What Factor Makes The Number Sentence True?$\[ 7 \times 4 = 28 \times \_ \\]

Feb 26, 2025 by ADMIN 77 views

Introduction

In mathematics, a number sentence is an equation that expresses a relationship between two or more numbers. It is a fundamental concept in arithmetic and algebra, and it plays a crucial role in solving mathematical problems. A number sentence can be true or false, depending on the values of the numbers involved. In this article, we will explore the factors that make a number sentence true, with a focus on the given example: $7 \times 4 = 28 \times \_$ .

Understanding the Number Sentence

The given number sentence is $7 \times 4 = 28 \times \_$ . To understand what makes this sentence true, we need to analyze the equation. The equation states that the product of 7 and 4 is equal to the product of 28 and an unknown number. The unknown number is represented by the underscore symbol.

The Importance of Order of Operations

When dealing with number sentences, it is essential to follow the order of operations (PEMDAS). This rule states that we should perform operations in the following order:

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

In the given number sentence, we have multiplication operations on both sides of the equation. Therefore, we need to follow the order of operations to evaluate the equation.

Evaluating the Equation

To evaluate the equation, we need to multiply 7 and 4 on the left side of the equation. This gives us:

$7 \times 4 = 28$

Next, we need to multiply 28 by the unknown number on the right side of the equation. Let's represent the unknown number as x. Then, we have:

$28 \times x = 28$

Solving for the Unknown Number

Now that we have evaluated the equation, we can solve for the unknown number x. To do this, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 28:

$\frac{28 \times x}{28} = \frac{28}{28}$

This simplifies to:

$x = 1$

Conclusion

In conclusion, the factor that makes the number sentence true is x = 1. This means that the unknown number is equal to 1. By following the order of operations and evaluating the equation, we were able to solve for the unknown number and determine the value that makes the number sentence true.

Real-World Applications

Understanding how to solve number sentences is essential in many real-world applications. For example, in finance, number sentences are used to calculate interest rates and investment returns. In science, number sentences are used to model complex systems and make predictions about future outcomes. In engineering, number sentences are used to design and optimize systems.

Tips for Solving Number Sentences

Here are some tips for solving number sentences:

Follow the order of operations: Always follow the order of operations (PEMDAS) when evaluating number sentences.
Simplify the equation: Simplify the equation by combining like terms and eliminating any unnecessary operations.
Isolate the unknown number: Isolate the unknown number on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation.
Check your work: Check your work by plugging the solution back into the original equation to ensure that it is true.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving number sentences:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
Not simplifying the equation: Failing to simplify the equation can make it difficult to solve.
Not isolating the unknown number: Failing to isolate the unknown number can make it difficult to solve.
Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

In conclusion, solving number sentences is an essential skill in mathematics and has many real-world applications. By following the order of operations, simplifying the equation, isolating the unknown number, and checking your work, you can solve number sentences with confidence. Remember to avoid common mistakes such as not following the order of operations, not simplifying the equation, not isolating the unknown number, and not checking your work.

Final Thoughts

Solving number sentences is a fundamental concept in mathematics that has many real-world applications. By understanding how to solve number sentences, you can develop problem-solving skills that will benefit you in many areas of life. Remember to always follow the order of operations, simplify the equation, isolate the unknown number, and check your work to ensure that your solutions are correct.

Introduction

Number sentences are a fundamental concept in mathematics that can be used to solve a wide range of problems. However, many people may have questions about how to solve number sentences, what makes a number sentence true, and how to apply number sentences in real-world situations. In this article, we will answer some of the most frequently asked questions about number sentences.

Q: What is a number sentence?

A: A number sentence is an equation that expresses a relationship between two or more numbers. It is a fundamental concept in arithmetic and algebra, and it plays a crucial role in solving mathematical problems.

Q: What makes a number sentence true?

A: A number sentence is true if the values of the numbers involved satisfy the equation. For example, the number sentence $2 \times 3 = 6$ is true because the product of 2 and 3 is equal to 6.

Q: How do I solve a number sentence?

A: To solve a number sentence, you need to follow the order of operations (PEMDAS) and simplify the equation. You can then isolate the unknown number by adding, subtracting, multiplying, or dividing both sides of the equation.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a rule that states that you should perform operations in the following order:

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

Q: How do I simplify a number sentence?

A: To simplify a number sentence, you need to combine like terms and eliminate any unnecessary operations. For example, the number sentence $2 \times 3 + 4 \times 2$ can be simplified to $6 + 8$ , which is equal to $14$ .

Q: How do I isolate the unknown number?

A: To isolate the unknown number, you need to add, subtract, multiply, or divide both sides of the equation by the same value. For example, if you have the number sentence $x + 2 = 5$ , you can isolate the unknown number by subtracting 2 from both sides of the equation, which gives you $x = 3$ .

Q: What are some common mistakes to avoid when solving number sentences?

A: Some common mistakes to avoid when solving number sentences include:

Not following the order of operations
Not simplifying the equation
Not isolating the unknown number
Not checking your work

Q: How do I check my work?

A: To check your work, you need to plug the solution back into the original equation to ensure that it is true. For example, if you have the number sentence $x + 2 = 5$ and you solve for x, you can plug the solution back into the equation to check that it is true.

Q: What are some real-world applications of number sentences?

A: Number sentences have many real-world applications, including:

Finance: Number sentences are used to calculate interest rates and investment returns.
Science: Number sentences are used to model complex systems and make predictions about future outcomes.
Engineering: Number sentences are used to design and optimize systems.

Q: How can I practice solving number sentences?

A: You can practice solving number sentences by working through examples and exercises in a textbook or online resource. You can also try solving number sentences on your own by creating your own problems and solutions.

Q: What are some resources for learning more about number sentences?

A: Some resources for learning more about number sentences include:

Textbooks: There are many textbooks available that cover number sentences and other mathematical concepts.
Online resources: There are many online resources available that provide examples, exercises, and tutorials on number sentences.
Teachers: Your teacher or tutor can provide additional guidance and support as you learn about number sentences.

Conclusion

In conclusion, number sentences are a fundamental concept in mathematics that can be used to solve a wide range of problems. By understanding how to solve number sentences, you can develop problem-solving skills that will benefit you in many areas of life. Remember to always follow the order of operations, simplify the equation, isolate the unknown number, and check your work to ensure that your solutions are correct.