Problem 16 - Fundamentals of Mathematics

Question

Find the sums. $$ 1.5+(-2) $$

Step-by-Step Solution

Answer

The sum of 1.5 and -2 is -0.5.

Step 1: Understand the operation

In this exercise, you're asked to find the sum of 1.5 and -2. It involves adding a positive number to a negative number.

Step 2: Change negative addition to subtraction

Since adding a negative number is the same as subtracting its positive counterpart, the expression can be rewritten from \(1.5 + (-2)\) to \(1.5 - 2\).

Step 3: Perform the subtraction

Subtract 2 from 1.5. Since 2 is greater than 1.5, you'll have a negative result. So, you take the difference of 2 and 1.5 which is 0.5, and then apply the negative sign. Thus, \(1.5 - 2 = -0.5\).

Key Concepts

Addition and Subtraction of Decimals

When you encounter decimals in arithmetic operations, especially in addition and subtraction, it can feel a bit different at first. But it is not difficult once you understand the process. Decimals represent fractions, or parts of a whole, and we use them frequently in everyday calculations. Here's how you handle them:

• Align the decimal points: This is crucial for accuracy. Make sure the numbers are placed so that their decimal points line up vertically.
• Fill in missing places with zeros: If one decimal number has fewer digits after the decimal point than another, add zeros to the end of the shorter decimal so they have the same number of decimal places.
• Add or subtract as usual: Once the decimals are aligned and any necessary zeros added, you can perform the addition or subtraction just like you would with whole numbers.

The key takeaway is to maintain proper decimal alignment throughout the calculation. Whether adding or subtracting, always watch those decimal places closely.

Working with Negative Numbers

Handling negative numbers in calculations can be tricky, but it's an essential skill in arithmetic. A negative sign simply indicates a reversal in direction from the positive axis on a number line. Here's how you can manage adding and subtracting when negatives are involved:

• Adding a Negative: This is equivalent to subtracting. For example, adding \(-2\) is the same as subtracting \(2\).
• Subtracting a Negative: This changes to an addition. Subtracting \(-2\) becomes \(+2\).
• Consider the Number Line: Visualize moving left for negative and right for positive numbers. This helps understand which direction your answer will go.

When dealing with operations like \(1.5 + (-2)\), treat the negative as a subtractor. You're essentially finding how much less 1.5 is by 2. These concepts can be visualized as movement along a number line, which makes it easier to grasp.

Understanding Sums

Understanding sums, especially when involving negative numbers or decimals, is about recognizing the relationship between the numbers involved. The term 'sum' refers to the result of adding numbers, but it can also mean combining numbers in a broader sense. Here's how you can approach it:

• Positives and Negatives Together: When you are asked to find the sum of a mix of positive and negative numbers, you're identifying the net effect after all increases and decreases.
• Context is Key: In practical situations, the sum represents a total value, which might be less than, greater than, or equal to the initial numbers based on what's combined.
• Connection to Real World: Think of sums as balances in a bank account. Deposits are positive additions, and withdrawals are subtractions (negatives), and together they form a net result.

For the expression \(1.5 + (-2)\), the sum is effectively a decrease, because you are moving from a positive starting point (1.5) towards zero or further into negatives. Ultimately, the sum gives you a clear view of the overall effect when all parts are considered.