Question - Mathematical Calculation of Mixed Numbers
Solution:
The problem in the image is:\[ 4 \frac{1}{2} (5 \frac{5}{8} - 15\frac{5}{8}) + (1 \frac{1}{2} - 3\frac{1}{4}) \]First, let's convert the mixed numbers into improper fractions:For $$ 4 \frac{1}{2} $$, we have $$ 4 \times 2 + 1 = 9/2 $$.For $$ 5 \frac{5}{8} $$, we have $$ 5 \times 8 + 5 = 45/8 $$.For $$ 15 \frac{5}{8} $$, we have $$ 15 \times 8 + 5 = 125/8 $$.For $$ 1 \frac{1}{2} $$, we have $$ 1 \times 2 + 1 = 3/2 $$.For $$ 3 \frac{1}{4} $$, we have $$ 3 \times 4 + 1 = 13/4 $$.Then the expression becomes:\[ \frac{9}{2} \left( \frac{45}{8} - \frac{125}{8} \right) + \left( \frac{3}{2} - \frac{13}{4} \right) \]Now we'll do the operations within the parentheses:\[ \frac{45}{8} - \frac{125}{8} = -\frac{80}{8} = -10 \]\[ \frac{3}{2} - \frac{13}{4} = \frac{6}{4} - \frac{13}{4} = -\frac{7}{4} \]Now our expression is:\[ \frac{9}{2} \times -10 + -\frac{7}{4} \]Multiplying $$ \frac{9}{2} $$ by -10:\[ \frac{9}{2} \times -10 = \frac{9 \times -10}{2} = -\frac{90}{2} = -45 \]We now have:\[ -45 - \frac{7}{4} \]To subtract these, we'll express -45 as a fraction with a denominator of 4:\[ -45 = -\frac{180}{4} \]Now subtract:\[ -\frac{180}{4} - \frac{7}{4} = -\frac{187}{4} \]The answer is $$-\frac{187}{4}$$, which can be left as an improper fraction or converted back into a mixed number:\[ -\frac{187}{4} = -46 \frac{3}{4} \] So the final answer is $$ -46 \frac{3}{4} $$.
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