Problem 55 - Beginning and Intermediate Algebra

Question

Add See Examples \(\ell\) through 7 . $$ -1.3+[0.5+(-0.3)+0.4] $$

Step-by-Step Solution

Answer

The result is -0.7.

Step 1: Simplify the Inner Expression

First, we need to calculate the sum inside the brackets: \(0.5 + (-0.3) + 0.4\). This involves adding the three numbers together.

Step 2: Add the First Two Numbers Inside Brackets

Calculate \(0.5 + (-0.3) = 0.2\). We simply subtract 0.3 from 0.5.

Step 3: Add the Result to the Third Number

Now, take the result from the previous step \(0.2\) and add \(0.4\) to it. This gives \(0.2 + 0.4 = 0.6\).

Step 4: Substitute Back into the Expression

Replace the expression inside the brackets with the result from Step 3. The expression now is \(-1.3 + 0.6\).

Step 5: Perform the Final Addition

Add the numbers from Step 4: \(-1.3 + 0.6 = -0.7\). We subtract 0.6 from -1.3 since 0.6 is positive.

Key Concepts

Addition

Addition is the process of calculating the sum of two or more numbers. In our exercise, mostly positive and negative numbers are being added. The importance of addition in solving equations can't be underestimated. Here are the basics:

• To add two numbers, line them up according to their sign.
• If they share the same sign, you add and keep the sign.
• If they have different signs, you subtract the smaller number from the larger and take the sign of the larger number.

In the exercise, we use these rules to carry out operations inside the brackets and then again when we combine the result with the number outside the brackets.

Simplifying Expressions

Simplifying expressions is all about making equations easier to solve. When faced with complex expressions, breaking them down can make calculations more straightforward. Here's how it works:

• Identify and simplify the innermost parts of the expression first.
• Combine terms where possible, especially those inside parentheses.
• Keep track of signs since they can change through the simplification process.

In the given exercise, the expression inside the brackets \(0.5 + (-0.3) + 0.4\) is simplified before turning to the outer numbers. Such step-by-step simplification helps in managing and solving longer expressions with multiple terms.

Negative Numbers

Dealing with negative numbers is integral when solving many mathematical problems. These numbers are less than zero and involve some rules different from positive numbers:

• When adding a negative number, it's akin to subtracting the positive counterpart.
• Negative numbers can change the outcome drastically if not handled with care.
• Always pay attention to the sign in front of the number, especially during addition and subtraction.

In the exercise, negative numbers like \(-1.3\) and \(-0.3\) are included. By understanding these rules, you can solve equations effectively, even when a mix of positive and negative numbers is involved.