Solving The Math Problem: -7×3-15-24÷2×5-7

Oct 22, 2025 by SD Solar 43 views

Hey guys! Today, we're diving into a classic math problem: -7×3-15-24÷2×5-7. Don't worry, it might look a little intimidating at first glance, but we'll break it down step-by-step to make it super easy to understand. This expression is a great example of how important it is to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Let's get started and see how we can solve it together! Understanding how to solve these types of equations is fundamental to building a strong math foundation. We will go through each step carefully, so you will fully understand how to solve this math problem.

First, let's talk about the order of operations, also known as the precedence of operators. This is the set of rules that tells us which operations to perform first in a mathematical expression. Without these rules, we might end up with different answers depending on the order in which we solve the equation. The acronym PEMDAS, as I mentioned earlier, is a handy way to remember the order:

Parentheses: Solve anything inside parentheses first.
Exponents: Deal with exponents (powers and roots) next.
Multiplication and Division: Perform these operations from left to right.
Addition and Subtraction: Finally, handle addition and subtraction from left to right.

In our expression, -7×3-15-24÷2×5-7, there are no parentheses or exponents. So, we'll start with multiplication and division. The correct application of these rules ensures that we all arrive at the same accurate answer. That is why it is very important to learn. So, let’s jump in and solve it step by step, so that you understand perfectly and solve it without making a mistake! Ready?

Step-by-Step Solution: Breaking Down the Math

Alright, let's get into the nitty-gritty of solving this math problem. We'll meticulously go through each step to ensure you understand every aspect. We'll follow PEMDAS to get the answer. Remember, the core of mathematics is built upon these principles, so let’s make sure we master them! Each step is very important, because if there is a mistake in any step the result will be wrong. So we need to pay attention to every detail!

Multiplication: -7 × 3

First up, we have the multiplication operation: -7 × 3. When you multiply a negative number by a positive number, the result is negative. So, -7 multiplied by 3 equals -21. We replace “-7 × 3” with “-21”, and rewrite the entire expression.

So the expression now becomes: -21 - 15 - 24 ÷ 2 × 5 - 7

Division: 24 ÷ 2

Next, we tackle the division: 24 ÷ 2. Twenty-four divided by 2 equals 12. We replace “24 ÷ 2” with “12” in our updated expression.

Now, the expression is: -21 - 15 - 12 × 5 - 7

Multiplication: 12 × 5

Next, we handle the second multiplication: 12 × 5. Twelve multiplied by 5 equals 60. We replace “12 × 5” with “60”.

Our expression simplifies to: -21 - 15 - 60 - 7

Addition and Subtraction: -21 - 15 - 60 - 7

Finally, we perform the addition and subtraction, working from left to right. This is where it’s super important to keep track of the signs (positive or negative) of each number.

-21 - 15 = -36
-36 - 60 = -96
-96 - 7 = -103

So, the solution to the expression is -103!

Conclusion: The Final Answer

We did it, guys! We successfully solved the math problem -7×3-15-24÷2×5-7, and the answer is -103. Remember, the key to solving these types of problems is to follow the order of operations (PEMDAS) carefully and to take your time. Don't rush; double-check your work at each step. Understanding the order of operations is more than just about answering a question; it builds a solid foundation for more complex mathematical concepts.

Summary of the solution:

Original Expression: -7×3-15-24÷2×5-7
Multiplication: -7 × 3 = -21
Division: 24 ÷ 2 = 12
Multiplication: 12 × 5 = 60
Addition and Subtraction: -21 - 15 - 60 - 7 = -103

Keep practicing, and you'll get better and faster at solving these expressions! Always remember the importance of order of operations.

Tips for Math Success

To really nail math problems like this, here are some helpful tips to keep in mind. I hope this tips can help you to improve your understanding and confidence in solving mathematical equations.

Practice Regularly: The more you practice, the more comfortable you'll become with different types of problems. Set aside some time each day or week to work through exercises. Start with easier ones and gradually move to more complex challenges.
Understand the Concepts: Don't just memorize formulas. Make sure you understand why the formulas work. This will help you solve problems more effectively.
Master the Basics: Make sure you have a solid grasp of basic arithmetic, including addition, subtraction, multiplication, and division. These are the building blocks for more advanced math.
Use Visual Aids: Diagrams, charts, and graphs can make complex concepts easier to understand. Draw them out to see the math in action.
Ask for Help: Don't hesitate to ask your teacher, classmates, or a tutor if you're stuck. Often, a fresh perspective can make all the difference.
Review Your Mistakes: When you make a mistake, don't just brush it off. Review it carefully to understand why you made the error. This is a great way to learn and improve.
Use Technology Wisely: Calculators and online tools can be helpful, but don't rely on them too much. Make sure you understand the concepts and can solve problems by hand first.
Stay Positive: Believe in yourself! Math can be challenging, but it's also rewarding. Keep a positive attitude and celebrate your successes.

Further Practice Problems

Ready for more? Here are a few similar problems for you to practice on. Try solving these using the steps we've covered. The more you practice, the easier it will become. Remember to always follow the order of operations!

-5 × 4 + 10 - 18 ÷ 3 × 2 + 8
20 ÷ 2 - 3 × 5 + 12 - 4
-3 × (6 - 2) + 15 ÷ 5 - 7

These problems are designed to reinforce your understanding of PEMDAS and to help you become more confident in solving mathematical expressions. Work through these exercises at your own pace, and don't be afraid to double-check your work.

Answers to Practice Problems

Here are the answers to the practice problems. Check your work to see how well you did!

-26
-3
-14

Importance of Understanding Math

Why is all of this math stuff important, anyway? Well, guys, math is way more useful than you might think! It's not just about passing tests; it's a fundamental skill that underpins many aspects of our lives. Strong math skills can open doors to various careers and help you in everyday situations.

Everyday Applications

Budgeting and Finances: Managing your money, understanding interest rates, and planning for the future all rely on math.
Shopping: Calculating discounts, comparing prices, and estimating costs are all math-related tasks.
Cooking and Baking: Adjusting recipes, measuring ingredients, and calculating cooking times require math skills.
Time Management: Planning your day, scheduling appointments, and estimating travel times all involve mathematical thinking.

Career Opportunities

Science, Technology, Engineering, and Mathematics (STEM) Fields: Careers in these fields heavily rely on math, including data science, software engineering, and scientific research.
Finance and Accounting: Managing finances, analyzing investments, and preparing financial statements all demand strong math skills.
Healthcare: Doctors, nurses, and other healthcare professionals use math for calculating dosages, interpreting medical data, and analyzing patient outcomes.
Business and Management: Understanding statistics, analyzing market trends, and making data-driven decisions all require mathematical literacy.

Math helps us develop critical thinking and problem-solving skills that are valuable in all areas of life. It teaches us to think logically, analyze information, and find creative solutions. So, keep at it, and you'll find that math is a powerful tool!