To determine if the rational numbers \( \frac{7}{12} \) and \( \frac{28}{48} \) are equivalent, we can follow these steps:
### Step 1: Identify the Rational Numbers
We have two rational numbers:
- \( \frac{7}{12} \)
- \( \frac{28}{48} \)
### Step 2: Simplify \( \frac{28}{48} \)
To check if \( \frac{28}{48} \) is equivalent to \( \frac{7}{12} \), we need to simplify \( \frac{28}{48} \) to its lowest terms.
### Step 3: Find the HCF (Highest Common Factor)
We need to find the HCF of the numerator (28) and the denominator (48).
- The factors of 28 are: 1, 2, 4, 7, 14, 28
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors of 28 and 48 are 1, 2, and 4. The highest of these is 4.
### Step 4: Divide by the HCF
Now, we will divide both the numerator and the denominator of \( \frac{28}{48} \) by their HCF (which is 4):
\[
\frac{28 \div 4}{48 \div 4} = \frac{7}{12}
\]
### Step 5: Compare the Results
After simplifying \( \frac{28}{48} \), we find that it equals \( \frac{7}{12} \).
### Conclusion
Since both fractions simplify to the same value, we conclude that the rational numbers \( \frac{7}{12} \) and \( \frac{28}{48} \) are equivalent.
### Final Answer
Yes, \( \frac{7}{12} \) and \( \frac{28}{48} \) are equivalent rational numbers.
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