Question - Multiplication of Mixed Fractions
Solution:
To solve the multiplication of mixed fractions, you first convert each mixed fraction into an improper fraction. For the first mixed fraction $$1 \frac{6}{7}$$:Multiply the whole number by the denominator and add the numerator to this product. This gives you the new numerator, while the denominator remains the same.So, $$1 \times 7 + 6 = 7 + 6 = 13$$, making the improper fraction $$\frac{13}{7}$$.For the second mixed fraction $$2 \frac{2}{3}$$:Multiply the whole number by the denominator and then add the numerator to get the new numerator.So, $$2 \times 3 + 2 = 6 + 2 = 8$$, which makes the improper fraction $$\frac{8}{3}$$.Now multiply the improper fractions together:$$\frac{13}{7} \times \frac{8}{3}$$Multiply the numerators together and the denominators together:Numerator: $$13 \times 8 = 104$$Denominator: $$7 \times 3 = 21$$The product is $$\frac{104}{21}$$.This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor if possible. In this case, 104 and 21 don't have a common divisor other than 1, so the fraction is already in its simplest form. Since the numerator is larger than the denominator, you can also convert it back into a mixed number:$$104 \div 21 = 4$$ with a remainder of $$16$$.So the mixed number is $$4 \frac{16}{21}$$. If you want to check whether the fraction $$\frac{16}{21}$$ can be simplified, you can look for common factors. In this case, there are none, and the final answer is:$$4 \frac{16}{21}$$
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