Choose the property of real numbers that justifies the equation.
| [tex]m * 9 = 9 * m[/tex] | (Choose one) |
| [tex]5 \cdot (c+3) = 5 \cdot c + 5 \cdot 3[/tex] | (Choose one) |
| [tex]n \cdot \frac{1}{n} = 1[/tex] | (Choose one) |
Answer (1)
The equation m ⋅ 9 = 9 ⋅ m demonstrates the commutative property of multiplication.
The equation 5 ⋅ ( c + 3 ) = 5 ⋅ c + 5 ⋅ 3 demonstrates the distributive property of multiplication over addition.
The equation n ⋅ n 1 = 1 demonstrates the multiplicative inverse property.
The properties that justify the equations are commutative property of multiplication, distributive property of multiplication over addition and multiplicative inverse property. C o mm u t a t i v e , D i s t r ib u t i v e , M u lt i pl i c a t i v e I n v erse
Explanation
Analyzing the Problem The problem asks us to identify the properties of real numbers that justify the given equations. Let's analyze each equation separately.
Identifying the First Property The first equation is m "."9 = 9"." m . This equation demonstrates that the order of multiplication does not affect the result. This is the commutative property of multiplication.
Identifying the Second Property The second equation is 5 ⋅ ( c + 3 ) = 5 ⋅ c + 5 ⋅ 3 . This equation shows that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products. This is the distributive property of multiplication over addition.
Identifying the Third Property The third equation is n ⋅ n 1 = 1 . This equation states that when a number is multiplied by its reciprocal, the result is 1. This is the multiplicative inverse property.
Final Answer Therefore, the properties that justify the equations are:
m ⋅ 9 = 9 ⋅ m : Commutative Property of Multiplication
5 ⋅ ( c + 3 ) = 5 ⋅ c + 5 ⋅ 3 : Distributive Property of Multiplication over Addition
n ⋅ n 1 = 1 : Multiplicative Inverse Property
Examples
Understanding the properties of real numbers is fundamental in algebra and arithmetic. For example, the distributive property is used extensively in simplifying algebraic expressions and solving equations. Imagine you are buying 5 identical sets of items, each containing a book and a pen. If the book costs c dollars and the pen costs 3 dollars, the total cost can be calculated as 5 ( c + 3 ) , which is the same as 5 c + 5 ( 3 ) , where 5 c is the total cost of the books and 5 ( 3 ) is the total cost of the pens. These properties make mathematical manipulations easier and more intuitive.
