Algebra - Mid-Chapter 1 Quiz

Explanation
The given equation a(1/a) = 1 represents the property of multiplicative inverse. The multiplicative inverse of a number is the reciprocal of that number, which when multiplied together, gives the result of 1. In this case, multiplying a with its multiplicative inverse 1/a results in 1. Therefore, the correct answer is Multiplicative Inverse.

Explanation
The given equation, a(b + c) = ab + ac, demonstrates the distributive property. The distributive property states that when multiplying a number by the sum of two other numbers, you can distribute the multiplication to each term inside the parentheses. In this case, the "a" is being multiplied by the sum of "b" and "c", and according to the distributive property, we can multiply "a" by each term inside the parentheses separately. Thus, the equation shows the distributive property in action.

Explanation
The property being identified in this question is the Multiplicative Identity property. This property states that when any number is multiplied by 1, the result is always the number itself. In this case, when "a" is multiplied by 1, the result is "a". Therefore, the correct answer is Multiplicative Identity.

Explanation
The given equation states that when any number 'a' is added to zero, the result will always be 'a'. This property is known as the additive identity property, which states that the sum of any number and zero is always equal to the original number. This property is a fundamental concept in mathematics and is used in various mathematical operations and equations.

Explanation
The given equation, a + (-a) = 0, represents the property of additive inverse. In this property, when a number is added to its additive inverse, the result is always zero. In this case, when a is added to its additive inverse (-a), the sum is zero. Therefore, the correct answer is Additive Inverse.

Explanation
The property being identified here is the Multiplicative Property of Zero. This property states that when any number is multiplied by zero, the result is always zero. In this case, when 0 is multiplied by any number, the result is always 0. This property is a fundamental concept in mathematics and is used in various calculations and equations.

Explanation
The given expression involves addition, subtraction, multiplication, and division. According to the order of operations, we should first perform the multiplication and division, and then the addition and subtraction.

Starting with the multiplication, 2 multiplied by 32 equals 64.

Next, we have the addition within parentheses, 7 plus 8 equals 15.

After that, we have the division, 15 divided by 5 equals 3.

Finally, we can perform the subtraction and addition from left to right:
20 minus 64 equals -44, and -44 plus 3 equals -41.

Therefore, the correct answer is not available.

Explanation
The given expression is a(b + c), where a = 2, b = 3, and c = 4. Plugging in these values, we get 2(3 + 4), which simplifies to 2(7) = 14. Therefore, the correct answer is 14.

Explanation
The given expression involves a combination of addition, subtraction, and multiplication. To solve it, we start by performing the subtraction within the parentheses: 11 - 32 = -21. Then, we multiply this result by 23: -21 * 23 = -483. Finally, we add 4 to this product: -483 + 4 = -479. Therefore, the correct answer is -479, not 20.

Explanation
The given equation is 8w - 10, where w = 5. Substituting the value of w into the equation, we get 8(5) - 10 = 40 - 10 = 30. Therefore, the answer is 30.