MATH

Module 3

Special Properties of Multiplication

A DepEd-BEAM Distance Learning Program supported by the Australian Agency for International Development

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Here we are again our beloved learner; In the previous lesson, you have learned the basic properties of addition and how it help you in adding numbers more easy and quickly. Today you will be learning the Special Properties of Multiplication of whole numbers.

This module deals with the Special Properties of Multiplication. The properties of multiplication will help you get the product easily and can speed the process of the multiplication.

So in this learning module, it is expected that you will be able to:

9 identify the properties of multiplication

9 find the product using the properties of multiplication

9 write the equation and the answer illustrating the properties of multiplication.

A. Complete each mathematical sentence.

1. 8 x 5 = ____ x 8

2. 1 x ____ = 456

3. 0 x 13 = ____

4. 63 x ____ = 25 x 63

5. (4 x 2) x 3 = 4 x (____ x 3)

6. 5 x (3 + 8) = (5 x 3) + (____ x 8)

Lets Learn This

To the Learner

Lets Try This

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B. Write True or False.

7. 4 threes = 6 twos ____

8. (3 x 0) x 8 = 8 ____

9. 4 is a factor of 20 ____

10. 4 x (6 x 2) = (4 x 6) x 4 ____

Multiplication is the sum as repeated addition of the same number.

6 buns by 3 buns

6 x3 = 6 + 6 + 6 = 18

The Following are the Special Properties of Multiplication

1. Commutative Property of Multiplication

The order in which two numbers are multiplied does not affect the product.

Example: 5 x 3 = 15 and 3 x 5 = 15 Therefore, 5 x 3 = 3 x 5

2. Associative Property of Multiplication

If the grouping of the factors is changed, the product remains the same.

Example: (3 x 5) x 2 = 15 x 2 = 30

And 3 x (5 x 2) = 3 x 10 = 30 Thus, (3 x 5) x 2 = 3 x (5 x 2)

Lets Study This

6 X 3 18 Product

Factors

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3. Zero Property of Multiplication

if one factor is 0, the product is always 0.

Example: 35 x 0 = 0 and 0 x 35 = 0 4. Identity (One) Property of Multiplication

the product of any number and 1 is that number.

Example: 56 x 1 = 56 and 1 x 56 = 56 5. Distributive Property of Multiplication over addition.

If one factor is a sum, multiplying before adding does not change the product.

Example: 3 (5 + 2) = 3 x 7 = 21

and (3 x 5) + (3 x 2) = 15 + 6 = 21 clearly, 3 x (5+2) = (3 x 5) + (3 x 2)

A. Use the properties to find the missing number and name the

multiplication property used. 1.) 3 250 x 1 = , _________________

2.) 65 x 72 = 72 x , _________________

3.) 25 x (12 x 15) = (25 x 12) x , _________________

4.) x 510 = 0 , ___________________

5.) 9 x (5 + 11) = ( x 5) + (9 x 11) ______________________

Lets Test Ourselves

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B. Solve for the product.

6.) 4 x (5 x 6) = (4 x 5) x 6

4 x ____ = ____ x 6 ____ = ____

7.) 6 x (20 + 5) = (6 x 20) + (6 x 5)

= ______ + ______

= ______

Read and Solve (2 pts.) 8.) Dino can type 12 three page letters in an hour. How many

pages can be type in 6 hours? ______________________________

A. Write true or false. If true, identify the property of multiplication

illustrated.

1. 8 x 4 = 4 x 8 ________________________________________________

2. 3 x (8 + 2) = (8 x 3) + (2 x 3) ________________________________

3. 7 x (4 + 2) = (7 x 4) + 2 _____________________________________

4. 457 x 0 = 0 _________________________________________________

5. 10 x 96 = 90 x 10 + 6 _______________________________________

B. Solve for the Product.

6. 7 x 8 = ____ x 7

_____ = _____

7. 10 x (6 + 4) = (10 x 6) + (____ x ____) = _______ + ___________ = ________________

Lets Enrich Ourselves

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A. Identify the property of multiplication illustrated.

1. 761 x 0 = 0 __________________________________________

2. 8 x 27 = 27 x 8 ______________________________________

3. 1204 x 1 = 1204 ____________________________________

4. 8 x (4 x 9) = (8 x 4) x 9 ______________________________

5. 5 x (4 + 6) = (5 x 4) + (5 x 6) _________________________

B. Use the properties to find the missing number. Then name the

multiplication Property used.

6. 92 x 65 = 65 x ___________________________________________ 7. 15 x (12 x 3) = (15 x 12) x ________________________________ 8. 2453 x = 2453 _________________________________________ 9. x 325 = 0 _______________________________________________

10. 5 x (7 + 6) = (5 x 7) + ( x 6) _______________________________

A. Use the Distributive property to find the product. Number 1 is done for you.

1. 6 x (40 + 3) = (6 x 40) + (6 x 3)

= 240 + 18

= 258

2. 9 x (8 + 6) = (_____ x _____) + (____ x ____)

= _____ + _____

Lets Do More

Lets Do This

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= _______

B. Rewrite these in simple form, using the distributive property of

multiplication over addition. Number 3 is done for you.

3. (8 + 7) + (8 x 3) = 8 x (7 + 3)

4. (15 x 8) + (15 x 2) = _____ x (___ + ___)

5. (14 x 5) + (14 x 7) = _____ x (___ + ___)

If you got above 12 proceed to the next module.

If you got 8-10 answer the next exercise.

If you got below 8, review the whole module.

Lets Consider This

The Properties of Multiplication are:

Commutative Property - the order of the factors does not change the product.

Associative Property - the way the factors are grouped does not change the

product.

Identify Property - the product of any number and one is that number.

Zero Property - the product of any number and zero is 0.

Lets Remember This

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Lets Try This

1. 5 2. 456 3. 0 4. 25 5. 2 6. 5 7. True 8. False 9. True 10. False

Lets Test Ourselves 1. 3250 , Identity 2. 65 , Commutative 3. 15 , Associative 4. 0 , zero 5. 9 , Distributive Property of

multiplication over addition 6. 4 x 30 = 20 x 6 120 = 120 7. (6 x 20) + (6 x 5) =120 + 30 = 150 8. (12 x 3) x 6 = 36 x 6 = 216 pages

Lets Do This

1. Zero Property 2. Commutative Prop. 3. Identity Prop. 4. Associative Prop. 5. Distributive Property of

Multiplication over addition 6. 92 , Commutative 7. 3 , Associative 8. 1 , Identity 9. 0 , Zero 10. 5 , Distributive Property of

Multiplication over addition

Lets Enrich Ourselves 1. True - Commutative 2. True Distributive Property of

Multiplication over addition 3. False 4. True Zero Prop. 5. False 6. 7 x 8 = 8 x 7 56 = 56 7. (10 x 6) + (10 x 4) = 60 + 40 = 100

Lets Do More

1.) (6 x 40) + (6 x 3) 3.) 8 x (7 + 3)

=240 + 18 =258 4.) 15 x (8 + 2)

2.) = (9 x 8) + (9 x 6) = 72 + 54 5.) 14 x (5 + 7) = 126

Answer Key

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