Question 4 [Integers]4.1 Determine The Number That Makes The Following Statement True: (1) $53 - (\text{a Certain Number}) = 65$ The Certain Number = ?4.2 Calculate The Following Without The Use Of A Calculator: 4.2.1 $\frac{50 \times

Mar 1, 2025 by ADMIN 239 views

**Solving Equations and Calculations: A Step-by-Step Guide**

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields, including science, technology, engineering, and mathematics (STEM). In this article, we will focus on solving equations and calculations, specifically on determining a certain number that makes a given statement true and calculating a product without the use of a calculator.

4.1 Determine the Number that Makes the Following Statement True

We are given the equation $53 - (\text{a certain number}) = 65$ . Our goal is to determine the value of the certain number.

Step 1: Understand the Equation

The equation $53 - (\text{a certain number}) = 65$ can be rewritten as $53 - x = 65$ , where $x$ represents the certain number.

Step 2: Isolate the Variable

To isolate the variable $x$ , we need to get rid of the constant term on the left-hand side of the equation. We can do this by adding $x$ to both sides of the equation, resulting in $53 = 65 + x$ .

Step 3: Solve for the Variable

Now, we can solve for the variable $x$ by subtracting $65$ from both sides of the equation, resulting in $-12 = x$ .

Step 4: Determine the Value of the Certain Number

Therefore, the value of the certain number is $-12$ .

4.2 Calculate the Following without the Use of a Calculator

We are given the expression $\frac{50 \times 30}{2}$ . Our goal is to calculate the value of this expression without the use of a calculator.

Step 4.2.1 Calculate the Product

First, we need to calculate the product of $50$ and $30$ . We can do this by multiplying the two numbers together, resulting in $1500$ .

Step 4.2.2 Divide the Product by 2

Next, we need to divide the product by $2$ . We can do this by dividing $1500$ by $2$ , resulting in $750$ .

Step 4.2.3 Determine the Value of the Expression

Therefore, the value of the expression $\frac{50 \times 30}{2}$ is $750$ .

Conclusion

In this article, we have discussed how to solve equations and calculate expressions without the use of a calculator. We have determined the value of a certain number that makes a given statement true and calculated the value of an expression. By following these steps, you can become proficient in solving equations and calculations, which is essential in various fields, including science, technology, engineering, and mathematics (STEM).

Key Takeaways

To solve an equation, we need to isolate the variable by getting rid of the constant term on the left-hand side of the equation.
To calculate an expression, we need to follow the order of operations (PEMDAS), which stands for parentheses, exponents, multiplication and division, and addition and subtraction.
By following these steps, you can become proficient in solving equations and calculations, which is essential in various fields, including science, technology, engineering, and mathematics (STEM).

Frequently Asked Questions

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, we need to get rid of the variable on one side of the equation by adding or subtracting the same value to both sides of the equation.

Q: How do I calculate an expression with multiple operations?

A: To calculate an expression with multiple operations, we need to follow the order of operations (PEMDAS), which stands for parentheses, exponents, multiplication and division, and addition and subtraction.

Q: Why is it essential to follow the order of operations?

A: It is essential to follow the order of operations because it ensures that we perform the operations in the correct order, which results in the correct answer.

References

Glossary

Equation: A statement that two mathematical expressions are equal.
Variable: A letter or symbol that represents a value that can change.
Expression: A mathematical statement that contains one or more variables and constants.
PEMDAS: An acronym that stands for parentheses, exponents, multiplication and division, and addition and subtraction, which represents the order of operations.
Solving Equations and Calculations: A Q&A Guide =====================================================

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields, including science, technology, engineering, and mathematics (STEM). In this article, we will focus on solving equations and calculations, specifically on answering frequently asked questions related to these topics.

Q&A

Q: What is an equation?

A: An equation is a statement that two mathematical expressions are equal. It is a mathematical statement that contains one or more variables and constants.

Q: What is a variable?

A: A variable is a letter or symbol that represents a value that can change. It is a mathematical symbol that can take on different values.

Q: What is an expression?

A: An expression is a mathematical statement that contains one or more variables and constants. It is a mathematical statement that can be evaluated to a single value.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. It is a mnemonic device that stands for parentheses, exponents, multiplication and division, and addition and subtraction.

Q: Why is it essential to follow the order of operations?

A: It is essential to follow the order of operations because it ensures that we perform the operations in the correct order, which results in the correct answer.

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, we need to get rid of the variable on one side of the equation by adding or subtracting the same value to both sides of the equation.

Q: How do I calculate an expression with multiple operations?

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

A: An equation is a statement that two mathematical expressions are equal, while an expression is a mathematical statement that can be evaluated to a single value.

Q: How do I determine the value of a variable in an equation?

A: To determine the value of a variable in an equation, we need to isolate the variable by getting rid of the constant term on the left-hand side of the equation.

Q: What is the purpose of solving equations and calculations?

A: The purpose of solving equations and calculations is to determine the value of a variable or expression, which is essential in various fields, including science, technology, engineering, and mathematics (STEM).

Conclusion

In this article, we have discussed how to solve equations and calculations, specifically on answering frequently asked questions related to these topics. By following these steps and understanding the concepts, you can become proficient in solving equations and calculations, which is essential in various fields, including science, technology, engineering, and mathematics (STEM).

Key Takeaways

To solve an equation, we need to isolate the variable by getting rid of the constant term on the left-hand side of the equation.
To calculate an expression, we need to follow the order of operations (PEMDAS), which stands for parentheses, exponents, multiplication and division, and addition and subtraction.
By following these steps, you can become proficient in solving equations and calculations, which is essential in various fields, including science, technology, engineering, and mathematics (STEM).

Frequently Asked Questions

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, we need to get rid of the variable on one side of the equation by adding or subtracting the same value to both sides of the equation.

Q: How do I calculate an expression with multiple operations?

Q: Why is it essential to follow the order of operations?

A: It is essential to follow the order of operations because it ensures that we perform the operations in the correct order, which results in the correct answer.

References

Glossary

Equation: A statement that two mathematical expressions are equal.
Variable: A letter or symbol that represents a value that can change.
Expression: A mathematical statement that can be evaluated to a single value.
PEMDAS: An acronym that stands for parentheses, exponents, multiplication and division, and addition and subtraction, which represents the order of operations.