Question

simplify rational ________ expression involving multiple operations.

Write expressions that represent real-world situations_________ numbers.

Answer 1

whats the answers

Answer 2

whats the answers to the blanks

Answer 3

To address your request, we'll first simplify a rational expression involving multiple operations, and then we will create examples of expressions that represent real-world situations using rational numbers.

### Part 1: Simplifying a Rational Expression

Let's simplify the following rational expression:

\[
\frac{2x^2 - 8}{4x}
\]

**Step 1: Factor the numerator**
The numerator \(2x^2 - 8\) can be factored. We can take out a common factor of 2:

\[
2(x^2 - 4) = 2(x - 2)(x + 2)
\]

**Step 2: Rewrite the expression**
Now, we can rewrite the rational expression:

\[
\frac{2(x - 2)(x + 2)}{4x}
\]

**Step 3: Simplify**
Next, we simplify the expression by canceling out common factors:

\[
\frac{2}{4} \cdot \frac{(x - 2)(x + 2)}{x} = \frac{1}{2} \cdot \frac{(x - 2)(x + 2)}{x}
\]

So, the simplified expression would be:

\[
\frac{(x - 2)(x + 2)}{2x}
\]

### Part 2: Real-World Situations Using Rational Numbers

1. **Example 1: Cooking Recipe**
A recipe requires \( \frac{3}{4} \) cup of sugar per batch of cookies, and you want to make \(2\) batches. The total sugar needed can be represented by the expression:

\[
\text{Total Sugar} = 2 \cdot \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \text{ cups}
\]

2. **Example 2: Distance and Time**
A train travels \( \frac{150}{2} \) miles in \(2\) hours. To find the speed of the train, you can express it as:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{75 \text{ miles}}{1 \text{ hour}} = 75 \text{ miles per hour}
\]

3. **Example 3: Budgeting**
You earn \( \frac{1200}{3} \) dollars per month from a part-time job. Over \(4\) months, your total earnings can be represented as:

\[
\text{Total Earnings} = 4 \cdot \frac{1200}{3} = \frac{4800}{3} = 1600 \text{ dollars}
\]

These examples illustrate how rational numbers can be used in real-world situations, making calculations relevant to everyday life.

Answer 4

Sure! Here are the simplified rational expression and examples with clear solutions:

### Simplified Rational Expression

We simplified the expression:

\[
\frac{2x^2 - 8}{4x}
\]

- After factoring the numerator and simplifying, the simplified form of the expression is:

\[
\frac{(x - 2)(x + 2)}{2x}
\]

### Real-World Situations Using Rational Numbers

1. **Cooking Recipe:**
- **Total Sugar** needed for 2 batches of cookies:
\[
\text{Total Sugar} = 2 \cdot \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \text{ cups (or 1.5 cups)}
\]

2. **Distance and Time:**
- **Speed of the Train**:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{75 \text{ miles}}{1 \text{ hour}} = 75 \text{ miles per hour}
\]

3. **Budgeting:**
- **Total Earnings** over 4 months:
\[
\text{Total Earnings} = 4 \cdot \frac{1200}{3} = \frac{4800}{3} = 1600 \text{ dollars}
\]

These are the answers to the simplified expression and the calculations for the real-world scenarios using rational numbers. If you have any further questions or need more examples, feel free to ask!

Answer 5

Apologies for misunderstanding your initial request. Here's the filled-in text for your prompts:

1. **Simplifying rational** **_expressions_** involving multiple operations.

2. **Write expressions that represent real-world situations** **_with rational_** **_numbers_**.

So the completed sentences would be:

- Simplifying rational **expressions** involving multiple operations.
- Write expressions that represent real-world situations **with rational numbers**.

If you need any further assistance or additional examples, feel free to ask!