Finding a Common Denominator for 7/8 and 1/4

Understanding fractions is an important skill, and part of working with fractions involves finding a common denominator. Let's go through the process step by step to find the common denominator for the fractions 7/8 and 1/4.

Step 1: Identify the Denominators

The denominators of our fractions are:

• 7/8: the denominator is 8
• 1/4: the denominator is 4

Step 2: Find the Least Common Multiple (LCM)

To find a common denominator, we need to find the Least Common Multiple (LCM) of 8 and 4. The LCM is the smallest number that both denominators can divide into without leaving a remainder.

Finding multiples:

• Multiples of 8: 8, 16, 24, 32, ...
• Multiples of 4: 4, 8, 12, 16, 20, 24, ...

Now we look for the smallest multiple that appears in both lists. The multiples of both 8 and 4 include:

• 8
• 16

The smallest of these is 8, which means the LCM of 8 and 4 is 8.

Step 3: Rewrite the Fractions with the Common Denominator

Now that we have our common denominator (8), we need to rewrite both fractions so that they both have this common denominator.

Rewriting 7/8:

• Since the denominator of 7/8 is already 8, we do not need to change it. It stays as 7/8.

Rewriting 1/4:

• To change 1/4 to have a denominator of 8:

We can multiply both the numerator and the denominator by 2:

• 1 × 2 = 2 (new numerator)
• 4 × 2 = 8 (new denominator)

So, 1/4 = 2/8.

Step 4: Final Result

Now we have both fractions with the common denominator of 8:

• 7/8
• 2/8

In summary, we found the common denominator for 7/8 and 1/4 to be 8, allowing us to easily compare or perform operations with these fractions.

Conclusion

Finding a common denominator is an important skill when adding, subtracting, or comparing fractions. With practice, you'll become more comfortable with this process!