Understanding Mathematical Properties Quiz

The commutative property of addition states that changing the order of the numbers being added does not change the result. This is why 83 + 6 is equal to 6 + 83.

The commutative property of addition states that changing the order of addends does not change the sum. In this case, x + y is equal to y + x, demonstrating the commutative property.

The commutative property of multiplication states that changing the order of the factors does not change the product. In this case, switching the order of the variables 'w' and 'r' results in the same value, demonstrating the commutative property of multiplication.

The Distributive Property states that for all real numbers a, b, and c: a(b + c) = ab + ac. In this equation, 7 is distributed to both terms inside the parentheses following the Distributive Property.

The question demonstrates the concept of the inverse property of multiplication, where multiplying a number by its reciprocal results in the multiplicative identity, which is 1. The incorrect answers do not apply in this context because they refer to different properties of multiplication.

The given equation exemplifies the inverse property of multiplication, which states that any number multiplied by its reciprocal will result in 1. The incorrect answers are not applicable in this context and do not represent the correct mathematical principle illustrated.

The distributive property states that for all real numbers a, b, and c, a(b + c) = ab + ac. In the given equation, 5 is distributed to both terms inside the parenthesis using the distributive property.

The inverse property of addition states that the sum of a number and its additive inverse is equal to zero. In this case, the sum of 15 and -15, which is the additive inverse of 15, equals zero.

The equation (2w) * 7 = 2(w * 7) showcases the associative property of multiplication, where the order in which multiplication is carried out does not affect the final result.

The reflexive property states that any value is equal to itself. This property is commonly used in mathematical equations and proofs.

The identity property of multiplication states that multiplying any number by 1 results in the original number. In this case, multiplying 4y by 1 results in 4y, showing the identity property in action.

The correct answer is based on the inverse property of multiplication, where multiplying a number by its reciprocal results in 1. This is why 3 * (1/3) equals 1.

The statement (6 + 4) + 5 = 6 + (4 + 5) exemplifies the Associative property of addition where the grouping of numbers does not affect the sum. In this case, regardless of which two numbers are added first, the overall sum remains the same.

The identity property of addition states that any number added to zero equals the original number. The other properties mentioned have different rules and applications in mathematics.

The commutative property of addition states that the order in which numbers are added does not change the sum. In this equation, rearranging the terms results in the same sum, demonstrating the commutative property of addition.

The correct answer is the associative property of addition because it involves regrouping the numbers to simplify the expression without changing the overall value.

The commutative property of multiplication states that the order of the factors does not change the product. In this case, mn = nm because of this property.

The correct answer refers to the symmetric property of equality which states that if a = b, then b = a. In this case, if 3.8 equals z, then z will also equal 3.8.

The correct answer is the distributive property because it describes the property of multiplication over addition that allows us to distribute the factor outside the parentheses to each term inside the parentheses.

The reflexive property states that any quantity is always equal to itself. In this case, -r is always equal to -r, which follows the reflexive property.

The correct answer is the inverse property of addition because when a number is added to its additive inverse, the result is always zero. The other properties mentioned do not apply in this specific equation.

The commutative property of addition states that changing the order of addends does not change the sum. This property allows for the expression 20(a+b) to be equal to 20(b+a) since addition is commutative.

The question tests the knowledge of the associative property of multiplication, which states that the way in which numbers are grouped does not affect the result of multiplication. This can be seen in this example where re-arranging the parentheses does not change the product.

The correct answer, 'Symmetric Property', states that if two variables are equal, then the order in which they are written does not matter. For example, if a = b, then it follows that b = a. The other incorrect answers do not apply to the given scenario.