30. Sure, let's create a real-world scenario to understand the product [tex]\(\left(\frac{6}{7}\right) \times 5\)[/tex].
### Scenario: Pizza Slices
Imagine you have a total of 5 full pizzas. Each pizza is divided into 7 slices. You decide to take 6 slices from each pizza. We want to find out how many total slices you have taken.
#### Step-by-Step Solution:
1. Understand the Parts Involved:
- You have 5 full pizzas.
- Each pizza is divided into 7 equal slices.
- You are taking 6 slices from each of these 5 pizzas.
2. Calculate the Fraction:
- Out of the 7 slices of each pizza, you are taking 6.
- This means you are taking [tex]\(\frac{6}{7}\)[/tex] of each pizza.
3. Multiply by the Number of Pizzas:
- Since you have 5 such pizzas, you multiply [tex]\(\frac{6}{7}\)[/tex] by 5 to get the total portion of pizza slices you are taking.
4. Performing the Multiplication:
- To find the product, we compute:
[tex]\[
\left(\frac{6}{7}\right) \times 5 = \frac{6 \times 5}{7} = \frac{30}{7}
\][/tex]
5. Simplify the Fraction (if needed):
- [tex]\(\frac{30}{7}\)[/tex] does not simplify further, so you can convert it into a decimal or mixed number if necessary.
- [tex]\(\frac{30}{7} \approx 4.285714285714286\)[/tex]
6. Interpret the Result in Context:
- Thus, by taking 6 slices out of 7 from each of the 5 pizzas, you end up with approximately [tex]\(4.29\)[/tex] whole pizzas worth of slices.
In the real-world context:
- You started with 5 pizzas, each cut into 7 slices.
- You took 6 slices from each of the 5 pizzas.
- In terms of whole pizza equivalents, you took approximately [tex]\(4.29\)[/tex] pizzas worth of slices in total.
This scenario shows how multiplication and division of whole numbers can help understand the concept of fractions and real-world applications of these mathematical operations.
