understand how to do multiplication through partial products.
  • Understand adding partial products.
  • Identify estimation for the given numbers.
  • Understand how to do multiplication through estimation.

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