Question

10-Verify the following properties:
a) Cumulative property of addition.
b) Associative property of multiplication.
c) Distributive property of multiplication over addition
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Answer 1

Commutative Property. The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.

The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

distributive property of multiplication over addition. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

Answer 2

he word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.

Use the Commutative Property to restate "3×4×x" in at least two ways.

They want me to move stuff around, not simplify. In other words, my answer should not be "12x"; the answer instead can be any two of the following:

4 × 3 × x

4 × x × 3

3 × x × 4

x × 3 × 4

x × 4 × 3

The associative property in Multiplication ♥

First, try to calculate (2 x 3) x 4. After, try 2 x (3 x 4). Did you get the same answer for both of them?

If you got the same answer, good job because multiplication has the associative property and the answer won’t change even if the number order of the problem changes. The order in which the numbers are associated doesn’t influence the final answer.

(a x b) x c = a x (b x c) = (a x c) x b

If a= 3, b= 5 y c = 10, we’re left with:

(3 x 5) x 10 = 15 x 10 =150

3 x (5 x 10) = 3 x 50 = 150

(3 x 10) x 5 = 30 x 5 = 150

Distributive Property of Multiplication over Addition

The distributive property of multiplication over addition is applied when you multiply a value by a sum. For example, suppose you want to multiply 5 by the sum of 10 + 3.

According to the property, you can first add the numbers and then multiply by 5.

5(10 + 3) = 5(13) = 65. Or, you can first multiply every addend by 5. This is known as distributing the 5 and then you can add the products.

The multiplication of 5(10) and 5(3) will be performed before you add. 5(10) + 5(3) = 50 + 15 = 65. You can note that the result is same as before.