Answered

properties if real numbers , name the property shown by each of the following
1. 3x · 2y = 3 · 2 · x ·y
2. 3(2x)y = (3 · 2)(xy)
3. 1/4 · 4y = 1y
4. 5x · (4y +3x) = 5x · (3x + 4y)
5. (6 + -6)y= 0y



Answer :

semsee45

Answer:

1.  Commutative Property of Multiplication

2.  Associative Property of Multiplication

3.  Inverse Property of Multiplication

4.  Commutative Property of Addition

5.  Inverse Property of Addition

Step-by-step explanation:

The main four mathematical property types are:

  • Associative Property
  • Commutative Property
  • Distributive Property
  • Inverse Property

Associative Property

Grouping of numbers by parentheses in a different way does not affect their sum or product.

Applies to addition and multiplication only.

Addition: (a + b) + c = a + (b + c) = (a + c) + b

Multiplication: (a × b) × c = a × (b × c) = (a × c) × b

Commutative Property

Changing the order or position of two numbers does not change the end result.

Applies to addition and multiplication only.

Addition: a + b = b + a

Multiplication: a × b = b × a

Distributive Property

Multiplying a number by a group of numbers added together is the same as multiplying each number separately.

Addition: a(b + c) = ab + ac

Subtraction: a(b - c) = ab – ac

Inverse Property

Two numbers cancel each other out by adding or multiplying by their inverse.  (The inverse of addition is subtraction and the inverse of multiplication is division).

[tex]\sf \bold{Addition}: \quad a+-a=0[/tex]

[tex]\sf \bold{Multiplication}: \quad a \times \dfrac{1}{a} = 1[/tex]

Question 1

[tex]3x \cdot 2y=3 \cdot 2 \cdot x \cdot y[/tex]

Commutative Property of Multiplication, as changing the order or position of the terms does not change the end result.

Question 2

[tex]3(2x)y=(3 \cdot 2)(xy)[/tex]

Associative Property of Multiplication, as the grouping of the terms by parentheses in a different way does not affect their product.

Question 3

[tex]\dfrac{1}{4} \cdot 4y=1y[/tex]

Inverse Property of Multiplication, as the product of 4 and its reciprocal 1/4 is 1.

Question 4

[tex]5x \cdot (4y+3x)=5x \cdot (3x+4y)[/tex]

Commutative Property of Addition, as changing the order or position of the terms in the parentheses does not change the end result.

Question 5

[tex](6+-6)y=0y[/tex]

Inverse Property of Addition, as adding a number and its inverse together always produces zero.

MisterBrainly

#1

Commutative property of distribution

  • ab=ba

Changing position doesn't change product

#2

Associative property of multiplication

  • a(bc)=(ab)c

#3

Inverse property of multiplication

  • a×1/a=1

#4

Commutative property of multiplication

#5

Inverse property of addition

a+(-a)=0