1.2 Add Brackets To The Following Equation So That The Answer Is Correct:$\[ (120 \div 2) \times 3 + 5 = 25 \\]1.3 State Whether The Following Statement Is True Or False: The Difference Between Two Whole Numbers Is Always A Whole Number.1.4
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), economics, finance, and many more. Mathematical equations are an essential part of mathematics, and solving them correctly is vital to understand the underlying concepts. In this article, we will discuss how to add brackets to a given equation to make it correct and explore the concept of whole numbers and their differences.
Adding Brackets to an Equation
Let's consider the equation: . To add brackets to this equation, we need to follow the order of operations (PEMDAS):
- 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.
Using this order of operations, let's evaluate the given equation:
- Evaluate the expression inside the parentheses:
- Multiply 60 by 3:
- Add 5 to 180:
However, the given equation states that the result is 25, which is incorrect. To make the equation correct, we need to add brackets to change the order of operations. Let's try to add brackets to the equation:
Using the order of operations, let's evaluate this equation:
- Evaluate the expression inside the parentheses:
- Divide 120 by 6:
- Add 5 to 20:
As we can see, the equation with added brackets is correct.
Whole Numbers and Their Differences
A whole number is a positive integer that is not a fraction or a decimal. For example, 1, 2, 3, and 4 are whole numbers. The difference between two whole numbers is always a whole number. Let's consider an example:
Suppose we have two whole numbers, 5 and 3. The difference between these two numbers is:
As we can see, the difference between 5 and 3 is 2, which is a whole number.
However, if we consider the difference between a whole number and a fraction or a decimal, the result will not be a whole number. For example:
Suppose we have a whole number, 5, and a fraction, 3/4. The difference between these two numbers is:
As we can see, the difference between 5 and 3/4 is 4.25, which is not a whole number.
Conclusion
In conclusion, adding brackets to an equation can change the order of operations and make the equation correct. The difference between two whole numbers is always a whole number, but the difference between a whole number and a fraction or a decimal is not always a whole number. Understanding and solving mathematical equations is essential to grasp the underlying concepts of mathematics.
Discussion
- Can you think of any other ways to add brackets to the given equation to make it correct?
- What are some real-life applications of whole numbers and their differences?
- How can we use mathematical equations to solve problems in our daily lives?
References
Further Reading
- Mathematics for Dummies
- Algebra for Dummies
- Geometry for Dummies
Mathematics Q&A =====================
Introduction
Mathematics is a vast and fascinating subject that has been a part of human culture for thousands of years. From simple arithmetic operations to complex calculus and geometry, mathematics has numerous applications in various fields, including science, technology, engineering, and mathematics (STEM), economics, finance, and many more. In this article, we will answer some frequently asked questions about mathematics, covering topics such as basic arithmetic operations, algebra, geometry, and more.
Q&A
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a fraction as a number with a point separating the whole number part from the fractional part. For example, 1/2 is a fraction, while 0.5 is a decimal.
Q: How do I add and subtract fractions?
A: To add or subtract fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and convert both fractions to have that LCM as the denominator. Then, you can add or subtract the numerators and keep the same denominator.
Q: What is the formula for the area of a circle?
A: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle.
Q: How do I solve a quadratic equation?
A: A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. To solve a quadratic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation of the form ax + b = 0, where a and b are constants. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants. The main difference between the two is that a linear equation has a straight line as its graph, while a quadratic equation has a parabola as its graph.
Q: How do I find the slope of a line?
A: The slope of a line is a measure of how steep the line is. To find the slope of a line, you can use the formula: m = (y2 - y1) / (x2 - x1), where m is the slope and (x1, y1) and (x2, y2) are two points on the line.
Q: What is the formula for the volume of a sphere?
A: The formula for the volume of a sphere is V = (4/3)Ï€r^3, where V is the volume and r is the radius of the sphere.
Q: How do I solve a system of linear equations?
A: A system of linear equations is a set of two or more linear equations that are solved simultaneously. To solve a system of linear equations, you can use the method of substitution or the method of elimination.
Q: What is the difference between a function and a relation?
A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation is a set of ordered pairs that satisfy a certain condition. The main difference between the two is that a function has a unique output for each input, while a relation may have multiple outputs for each input.
Conclusion
In conclusion, mathematics is a vast and fascinating subject that has numerous applications in various fields. From basic arithmetic operations to complex calculus and geometry, mathematics has something to offer for everyone. We hope that this Q&A article has helped you to understand some of the fundamental concepts of mathematics and has inspired you to learn more.
Discussion
- What are some of the most interesting mathematical concepts that you have learned?
- How do you think mathematics can be used to solve real-world problems?
- What are some of the challenges that you face when learning mathematics, and how do you overcome them?