Question - Multiplying mixed numbers
Solution:
The image displays an arithmetic problem involving the multiplication of two mixed numbers: $$3\frac{1}{4}$$ and $$4\frac{2}{3}$$.First, we need to convert each mixed number into an improper fraction. To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator, then write the result over the original denominator.For $$3\frac{1}{4}$$:$$3 \cdot 4 + 1 = 12 + 1 = 13$$So, $$3\frac{1}{4}$$ as an improper fraction is $$\frac{13}{4}$$.For $$4\frac{2}{3}$$:$$4 \cdot 3 + 2 = 12 + 2 = 14$$So, $$4\frac{2}{3}$$ as an improper fraction is $$\frac{14}{3}$$.Now, multiply the two improper fractions:$$\frac{13}{4} \times \frac{14}{3}$$Multiply the numerators together and the denominators together:$$ \frac{13 \times 14}{4 \times 3} = \frac{182}{12} $$To simplify the resulting fraction, we need to find the greatest common divisor (GCD) of 182 and 12. The GCD of 182 and 12 is 2.Now, divide both the numerator and the denominator by the GCD to simplify:$$ \frac{182 \div 2}{12 \div 2} = \frac{91}{6} $$The fraction $$\frac{91}{6}$$ is an improper fraction. To express it as a mixed number, divide 91 by 6:$$ 91 \div 6 = 15 $$ remainder $$1$$So, the mixed number is $$15\frac{1}{6}$$. Therefore, $$3\frac{1}{4} \times 4\frac{2}{3} = 15\frac{1}{6}$$.
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