convert from unlike fractions to like fractions - 9/16,24/18,15/45 

To convert unlike fractions to like fractions, we need to find a common denominator for all the fractions. Here's how we do it step by step:

### Fractions given:
- \( \frac{9}{16}, \frac{24}{18}, \frac{15}{45} \)

### Step 1: Find the Least Common Denominator (LCD)

The denominators are \( 16, 18, \) and \( 45 \). To find the least common denominator, we determine the least common multiple (LCM) of these numbers.

#### Prime factorization of the denominators:
- \( 16 = 2^4 \)
- \( 18 = 2 \times 3^2 \)
- \( 45 = 3^2 \times 5 \)

Now, the LCM is found by taking the highest powers of all prime factors involved:
- \( 2^4 = 16 \)
- \( 3^2 = 9 \)
- \( 5 = 5 \)

So, the LCM of \( 16, 18, \) and \( 45 \) is:
\[
16 \times 9 \times 5 = 720
\]
Thus, the least common denominator (LCD) is 720.

### Step 2: Convert each fraction to an equivalent fraction with a denominator of 720

#### 1. Convert \( \frac{9}{16} \) to a denominator of 720:
\[
\frac{9}{16} = \frac{9 \times 45}{16 \times 45} = \frac{405}{720}
\]

#### 2. Convert \( \frac{24}{18} \) to a denominator of 720:
\[
\frac{24}{18} = \frac{24 \times 40}{18 \times 40} = \frac{960}{720}
\]

#### 3. Convert \( \frac{15}{45} \) to a denominator of 720:
\[
\frac{15}{45} = \frac{15 \times 16}{45 \times 16} = \frac{240}{720}
\]

### Step 3: Resulting like fractions
Now, the fractions with a common denominator are:
\[
\frac{405}{720}, \frac{960}{720}, \frac{240}{720}
\]

Would you like further details or have any questions?

### 5 Related Questions:
1. How do you simplify fractions after finding a common denominator?
2. What is the importance of the least common denominator in adding and subtracting fractions?
3. Can you demonstrate adding or subtracting the like fractions found here?
4. How do you find the greatest common divisor (GCD) for simplifying fractions?
5. What are some shortcuts to find the least common multiple for larger numbers?

### Tip:
When finding the least common denominator, prime factorization helps to ensure accuracy in determining the lowest possible common denominator.

convert from unlike fractions to like fractions - 9/16, 24/18, 15/45

Learn how to convert unlike fractions 9/16, 24/18, and 15/45 into like fractions by finding the least common denominator (LCD) of 720 using prime factorization. Detailed step-by-step instructions suitable for Grades 5-7 students.

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