Question - Adding and Converting Mixed Numbers
mathimproper fractionsadding mixed numbersconverting mixed numbersadding fractions with common denominator
Solution:
To solve this problem, we need to add the two amounts of newspapers collected by the two sections of Payapa School:First, let's convert the mixed numbers to improper fractions so that we can add them easily.For 18 2/5, we have:$$ 18 + \frac{2}{5} = \frac{18 \times 5}{5} + \frac{2}{5} = \frac{90}{5} + \frac{2}{5} = \frac{92}{5} $$For 22 1/2, we have:$$ 22 + \frac{1}{2} = \frac{22 \times 2}{2} + \frac{1}{2} = \frac{44}{2} + \frac{1}{2} = \frac{45}{2} $$Now, we need to add these two improper fractions:$$ \frac{92}{5} + \frac{45}{2} $$To add them, we need a common denominator, which for 2 and 5 is 10. We need to convert each fraction to have this common denominator:$$ \frac{92}{5} = \frac{92 \times 2}{5 \times 2} = \frac{184}{10} $$$$ \frac{45}{2} = \frac{45 \times 5}{2 \times 5} = \frac{225}{10} $$Now we can add the two fractions:$$ \frac{184}{10} + \frac{225}{10} = \frac{184+225}{10} = \frac{409}{10} $$Now, we convert this improper fraction back to a mixed number:$$ \frac{409}{10} = 40 + \frac{9}{10} = 40 \frac{9}{10} $$The correct answer is C) $$ 40 \frac{9}{10} $$ kg.
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