Question - Multiplication of Mixed Numbers and Fractions
Solution:
The image shows a multiplication problem involving two mixed numbers:$$ 2\frac{1}{4} \times 5\frac{2}{3} $$To solve this problem, we should first convert each mixed number to an improper fraction.For $$ 2\frac{1}{4} $$:Multiply the whole number by the denominator of the fraction and then add the numerator:$$ 2 \times 4 + 1 = 8 + 1 = 9 $$So $$ 2\frac{1}{4} $$ becomes $$ \frac{9}{4} $$.For $$ 5\frac{2}{3} $$:Multiply the whole number by the denominator of the fraction and then add the numerator:$$ 5 \times 3 + 2 = 15 + 2 = 17 $$So $$ 5\frac{2}{3} $$ becomes $$ \frac{17}{3} $$.Now we multiply the two improper fractions:$$ \frac{9}{4} \times \frac{17}{3} = \frac{9 \times 17}{4 \times 3} $$Calculate the multiplication:$$ 9 \times 17 = 153 $$$$ 4 \times 3 = 12 $$Thus, the expression becomes:$$ \frac{153}{12} $$To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 3 in this case:$$ \frac{153 \div 3}{12 \div 3} = \frac{51}{4} $$The fraction $$ \frac{51}{4} $$ can also be written as a mixed number. To convert it back to a mixed number, divide 51 by 4:$$ 51 \div 4 = 12 $$ with a remainder of 3.So the mixed number is $$ 12\frac{3}{4} $$, which is the product of the original problem.
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