**Properties of multiplication worksheets :**

Worksheets on properties of multiplication are much useful to the students who would like to practice problems on "Multiplication"

1. A person wants to give $20 cash to his six sons. To know the total money spent, He writes 20 six times and add them all. Instead of doing so, what can he do to know the total amount spent ?

2. Are 5 × (– 6) and (– 6) × 5 equal ? What do you come to know from the result ?

3. Do the multiplication given below and discuss your result.

5 x 0, -100 x 0, 0 x a

4. Are [2 x (-5)] x 6 and 2 x [(- 5) x 6] equal ? What do you come to know from the result ?

5. Do the multiplication given below and discuss your result.

5 x 1, -100 x 1, 0 x 1

6. Are 12 x (9 + 7) and (12 x 9) + (12 x 7) equal ? What do you come to know from the result ?

7. Are 12 x (9 - 7) and (12 x 9) - (12 x 7) equal ? What do you come to know from the result ?

**Problem 1 : **

A person wants to give $20 cash to his six sons. To know the total money spent, He writes 20 six times and add them all. Instead of doing so, what can he do to know the total amount spent ?

**Solution :**

He writes 20 six time and add them all as given below.

20 + 20 + 20 + 20 + 20 + 20

Adding 20 six times can be written as (6x20).

Here, the fact what we have to understand is, the result of adding 20 six times is equal to multiplying 6 and 20.

More clearly,

**20+20+20+20+20+20 = 6x20 = 120**

From the above calculation, it is clear that instead of writing 20 six times and adding them all, we can multiply 6 and 20 to get the total money spent.

**Problem 2 :**

Are 5 × (– 6) and (– 6) × 5 equal ? What do you come to know from the result ?

**Solution :**

5 × (– 6) = – 30 and (– 6) × 5 = – 30

Therefore, 5 × (– 6) = (– 6) × 5

Therefore, multiplication is commutative for all real numbers.

In general, for any two real numbers a and b, a × b = b × a.

**Problem 3 :**

Do the multiplication given below and discuss your result.

5 x 0, -100 x 0, 0 x a

**Solution :**

5 × 0 = 0

– 100 × 0 = 0

0 x a = 0

When we multiply any real number by zero, we get the result zero.

In general, for any nonzero real number "a"

a × 0 = 0 × a = 0

**Problem 4 :**

Are [2 x (-5)] x 6 and 2 x [(- 5) x 6] equal ? What do you come to know from the result ?

**Solution :**

[2 x (-5)] x 6 = -10 x 6 = -60

and

2 x [(- 5) x 6] = 2 x (-30) = -60

Thus [2 x (-5)] x 6 = 2 x [(- 5) x 6]

So we can say that real numbers are associative under multiplication.

In general, for any real numbers a, b, c,

(a × b) × c = a × (b × c)

**Problem 5 :**

Do the multiplication given below and discuss your result.

5 x 1, -100 x 1, 0 x 1

**Solution :**

5 x 1 = 5

-100 x 1 = -100

0 x 1 = 1

This shows that ‘1’ is the multiplicative identity for real numbers.

In general, for any real number "a" we have

a x 1 = 1 x a = a

**Problem 6 :**

Are 12 x (9 + 7) and (12 x 9) + (12 x 7) equal ? What do you come to know from the result ?

**Solution :**

12 x (9 + 7) = 12 x 16 = 192

and

12 x (9 + 7) = 12 x 9 + 12 x 7 = 108 + 84 = 192

Thus 12 x (9 + 7) = (12 x 9) + (12 x 7)

In general, for any real numbers a, b, c.

a x (b + c) = (a x b) + (a x c).

Therefore, multiplication is distributive over addition.

**Problem 7 :**

Are 12 x (9 - 7) and (12 x 9) - (12 x 7) equal ? What do you come to know from the result ?

**Solution :**

12 x (9 - 7) = 12 x 2 = 24

and

12 x (9 - 7) = 12 x 9 - 12 x 7 = 108 - 84 = 24

Thus 12 x (9 - 7) = (12 x 9) - (12 x 7)

In general, for any real numbers a, b, c.

a x (b - c) = (a x b) - (a x c).

Therefore, multiplication is distributive over subtraction.

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