Reduce the following to the lowest term show how to calculate the greatest common divisor by the step approach 22/52

To reduce the fraction \( \frac{22}{52} \) to its lowest terms, we need to calculate the **greatest common divisor (GCD)** of 22 and 52. Here's the step-by-step approach:

### Step 1: Prime Factorization
First, find the prime factors of both numbers.

- \( 22 = 2 \times 11 \)
- \( 52 = 2^2 \times 13 \)

### Step 2: Identify Common Factors
The only common prime factor between 22 and 52 is **2**.

### Step 3: Calculate the GCD
The GCD is the product of all the common factors. In this case, the only common factor is \( 2 \), so the GCD is:

\[
\text{GCD}(22, 52) = 2
\]

### Step 4: Simplify the Fraction
Now, divide both the numerator and the denominator by the GCD (which is 2):

\[
\frac{22}{52} = \frac{22 \div 2}{52 \div 2} = \frac{11}{26}
\]

So, the fraction \( \frac{22}{52} \) reduces to \( \frac{11}{26} \) in its lowest terms.

---

Would you like more details on any part of this process or another example? Here are 5 related questions to deepen your understanding:

1. How can you find the GCD using the Euclidean algorithm instead of prime factorization?
2. What is the lowest term of the fraction \( \frac{36}{48} \)?
3. How do you reduce a fraction where the GCD is not obvious (e.g., large numbers)?
4. How does simplifying a fraction help in real-world problem-solving?
5. What is the LCM (Least Common Multiple), and how does it differ from the GCD?

**Tip:** Using the Euclidean algorithm is a faster method for finding the GCD of larger numbers!

Discover how to simplify the fraction 22/52 using the greatest common divisor (GCD) through prime factorization. This step-by-step guide breaks down the prime factors of 22 and 52 and shows how to reduce the fraction to 11/26. Suitable for Grades 6-8 math students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation