Question

Directions: Determine the axiom that justifies each of the following statements.

1. 2( -a + 5) = (2)(-a) + (2)(5)

2. 2/5 ⋅ 1 = 2/5

3. (x + 5) + 2 = x + (5 + 2)


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Answer 1

1. Distributive Property of Multiplication
2. Identity Property of Multiplication
3. Associative Property of Addition

Explanation:

Distributive Property of Multiplication

The distributive property of multiplication is to distribute or multiply one term by all terms.

• 2(-a + 5) Distrbute 2 to -a and 5
• 2(-a) + 2(5)
• -2a + 10

Identity Property of Multiplication

Identity property is to multiply by 1. This doesn't change the value, so it keeps the value, identity, the same.

• 2/5 * 1 = 2/5

Associative Property of Addition

The associative property is to group terms differently, preferably like terms. 2 and 5 are like terms, because they are integers.

• (x + 5) + 2
• x + (5 + 2)
• x + 10

-Chetan K

Answer 2

1. distributive property
2. multiplicative identity element
3. associative property of addition

Explanation:

1.

The distributive property of multiplication over addition tells you a factor outside parentheses will multiply each term inside parentheses. That fact is used to expand the given expression. In general, ...

a(b +c) = ab +ac

2(-a +5) = 2(-a) +2(5)

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2.

The multiplicative identity element is the value that can multiply any expression and leave it unchanged. It is 1. That is, multiplying anything by 1 leaves it unchanged.

This fact is generally used to cancel factors common to a numerator and denominator: (2x)/2 = x(2/2) = x(1) = x, for example. It is also used extensively in units conversion.

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3.

The associative property of addition lets you group the terms of a sum any way you like. It lets you move parentheses at will. (Beware subtraction.)

Here, the parentheses are moved from grouping the first two terms to instead grouping the last two terms.

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Additional comment

These are part of the vocabulary of math. Even if you don't remember the specific definitions, it is essential to remember what these properties allow. Making use of them is the way that expressions are simplified and equations are solved.