Problem 158 - Intermediate Algebra

Question

In the following exercises, perform the indicated operation. $$ \frac{5}{6} \cdot 30 m $$

Step-by-Step Solution

Answer

25 meters

Step 1: Understand the Problem

The problem requires finding the result of multiplying the fraction \( \frac{5}{6} \) by 30 meters.

Step 2: Perform the Multiplication

Multiply the fraction \( \frac{5}{6} \) by 30 meters. This can be written as: \[ \frac{5}{6} \times 30 \text{ meters} \]

Step 3: Simplify the Multiplication

To simplify, multiply the numerator 5 by 30 and then divide by the denominator 6: \[ \frac{5 \times 30}{6} \text{ meters} \] This simplifies to \[ \frac{150}{6} \text{ meters} \]

Step 4: Complete the Division

Divide 150 by 6 to find the final answer: \[ 150 \text{ meters} \right / 6 \text{ meters} = 25 \text{ meters} \]

Key Concepts

Fraction Multiplication

In this exercise, we are multiplying a fraction by a whole number. Understanding how to perform fraction multiplication is crucial for solving the problem. When multiplying a fraction, such as \( \frac{5}{6} \), by a whole number, like 30 meters, you multiply the numerator of the fraction by the whole number. The numerator in our fraction is 5. So, you multiply 5 by 30. This operation is represented as:
\[ \frac{5}{6} \times 30 \text{ meters} \]
The next step involves simplifying the multiplication to ensure a clear result.

Simplification

Simplification is a key step when working with fractions and algebraic operations. After multiplying the numerator by the whole number, the result is:
\[ \frac{5 \times 30}{6} \text{ meters} = \frac{150}{6} \text{ meters} \]
Here, we need to simplify \( \frac{150}{6} \). Simplification involves reducing the fraction to its lowest terms. In this case, dividing 150 (the numerator) by 6 (the denominator) gives us:
\[ 150 \text{ meters} \right/ 6 \text{ meters} = 25 \text{ meters} \]
It's important to perform these steps carefully to ensure the correct answer.

Basic Algebra Operations

Basic algebra operations are fundamental in solving problems involving fractions and whole numbers. Multiplication and division are the primary operations used in this exercise. Start by:

• Multiplying the fraction's numerator by the whole number.
• After obtaining the product, simplify the resulting fraction by dividing the numerator by the denominator.

This approach ensures the fraction multiplication process is accurate and comprehensible. Breaking down each step helps in understanding the concept better, leading to more accurate solutions in subsequent problems.