Rewrite the fraction 3/7 with the indicated denominator of 49.
Understand the Problem
The question is asking us to rewrite the fraction 3/7 so that it has a denominator of 49. This involves finding a suitable numerator that corresponds to this new denominator while keeping the value of the fraction the same.
Answer
The fraction $ \frac{3}{7} $ rewritten with a denominator of 49 is $ \frac{21}{49} $.
Answer for screen readers
The fraction $ \frac{3}{7} $ rewritten with a denominator of 49 is $ \frac{21}{49} $.
Steps to Solve
- Identify the Current and New Denominators
The current fraction is $\frac{3}{7}$, and we want to rewrite it with a denominator of 49.
- Determine the Factor Needed for Denominator Change
To change the denominator from 7 to 49, we need to find what to multiply 7 by:
$$ 7 \times x = 49 $$
Calculating for $x$ gives:
$$ x = \frac{49}{7} = 7 $$
- Adjust the Numerator Accordingly
Since we multiplied the denominator by 7, we must also multiply the numerator by 7 to keep the value of the fraction the same:
$$ 3 \times 7 = 21 $$
- Rewrite the Fraction
Now we can rewrite the fraction with the new numerator and denominator:
$$ \frac{3}{7} = \frac{21}{49} $$
The fraction $ \frac{3}{7} $ rewritten with a denominator of 49 is $ \frac{21}{49} $.
More Information
This method of adjusting fractions is known as finding an equivalent fraction. It is particularly useful in problems involving addition or subtraction of fractions with different denominators.
Tips
- Not Multiplying Both Numerator and Denominator: A common mistake is to only change the denominator without adjusting the numerator, leading to incorrect answers. Always ensure both are scaled equally.
- Forgetting the Factor Calculation: Sometimes, students forget to check what factor is needed to change the denominator, leading to unnecessary complexity.
AI-generated content may contain errors. Please verify critical information
