Question

Simplify Name two properties used to evaluate 7 ∙ 1 – 4 ∙ 1/4

Answer 1

Two properties are the order of operations and multiplication distributed over subtraction.

Explanation:

`\textsf{The two properties used to evaluate $ \sf 7 \cdot 1 -4 \cdot (1)/(4) $ are:}`

• Order of operations:
  This property states that we should perform operations inside parentheses first, followed by exponents, multiplication, division from left to right, and addition and subtraction from left to right.

• Multiplication distributed over subtraction:
  This property states that we can distribute the multiplication over the subtraction, as follows:
  
  `\sf 7 \cdot 1 - 4 \cdot (1)/(4) = 7 \cdot 1 - (4 \cdot (1)/(4))`

Simplifying the expression using the order of operations and the multiplication distributes over subtraction properties, we get:

`\sf 7 \cdot 1 - 4 \cdot (1)/(4) = 7 - 1 = 6`

Therefore, the simplified expression is 6.

Answer 2

1. Identity Property of Multiplication

2. Multiplicative Inverse Property

Explanation:

Given expression:

`\large\boxed{7 \cdot 1 - 4 \cdot (1)/(4)}`

The two properties that are being used in this expression are:

1. Identity Property of Multiplication
2. Multiplicative Inverse Property

`\dotfill`

Identity Property of Multiplication

This property states that any number multiplied by 1 retains its original value. In other words, the product of any number and 1 is equal to the original number itself.

1 is the multiplicative identity, as it is the unique number that doesn't change the value of other numbers when multiplied by them.

In this case, the product of the number 7 and 1 is equal to the original number, 7.

`\dotfill`

Multiplicative Inverse Property

This property states that the product of a non-zero number and its reciprocal (multiplicative inverse) is always equal to 1.

In this case, 4 is the number, and 1/4 is the multiplicative inverse (reciprocal) of 4. So their product is 1.

`\dotfill`