Question - Subtracting Mixed Numbers
Solution:
The image displays a fraction subtraction problem, which is part (iii) of a larger set of problems. Here's how to solve it:$$ 1\frac{1}{5} - 1\frac{2}{3} $$First, convert the mixed numbers into improper fractions to make subtraction easier.For the first number:$$ 1\frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} $$For the second number:$$ 1\frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} $$Now, subtract the second improper fraction from the first:$$ \frac{6}{5} - \frac{5}{3} $$To subtract fractions, they must have a common denominator. The least common multiple (LCM) of the denominators 5 and 3 is 15, so convert each fraction to have the same denominator:$$ \frac{6}{5} \times \frac{3}{3} = \frac{18}{15} $$ $$ \frac{5}{3} \times \frac{5}{5} = \frac{25}{15} $$Now perform the subtraction:$$ \frac{18}{15} - \frac{25}{15} = \frac{18 - 25}{15} = \frac{-7}{15} $$The answer is a negative fraction because the second number was larger than the first one. Therefore, $$ 1\frac{1}{5} - 1\frac{2}{3} = -\frac{7}{15} $$.
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