Choose the property of real numbers that justifies the equation.
Answer (1)
The equation 9"." ( c + 2 ) = 9"." c + 9"."2 demonstrates the distributive property.
The equation 7 + ( − 7 ) = 0 demonstrates the additive inverse property.
The equation ( 5"."6 ) "." b = 5"." ( 6"." b ) demonstrates the associative property of multiplication.
The equation 8"."1 = 8 demonstrates the multiplicative identity property.
Explanation
Analyzing the Equations We are asked to identify the properties of real numbers demonstrated by the given equations. Let's analyze each equation separately.
Identifying the First Property The first equation is 9"." ( c + 2 ) = 9"." c + 9"."2 . 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 Second Property The second equation is 7 + ( − 7 ) = 0 . This equation shows that the sum of a number and its additive inverse (negative) is zero. This is the additive inverse property.
Identifying the Third Property The third equation is ( 5"."6 ) "." b = 5"." ( 6"." b ) . This equation shows that when multiplying three or more numbers, the grouping of the numbers does not affect the result. This is the associative property of multiplication.
Identifying the Fourth Property The fourth equation is 8"."1 = 8 . This equation shows that when a number is multiplied by 1, the result is the original number. This is the multiplicative identity property.
Final Answer In summary:
9"." ( c + 2 ) = 9"." c + 9"."2 demonstrates the distributive property.
7 + ( − 7 ) = 0 demonstrates the additive inverse property.
( 5"."6 ) "." b = 5"." ( 6"." b ) demonstrates the associative property of multiplication.
8"."1 = 8 demonstrates the multiplicative identity property.
Examples
Understanding properties of real numbers is crucial in algebra and beyond. For example, the distributive property is used extensively in simplifying expressions and solving equations. Imagine you're buying multiple items at a store, each with a price and a sales tax. The distributive property helps you calculate the total cost efficiently by either adding the prices first and then applying the tax to the sum, or by calculating the tax for each item separately and then adding those amounts to the original prices. Both methods yield the same result, showcasing the practical application of the distributive property in everyday transactions.
