Question
12. \( 1 \frac{24}{25} \times 1 \frac{3}{25}= \)
Ask by Fitzgerald Young. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 1 \frac{24}{25} \times 1 \frac{3}{25} = 2 \frac{122}{625} \)
Solution
To calculate \( 1 \frac{24}{25} \times 1 \frac{3}{25} \), follow these steps:
1. **Convert Mixed Numbers to Improper Fractions:**
\[
1 \frac{24}{25} = \frac{25 + 24}{25} = \frac{49}{25}
\]
\[
1 \frac{3}{25} = \frac{25 + 3}{25} = \frac{28}{25}
\]
2. **Multiply the Improper Fractions:**
\[
\frac{49}{25} \times \frac{28}{25} = \frac{49 \times 28}{25 \times 25} = \frac{1372}{625}
\]
3. **Convert the Improper Fraction Back to a Mixed Number:**
\[
\frac{1372}{625} = 2 \frac{122}{625}
\]
(Since \( 625 \times 2 = 1250 \) and \( 1372 - 1250 = 122 \).)
4. **Simplify if Possible:**
The fraction \( \frac{122}{625} \) cannot be simplified further as 122 and 625 have no common factors other than 1.
**Final Answer:**
\[
1 \frac{24}{25} \times 1 \frac{3}{25} = 2 \frac{122}{625}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To tackle this problem, let's first convert the mixed numbers into improper fractions. For \(1 \frac{24}{25}\), we multiply 1 by 25 and add 24, giving us \(\frac{49}{25}\). For \(1 \frac{3}{25}\), we do the same: \(1 \times 25 + 3 = \frac{28}{25}\). Now we multiply the two fractions: \[ \frac{49}{25} \times \frac{28}{25} = \frac{49 \times 28}{25 \times 25} = \frac{1372}{625}. \] Now, we can convert back to a mixed number. Dividing 1372 by 625 gives us approximately 2.1952, so the mixed number is \(2 \frac{122}{625}\). Thus, the answer is: \( 1 \frac{24}{25} \times 1 \frac{3}{25}= 2 \frac{122}{625} \).
