Bot GPT 4-o mini To multiply the mixed numbers \(3 \frac{3}{10}\) and \(5 \frac{2}{3}\), we first convert them to improper fractions.
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Convert \(3 \frac{3}{10}\) to an improper fraction: \[ 3 \frac{3}{10} = \left(3 \times 10 + 3\right) / 10 = (30 + 3) / 10 = 33 / 10 \]
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Convert \(5 \frac{2}{3}\) to an improper fraction: \[ 5 \frac{2}{3} = \left(5 \times 3 + 2\right) / 3 = (15 + 2) / 3 = 17 / 3 \]
Now, we multiply the two improper fractions: \[ \frac{33}{10} \times \frac{17}{3} = \frac{33 \times 17}{10 \times 3} \]
Calculating the numerator and the denominator: \[ 33 \times 17 = 561 \] \[ 10 \times 3 = 30 \]
So, we have: \[ \frac{561}{30} \]
Next, we can simplify the fraction. First, let's check if \(561\) and \(30\) have any common factors.
\(561\) is not divisible by \(2\), \(3\), or \(5\). To check for divisibility by smaller prime numbers:
- \(561\) divided by \(3\) yields \(187\) (so, it's divisible by \(3\)).
Now, simplifying: \[ \frac{561 \div 3}{30 \div 3} = \frac{187}{10} \]
To convert this back to a mixed number, note that: \[ \frac{187}{10} = 18 \frac{7}{10} \]
Thus, the product of \(3 \frac{3}{10}\) and \(5 \frac{2}{3}\) is: \[ 18 \frac{7}{10} \]
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