Which Property of Real Numbers Is Shown Below?

The property of real numbers shown below is the distributive property. This property states that for any real numbers a, b, and c, the following is true: a(b+c) = ab+ac. In other words, when multiplying a real number by the sum of two other real numbers, the result is the same as if the first number were multiplied by each of the other two numbers separately and then the products were added together. This property is a fundamental principle of algebra that is often used to simplify equations.

The distributive property is illustrated in the equation below:

a(b+c) = ab+ac

In this equation, a is multiplied by the sum of b and c. This is equivalent to multiplying a by b and then multiplying a by c and adding the two products together. The distributive property allows us to simplify this equation by breaking it down into simpler operations.

The distributive property is a powerful tool that can be used to simplify many equations. In particular, it is often used to simplify equations that involve more than one set of parentheses. For example, consider the following equation:

(a+b)+(c+d) = a+b+c+d

This equation can be simplified using the distributive property as follows:

(a+b)+c+d = a(1+1)+b(1+1)+c+d = a+a+b+b+c+d = a+b+c+d

As this example shows, the distributive property can be used to quickly simplify equations that would otherwise be quite difficult to solve.

In summary, the distributive property is a very important property of real numbers that allows us to simplify many equations. It is a fundamental principle of algebra that is often used to simplify equations.

The distributive property is a property of real numbers that states that for any real numbers a, b, and c, a(b + c) = ab + ac. This property is key in simplifying algebraic expressions and solving equations.

The distributive property is one of the most fundamental properties of real numbers. It is often used without conscious thought by experienced mathematicians. However, it is worth taking some time to think about why the distributive property works.

At a basic level, the distributive property simply states that when you are multiplying a number by a sum, you can get the same result by multiplying the number by each addend in the sum and then adding the products together. For example, let's say you want to multiply 3 by 6. Using the distributive property, you can break down the 6 into 2 + 4 and then multiply 3 by each addend, 2 and 4, and add the results together. So 3(2 + 4) = 3(2) + 3(4) = 6 + 12 = 18. As you can see, the distributive property can be a very powerful tool in simplifying complex algebraic expressions.

The distributive property is also very useful in solving equations. Many equations can be solved by using the distributive property to "clear" fractions or decimal points from variables. For example, the equation 3x + 2 = 10 can be solved by using the distributive property to clear the 2 from the left hand side of the equation. 3x + 2 = 10 becomes 3x = 8, and then x = 8/3 or 2.2.

In summary, the distributive property is a very important property of real numbers that can be used to simplify algebraic expressions and solve equations. It is worth taking some time to understand why the distributive property works so that you can more effectively use it in your mathematical work.

The distributive property is a mathematical rule that allows you to simplify expressions that contain addition or multiplication. It states that the operations of addition and multiplication can be distributed over the terms of an expression. For example, if you have the expression "3 + 4x", you can use the distributive property to simplify it to "3 + (4x)" or "3x + 4".

The distributive property is often used when simplifying complex mathematical expressions. It is also useful when solving equations. For example, if you have the equation "x + 3 = 7", you can use the distributive property to simplify it to "x = 4".

The distributive property is a powerful tool that can be used to simplify many different types of equations. However, it is important to remember that the distributive property does not always work. For example, the expression "4 / (2 + 3)" cannot be simplified using the distributive property.

The distributive property is used to simplify expressions that have multiple terms. It states that for any real numbers a, b, and c, a(b + c) = ab + ac. In other words, the distributive property allows you to multiply a single term by each term in a set of parentheses. This is helpful because it means you can break down a complicated expression into simpler parts.

For example, consider the expression 3(2x + 5). Using the distributive property, we can simplify this to 6x + 15. We do this by multiplying 3 by each term in the parentheses: 3(2x + 5) = 3(2x) + 3(5) = 6x + 15.

The distributive property is also useful when solving equations. For instance, suppose we want to solve the equation 2(x + 3) = 16. We can use the distributive property to simplify this equation so that it becomes 2x + 6 = 16. Then, we can solve for x by subtracting 6 from each side: 2x + 6 = 16; 2x = 10; x = 5.

In summary, the distributive property is a helpful tool for simplifying expressions and solving equations. It is a fundamental concept in algebra, so it is important to understand how it works.

In mathematics, the distributive property is a property of certain binary operations that states that for each operand, the operands can be distributed over the other operand. This property is used to simplify many algebraic expressions.

The distributive property is most commonly used with addition and multiplication. It states that for any real numbers a and b, and for any real number c:

a \times \left( b + c \right) = \left( a \times b \right) + \left( a \times c \right)

or equivalently:

a \times \left( b + c \right) = a \times b + a \times c

This can be written in symbolic form as:

\forall a, b, c \in \mathbb{R}: a \times \left( b + c \right) = \left( a \times b \right) + \left( a \times c \right)

or:

\forall a, b, c \in \mathbb{R}: a \times \left( b + c \right) = a \times b + a \times c

The distributive property also holds for multiplication by negative numbers:

\forall a, b, c \in \mathbb{R}: a \times \left( b - c \right) = \left( a \times b \right) - \left( a \times c \right)

The distributive property can also be applied to other algebraic operations, such as subtraction and division, although it is not as commonly used. For example, for any real numbers a and b, and for any non-zero real number c:

a \div \left( b + c \right) = \left( a \div b \right) + \left( a \div c \right)

If the distributive property is applied to addition and multiplication, it can be used to simplify many algebraic expressions. For example, consider the expression:

2 \times \left( 3 + 4 \right)

By applying the distributive property, this expression can be simplified to:

2 \times 3 + 2 \times 4

Which is equal to:

6 + 8

The distributive property states that for any numbers a, b, and c, we have a(b + c) = ab + ac. The associative property states that for any numbers a, b, and c, we have (a + b) + c = a + (b + c). Both properties are algebraic properties that hold for addition and multiplication, but the distributive property also holds for division and subtraction.

The distributive property is often used to simplify expressions. For example, suppose we want to simplify the expression 3(2 + 4). We can use the distributive property to break up the expression into 3(2) + 3(4), which is 6 + 12, which is 18.

The associative property is often used to regroup terms. For example, suppose we want to add the numbers 2, 3, and 4. We can use the associative property to regroup the terms as (2 + 3) + 4, which is 5 + 4, which is 9.

The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac. The commutative property, on the other hand, says that for any real numbers a and b, a + b = b + a. So, the main difference between the distributive property and the commutative property is that the distributive property is applied to multiplication while the commutative property is applied to addition.

The distributive property is a powerful tool that can be used to simplify complex algebraic expressions. For instance, consider the expression 3(2x + 5). Applying the distributive property, we have 3(2x + 5) = 6x + 15. This is much easier to work with than the original expression.

The commutative property is also useful for simplifying expressions. For example, consider the expression 5 + 3x. Using the commutative property, we can rewrite this as 3x + 5. This is again easier to work with than the original expression.

These two properties are both extremely important in mathematics and can be used to simplify a wide variety of expressions.

The distributive property is a mathematical property that allows the distribution of a multiplicative operation over an addition. It states that, for any real numbers a, b, and c, the following equation holds:

a(b + c) = ab + ac

The distributive law is a rule of thumb used in algebra that states that the distributive property can be applied to addition and multiplication. In other words, the distributive law states that the order of operations can be reversed when distributing multiplication over addition.

The distributive property is a fundamental principle of algebra that allows us to simplify expressions that contain grouped terms. The distributive rule is a specific instance of the distributive property that allows us to distributive terms that are being divided by a common factor. Although the distributive property is a more general concept, the distributive rule is a useful tool that can be applied to a variety of problems.

The distributive property states that for any real numbers a, b, and c, we have:

a(b + c) = ab + ac

This equation tells us that we can distributive a term across a sum or difference. In other words, we can distribute a term to each term within parentheses. For example, if we want to simplify the expression 2(x + 3), we can use the distributive property to get:

2(x + 3) = 2x + 2(3)

= 2x + 6

= 2x + 3 + 3

= 2x + 3 + 2x

= 4x + 3

The distributive rule is a specific instance of the distributive property that allows us to distributive terms that are being divided by a common factor. The distributive rule states that for any real numbers a, b, and c, we have:

a(b/c) = (ab)/c

This equation tells us that we can distributive a term across a term that is being divided by a common factor. In other words, we can distribute a term to each term within parentheses that is being divided by the common factor. For example, if we want to simplify the expression 2(x/3), we can use the distributive rule to get:

2(x/3) = (2x)/3

= 2(x)/3

= 2x/3 + 2x/3

= (2x + 2x)/3

= 4x/3

Although the distributive property is a more general concept, the distributive rule is a useful tool that can be applied to a variety of problems. The distributive rule can be used to simplify expressions that contain fractions. It can also be used to distributive terms that are being raised to a power. The distributive property is a powerful tool that can be used to simplify a wide variety of algebraic expressions.

The distributive property is a mathematical rule that is used to multiply numbers within parentheses. The distributive property of multiplication states that when multiplying a number by a sum, the product is equal to the sum of the products of themultiplicand and each addend within the parentheses. In other words, the distributive property of multiplication allows you to multiply a number by each number within a set of parentheses, and the answer will be the same as if you had multiplied the number by the sum of all the numbers within the parentheses.

For example, if you wanted to multiply 2 by the sum of 3 + 4, you could use the distributive property of multiplication and multiply 2 by 3 and 2 by 4, and then add the results together. This would give you the same answer as if you had simply multiplied 2 by (3 + 4), which is 14.

The distributive property is a useful mathematical tool that can be used to simplify calculations. It is important to note that the distributive property is not the same as the distributive property of multiplication. The distributive property of multiplication states that when multiplying a number by a sum, the product is equal to the sum of the products of the multiplicand and each addend within the parentheses. In other words, the distributive property of multiplication allows you to multiply a number by each number within a set of parentheses, and the answer will be the same as if you had multiplied the number by the sum of all the numbers within the parentheses.

For example, if you wanted to multiply 2 by the sum of 3 + 4, you could use the distributive property of multiplication and multiply 2 by 3 and 2 by 4, and then add the results together. This would give you the same answer as if you had simply multiplied 2 by (3 + 4), which is 14.

The distributive property is a useful mathematical tool that can be used to simplify calculations. It is important to note that the distributive property is not the same as the distributive property of multiplication. The distributive property is used to multiply numbers within parentheses, while the distributive property of multiplication is used to multiply a number by each number within a set of parentheses.