Which Equation Is Made True With The Number 7?Choose The Correct Answer Below.A. $3 \div 7 = \frac{3}{4}$B. $7 \div 9 = \frac{7}{9}$C. $28 \div 7 = \frac{7}{4}$D. $5 \div 35 = 7$

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Introduction

In mathematics, equations are used to represent relationships between variables. When we are given a number, we can use it to solve equations and find the truth value of a statement. In this article, we will explore which equation is made true with the number 7.

Understanding the Options

Before we dive into the solutions, let's understand the options given:

  • Option A: 3÷7=343 \div 7 = \frac{3}{4}
  • Option B: 7÷9=797 \div 9 = \frac{7}{9}
  • Option C: 28÷7=7428 \div 7 = \frac{7}{4}
  • Option D: 5÷35=75 \div 35 = 7

Analyzing Option A

Let's start by analyzing option A: 3÷7=343 \div 7 = \frac{3}{4}. To determine if this equation is true, we need to evaluate the left-hand side of the equation.

3÷7=373 \div 7 = \frac{3}{7}

This is not equal to 34\frac{3}{4}, so option A is not the correct answer.

Analyzing Option B

Next, let's analyze option B: 7÷9=797 \div 9 = \frac{7}{9}. To determine if this equation is true, we need to evaluate the left-hand side of the equation.

7÷9=797 \div 9 = \frac{7}{9}

This is equal to 79\frac{7}{9}, so option B is the correct answer.

Analyzing Option C

Now, let's analyze option C: 28÷7=7428 \div 7 = \frac{7}{4}. To determine if this equation is true, we need to evaluate the left-hand side of the equation.

28÷7=428 \div 7 = 4

This is not equal to 74\frac{7}{4}, so option C is not the correct answer.

Analyzing Option D

Finally, let's analyze option D: 5÷35=75 \div 35 = 7. To determine if this equation is true, we need to evaluate the left-hand side of the equation.

5÷35=175 \div 35 = \frac{1}{7}

This is not equal to 7, so option D is not the correct answer.

Conclusion

In conclusion, the correct answer is option B: 7÷9=797 \div 9 = \frac{7}{9}. This equation is made true with the number 7.

Why is Option B the Correct Answer?

Option B is the correct answer because it is the only equation that is true when the number 7 is used. The other options are either false or do not involve the number 7.

What is the Importance of Understanding Equations?

Understanding equations is important because it helps us to solve problems and make decisions. In mathematics, equations are used to represent relationships between variables, and by solving them, we can find the truth value of a statement.

Real-World Applications of Equations

Equations have many real-world applications, including:

  • Science: Equations are used to describe the laws of physics and chemistry.
  • Engineering: Equations are used to design and optimize systems.
  • Economics: Equations are used to model economic systems and make predictions.

Tips for Solving Equations

Here are some tips for solving equations:

  • Read the equation carefully: Make sure you understand what the equation is asking.
  • Use inverse operations: Use inverse operations to isolate the variable.
  • Check your answer: Make sure your answer is correct by plugging it back into the equation.

Conclusion

Introduction

In our previous article, we explored which equation is made true with the number 7. In this article, we will answer some frequently asked questions (FAQs) about equations.

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS).

Q: What is the difference between an equation and an expression?

A: An expression is a mathematical statement that does not contain an equal sign (=). An equation, on the other hand, is a mathematical statement that contains an equal sign (=).

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable (the letter or symbol that represents the unknown value). You can do this by using inverse operations, such as addition and subtraction, multiplication and division.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation.

Q: What is a quadratic equation?

A: A quadratic equation is an equation in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I graph an equation?

A: To graph an equation, you need to plot the points that satisfy the equation on a coordinate plane. You can use a graphing calculator or a computer program to help you graph the equation.

Q: What is the difference between a function and an equation?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An equation, on the other hand, is a statement that expresses the equality of two mathematical expressions.

Q: Can I have multiple solutions to an equation?

A: Yes, it is possible to have multiple solutions to an equation. This is called a system of equations.

Q: How do I solve a system of equations?

A: To solve a system of equations, you need to find the values of the variables that satisfy both equations. You can use substitution or elimination methods to solve a system of equations.

Conclusion

In conclusion, equations are an important part of mathematics, and understanding them is crucial for solving problems and making decisions. By answering these frequently asked questions, we hope to have provided you with a better understanding of equations and how to work with them.

Additional Resources

If you want to learn more about equations, here are some additional resources:

  • Math textbooks: There are many math textbooks available that cover equations and other mathematical concepts.
  • Online resources: There are many online resources available that provide tutorials, examples, and practice problems for equations.
  • Math software: There are many math software programs available that can help you graph equations and solve systems of equations.

Conclusion

In conclusion, equations are an important part of mathematics, and understanding them is crucial for solving problems and making decisions. By answering these frequently asked questions, we hope to have provided you with a better understanding of equations and how to work with them.