Solving: -2.1 + 3 3/5 + (-1 7/15) Calculation Steps

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Hey guys! Today, we're going to dive into solving a math problem that might seem a bit tricky at first glance, but trust me, we'll break it down step by step. We're tackling the expression -2.1 + 3 3/5 + (-1 7/15). This involves working with decimals, mixed numbers, and both positive and negative values. Don't worry; we'll make it super clear and easy to follow. So, grab your pencils and let's get started!

Breaking Down the Problem

Before we jump into the actual calculation, let's understand what we're dealing with. We have a mix of decimals and mixed numbers. To make our lives easier, we'll convert everything into a single format—decimals. This way, we can perform the addition and subtraction more smoothly. We'll start by converting the mixed numbers into decimals.

Converting Mixed Numbers to Decimals

First, let's convert 3 3/5 into a decimal. Remember, a mixed number is a whole number plus a fraction. So, 3 3/5 means 3 + 3/5. To convert the fraction 3/5 to a decimal, we divide 3 by 5. This gives us 0.6. Adding this to the whole number, we get 3 + 0.6 = 3.6. So, 3 3/5 is equal to 3.6.

Next, let's convert -1 7/15 into a decimal. Similarly, -1 7/15 means -1 + (-7/15). To convert the fraction 7/15 to a decimal, we divide 7 by 15. This gives us approximately 0.4667. Adding this to the whole number -1, we get -1 + (-0.4667) = -1.4667. So, -1 7/15 is approximately equal to -1.4667.

Rewriting the Expression

Now that we've converted the mixed numbers to decimals, we can rewrite the original expression as:

-2.1 + 3.6 + (-1.4667)

This looks much simpler to work with, right? We've eliminated the fractions and mixed numbers, making the addition and subtraction straightforward.

Performing the Calculation

Now, let's perform the calculation step by step. We'll start by adding the first two numbers, then add the result to the third number.

Step 1: Adding -2.1 and 3.6

To add -2.1 and 3.6, we perform the operation 3.6 - 2.1. This is because we're adding a negative number to a positive number, which is the same as subtracting the absolute values. So, 3.6 - 2.1 = 1.5.

Step 2: Adding 1.5 and -1.4667

Next, we need to add 1.5 and -1.4667. Again, this is the same as subtracting the absolute values. So, we perform the operation 1.5 - 1.4667. This gives us 0.0333. This is our final result.

Final Result

Therefore, the value of the expression -2.1 + 3 3/5 + (-1 7/15) is approximately 0.0333.

Why Each Step Matters

Let's quickly recap why each step is crucial in solving this problem. First, converting mixed numbers to decimals simplifies the calculation process. It allows us to work with a uniform set of numbers, making addition and subtraction easier. Without this conversion, we'd be dealing with fractions, which can be more complex to handle.

Next, performing the addition and subtraction step by step ensures accuracy. We avoid making mistakes by breaking the problem into smaller, manageable parts. This approach is particularly helpful when dealing with multiple numbers and operations.

Finally, understanding the concept of adding negative numbers is essential. Adding a negative number is the same as subtracting its absolute value. This understanding helps us perform the calculations correctly and avoid common errors.

Alternative Approach: Converting to Fractions

While we solved this problem by converting to decimals, there's another approach we could have taken: converting everything to fractions. Let's explore this alternative method to give you a broader understanding of how to tackle such problems.

Converting Decimals to Fractions

First, we'd convert -2.1 to a fraction. -2.1 is the same as -2 1/10, which can be written as -21/10. Now, we have all the numbers in fractional form: -21/10, 3 3/5, and -1 7/15.

Finding a Common Denominator

To add or subtract fractions, we need a common denominator. The least common multiple (LCM) of 10, 5, and 15 is 30. So, we'll convert each fraction to have a denominator of 30.

  • -21/10 becomes -63/30 (multiply numerator and denominator by 3)
  • 3 3/5 is 3 + 3/5, which is 3 + 18/30 (3/5 becomes 18/30)
  • -1 7/15 is -1 + (-7/15), which is -1 + (-14/30) (-7/15 becomes -14/30)

Performing the Calculation with Fractions

Now we have: -63/30 + (3 + 18/30) + (-1 + (-14/30)). Let's combine the whole numbers and fractions separately.

Whole numbers: 3 - 1 = 2 Fractions: -63/30 + 18/30 - 14/30 = -59/30

So, we have 2 + (-59/30). To combine these, we convert 2 to a fraction with a denominator of 30, which is 60/30. Thus, we have 60/30 - 59/30 = 1/30.

Converting Back to Decimal

Finally, we convert 1/30 back to a decimal, which is approximately 0.0333. This matches the result we obtained using the decimal approach.

Conclusion

There you have it, guys! We've successfully solved the expression -2.1 + 3 3/5 + (-1 7/15) using both decimal and fractional approaches. Whether you prefer working with decimals or fractions, understanding the underlying concepts is key. Remember, breaking down the problem into smaller steps and paying attention to details will help you avoid errors and arrive at the correct answer. Keep practicing, and you'll become a math whiz in no time! Isn't math fun when you get the hang of it? Keep exploring and challenging yourselves!