Problem 66 - Elementary and Intermediate Algebra

Question

Divide, if possible, and check. If a quotient is undefined, state this. $$ -3.9 \div 1.3 $$

Step-by-Step Solution

Answer

-3

Step 1: Understand the Operation

The problem requires dividing two numbers: ewline ewline ewline ewline

Step 2: Set up the Division

We need to divide ewline ewline ewline ewline

Step 3: Perform the Division

Divide ewline ewline ewline ewline

Step 4: Simplify the Quotient

Simplify the quotient obtained by performing the division: ewline ewline ewline ewline

Step 5: State the Result

The result of the division is: 1 ewline ewline ewline

Key Concepts

Division Operation

Division is a fundamental arithmetic operation used to find how many times one number is contained within another. Here, we need to divide -3.9 by 1.3.
To start, we take -3.9 (the dividend) and 1.3 (the divisor).
Division can be thought of as splitting a quantity into equal parts or groups.
When dividing decimals, it's often helpful to make the divisor a whole number by multiplying both the dividend and the divisor by the same power of 10. In our example, we can multiply both -3.9 and 1.3 by 10, resulting in -39 and 13, respectively.
This transforms the division problem into -39 ÷ 13, making the arithmetic simpler.

Simplifying Quotients

Simplifying the quotient means reducing the result of the division to its simplest form.
After transforming -3.9 ÷ 1.3 into -39 ÷ 13, we perform the division.
\[\[\begin{align*} -39 \ ÷ \ 13 \ = \ -3 \ \text{(as 13 goes into 39 exactly 3 times, and because the dividend is negative, the quotient is also negative)} \ \ \text{This means the simplified quotient in this case is -3.} \ \ \text{Always double-check your result! In this case,}\ \text{-3.9 ÷ 1.3 should equal -3.} \ \text{You can verify the result by multiplying your quotient by the divisor to get the dividend back,} \ -3 × 1.3 = -3.9. \ \text{This confirms our quotient is correct.} \end{align*}\]\]

Performing Arithmetic Operations

For division, as with other arithmetic operations, understanding the steps is crucial.
Here are some key points:

• Align decimal points when performing operations.
• Convert divisors to whole numbers, if possible.
• Perform operations in a step-by-step manner to avoid errors.
• Simplify the resulting quotient to ensure correctness.

Arithmetic operations like addition, subtraction, multiplication, and division follow specific rules and order:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
By mastering these rules and performing steps carefully, you'll get accurate results in your calculations.