Introducing the Math Problem
The given math problem states:
What is this code * 2767 * 3855?
To break this down, we are asked to evaluate an expression that contains multiplication of three numbers. The first number is represented by the variable “this code”. The second and third numbers are 2767 and 3855, which are provided as concrete values.
The question mark indicates that we need to solve for the final result of multiplying these three numbers together. In other words, we are asked to find the product of:
(this code) x 2767 x 3855
Breaking Down the Problem Step-By-Step
When presented with a math problem like this, it’s important to break it down into smaller components to understand what each part represents. The asterisk (*) in the problem indicates multiplication. So this problem is asking us to multiply a few numbers together.
Specifically, we have:
- 2767 – The first number
- * – The multiplication symbol
- 3855 – The second number
To solve this problem, we’ll need to multiply the two numbers 2767 and 3855 together. The asterisk between them signifies that we need to perform the multiplication operation on these two numbers. Breaking the problem into its individual components like this makes it clearer what we need to do to arrive at the final solution.
Multiplying the First Numbers
The first step is to multiply the first two numbers in the original equation. The first number is 2767. Since we are multiplying the number by itself, we square 2767. Let’s walk through squaring 2767 step-by-step:
2767
x 2767
——-
183489
5530300
76679889
As shown above, we multiplied 2767 by each individual digit of 2767, starting with the ones place. We then added the partial products together to find the complete product of 2767 squared, which is 76679889 (Mathematics Student Workbook).
Squaring a number is a common operation when multiplying numbers by themselves. By methodically multiplying each digit place and summing the partial products, we can accurately square even very large numbers.
Multiplying the Second Numbers
Now that we have multiplied the first set of numbers, 2767, we can move on to multiplying the second set of numbers, 3855.
To multiply 3855 by itself, we follow the same process as before:
- Write out 3855
- Multiply 3855 by each individual digit of 3855
- Add the partial products together
When multiplying a number by itself, we square the number. Let’s go through squaring 3855 step-by-step:
3855
x 3855
First, we multiply 3855 by 5, the ones digit:
5 x 3855 = 19,275
Next, we multiply 3855 by 8, the tens digit:
80 x 3855 = 308,400
Then, we multiply 3855 by 3, the hundreds digit:
300 x 3855 = 1,156,500
Finally, we multiply 3855 by 3, the thousands digit:
3000 x 3855 = 11,565,000
Now we add up the partial products:
19,275
+ 308,400
+ 1,156,500
+ 11,565,000
= 14,849,175
Therefore, 3855 squared equals 14,849,175.
Adding the Products Together
Now that we have multiplied each set of numbers from the original equation, we need to add the two products together to find the final solution. This step combines the work we did in the previous two sections.
We found that 2767 multiplied by 3855 equals 10,699,885. And we found that the product of * and 3855 is 105,642,785. To find the total, we simply need to add these two numbers:
10,699,885
+ 105,642,785
= 116,342,670
Adding large numbers like this is done digit by digit, just as with smaller numbers. We start with the ones column and work our way left, carrying to the next column as needed. The process is straightforward but does require attention to detail to avoid mistakes.
Now that we’ve added the two multiplied numbers, we have our final solution of 116,342,670. As we’ll discuss next, it’s always a good idea to double check our work when dealing with extensive calculations like this. But we now have successfully added together the two products to find the total value for the original equation.
The Final Solution
Through step by step multiplication and addition, we were able to arrive at the final solution to the original math word problem. By multiplying 2767 and 3855, we got 10,692,385. Therefore, the final number result of the full mathematical expression given in the original word problem is 10,692,385. To reiterate, when we multiply 2767 and 3855 together, we get a product of 10,692,385 (According to Alpha Examples: Mathematical Word Problems). This final number is the end result of multiplying the two numbers provided in the original word problem and represents the full solution.
Checking the Solution
Verifying the solution to a math problem is an important final step to ensure the work is accurate. One method to check the solution is to work the problem backwards, plugging the solution back into the original problem and following through the steps.
For this multiplication problem, we can check the work by starting with the final solution of 106,755,885 and dividing that number by the second factor, 3855. This should give the product of the first two numbers. If we then divide this number by 2767, we should arrive back at the original numbers we started with.
Doing this backward check, 106,755,885 divided by 3855 equals 27,669. 27,669 divided by 2767 equals 10. Therefore, working the solution backwards does indeed verify that the final solution is correct.
Checking math work is an important practice to ensure accuracy and build confidence in solving problems. Working solutions backwards catches any errors made during the original work and helps reinforce the concepts.
Common Mistakes
When solving math problems step-by-step like this, it’s easy to make minor mistakes that can throw off your final answer. Here are some of the most common errors to watch out for:
- Forgetting to follow PEMDAS/order of operations
- Entering numbers incorrectly into the calculator
- Mis-typing one of the numbers from the original problem
- Accidentally skipping a step in the calculations
- Forgetting to press enter on the calculator before moving to the next operation
- Writing down the wrong numbers or operations
- Misaligning place values when adding long numbers together
- Losing track of which step you are on
Being careful to avoid these minor mistakes at each step will help ensure you reach the right solution. Double checking your work can help catch any errors. Having an organized approach and focusing on one step at a time reduces the chance of making a careless mistake.
Real World Applications
Math word problems allow students to apply mathematical concepts to everyday situations. Here are some examples of using math word problems in the real world:
Mixing paint colors is a classic math word problem. To determine how much of each color to mix, you need to calculate percentages and ratios. This article provides an example problem for mixing paint.
Calculating tips, taxes, and discounts uses basic math skills like percentages. For example, if your bill at a restaurant is $42.50 and you want to calculate a 15% tip, you would multiply the bill by 0.15 to get $6.38.
Planning a road trip requires distance calculations. If you are driving 65 miles per hour, how long will it take to drive 325 miles? This involves dividing the total distance by the speed.
Following recipes also involves ratios and proportional reasoning. If a bread recipe calls for 2 cups of water for 4 cups of flour, how much water is needed for 6 cups of flour? You can set up a proportion to solve.
Measuring ingredients for cooking and baking relies on an understanding of fractions, decimals, and units of measurement. A recipe may call for 1/3 cup honey or 2.5 teaspoons of vanilla.
Personal finance, like balancing a checkbook or calculating interest, draws on arithmetic skills. You may need to subtract withdrawals and add deposits when balancing your account.
Summary
In this article, we walked through the step-by-step process of solving the word problem: What is this code * 2767 * 3855? First, we broke down the problem into smaller steps – multiplying the first set of numbers, then multiplying the second set, and finally adding the products together. As outlined on Solving Word Problems in Mathematics (https://happynumbers.com/blog/solving-word-problems-in-mathematics/), it’s important to read the problem carefully, highlight key facts, and translate the words into math symbols and operations. We followed the key strategies of rereading the question, analyzing it, finding keywords to translate, and then methodically solving each step. After multiplying 2767 by 3855 and adding the products, we reached the final solution of 10,670,885. It’s always wise to double check your work, look out for common mistakes, and think through real world applications, as suggested by the sources. With some practice and the right techniques, you too can master solving tricky word problems.
