Which Property Of Equality Was Used To Solve This Equation?$\[ \begin{array}{l} 9x = 88 \\ \frac{9x}{9} = \frac{88}{9} \\ x = 9 \frac{7}{9} \end{array} \\]A. Addition Property Of Equality B. Subtraction Property Of Equality C. Multiplication
Introduction
In mathematics, solving equations is a fundamental concept that involves using various properties of equality to isolate the variable and find its value. One of the most common properties used in solving equations is the multiplication property of equality, which states that if two quantities are equal, then their products with the same non-zero number are also equal. In this article, we will explore how the multiplication property of equality is used to solve equations, and we will examine a specific example to illustrate this concept.
The Multiplication Property of Equality
The multiplication property of equality is a fundamental concept in mathematics that states that if two quantities are equal, then their products with the same non-zero number are also equal. This property can be expressed mathematically as:
a = b
ac = bc
where a and b are two quantities, and c is a non-zero number.
Example: Solving the Equation 9x = 88
Let's consider the equation 9x = 88. To solve for x, we can use the multiplication property of equality. We can multiply both sides of the equation by the reciprocal of 9, which is 1/9.
9x = 88
x = 88/9
x = 9 7/9
In this example, we used the multiplication property of equality to isolate the variable x. We multiplied both sides of the equation by 1/9, which is the reciprocal of 9, to solve for x.
Why the Multiplication Property of Equality is Used
The multiplication property of equality is used to solve equations because it allows us to isolate the variable and find its value. By multiplying both sides of the equation by a non-zero number, we can eliminate the coefficient of the variable and solve for its value. This property is particularly useful when the coefficient of the variable is a fraction or a decimal.
Other Properties of Equality
In addition to the multiplication property of equality, there are other properties of equality that are used to solve equations. These include:
- Addition property of equality: If two quantities are equal, then their sums with the same number are also equal.
- Subtraction property of equality: If two quantities are equal, then their differences with the same number are also equal.
Conclusion
In conclusion, the multiplication property of equality is a fundamental concept in mathematics that is used to solve equations. By multiplying both sides of the equation by a non-zero number, we can isolate the variable and find its value. This property is particularly useful when the coefficient of the variable is a fraction or a decimal. In this article, we examined a specific example to illustrate the use of the multiplication property of equality in solving equations.
Frequently Asked Questions
Q: What is the multiplication property of equality?
A: The multiplication property of equality states that if two quantities are equal, then their products with the same non-zero number are also equal.
Q: How is the multiplication property of equality used to solve equations?
A: The multiplication property of equality is used to solve equations by multiplying both sides of the equation by a non-zero number to isolate the variable and find its value.
Q: What are some other properties of equality that are used to solve equations?
A: Some other properties of equality that are used to solve equations include the addition property of equality and the subtraction property of equality.
Q: Why is the multiplication property of equality useful in solving equations?
A: The multiplication property of equality is useful in solving equations because it allows us to isolate the variable and find its value, particularly when the coefficient of the variable is a fraction or a decimal.
References
- [1] "Algebra and Trigonometry" by Michael Sullivan
- [2] "College Algebra" by James Stewart
- [3] "Mathematics for the Nonmathematician" by Morris Kline
Frequently Asked Questions: Properties of Equality =====================================================
Q: What is the addition property of equality?
A: The addition property of equality states that if two quantities are equal, then their sums with the same number are also equal. This can be expressed mathematically as:
a = b
a + c = b + c
where a and b are two quantities, and c is a number.
Q: How is the addition property of equality used to solve equations?
A: The addition property of equality is used to solve equations by adding the same number to both sides of the equation to isolate the variable and find its value.
Q: What is the subtraction property of equality?
A: The subtraction property of equality states that if two quantities are equal, then their differences with the same number are also equal. This can be expressed mathematically as:
a = b
a - c = b - c
where a and b are two quantities, and c is a number.
Q: How is the subtraction property of equality used to solve equations?
A: The subtraction property of equality is used to solve equations by subtracting the same number from both sides of the equation to isolate the variable and find its value.
Q: What is the multiplication property of equality?
A: The multiplication property of equality states that if two quantities are equal, then their products with the same non-zero number are also equal. This can be expressed mathematically as:
a = b
ac = bc
where a and b are two quantities, and c is a non-zero number.
Q: How is the multiplication property of equality used to solve equations?
A: The multiplication property of equality is used to solve equations by multiplying both sides of the equation by a non-zero number to isolate the variable and find its value.
Q: What is the division property of equality?
A: The division property of equality states that if two quantities are equal, then their quotients with the same non-zero number are also equal. This can be expressed mathematically as:
a = b
a/c = b/c
where a and b are two quantities, and c is a non-zero number.
Q: How is the division property of equality used to solve equations?
A: The division property of equality is used to solve equations by dividing both sides of the equation by a non-zero number to isolate the variable and find its value.
Q: What is the zero property of equality?
A: The zero property of equality states that if two quantities are equal, then their sum with zero is also equal. This can be expressed mathematically as:
a = b
a + 0 = b + 0
where a and b are two quantities.
Q: How is the zero property of equality used to solve equations?
A: The zero property of equality is used to solve equations by adding zero to both sides of the equation to isolate the variable and find its value.
Q: What is the identity property of equality?
A: The identity property of equality states that if two quantities are equal, then their sum with the additive identity (0) or their product with the multiplicative identity (1) is also equal. This can be expressed mathematically as:
a = b
a + 0 = b + 0
a × 1 = b × 1
where a and b are two quantities.
Q: How is the identity property of equality used to solve equations?
A: The identity property of equality is used to solve equations by adding or multiplying both sides of the equation by the additive or multiplicative identity to isolate the variable and find its value.
Conclusion
In conclusion, the properties of equality are fundamental concepts in mathematics that are used to solve equations. By understanding and applying these properties, we can isolate the variable and find its value. In this article, we have explored the addition, subtraction, multiplication, division, zero, and identity properties of equality, and we have provided examples of how these properties are used to solve equations.