Question - Fraction Subtraction and Addition
Solution:
To solve the expression given in the image, you need to perform the operations (subtraction and addition) between fractions:The expression is: $$-\frac{4}{2} - \frac{4}{5} - \frac{1}{2} + \frac{3}{5}$$First, simplify the fractions where possible before combining them. The fraction $$-\frac{4}{2}$$ can be simplified to $$-2$$ since $$4 \div 2 = 2$$, and $$-\frac{1}{2}$$ is already in its simplest form.Now we have: $$-2 - \frac{4}{5} - \frac{1}{2} + \frac{3}{5}$$Next, to combine the fractions $$-\frac{4}{5}$$ and $$\frac{3}{5}$$, you can simply add their numerators because they have a common denominator:$$-\frac{4}{5} + \frac{3}{5} = -\frac{4 - 3}{5} = -\frac{1}{5}$$Now we have: $$-2 - \frac{1}{2} - \frac{1}{5}$$To add $$-2$$ and $$-\frac{1}{2}$$, you can convert $$-2$$ to a fraction with a denominator of $$2$$ to get $$-\frac{4}{2}$$:$$-\frac{4}{2} - \frac{1}{2} = -\frac{5}{2}$$Now we have: $$-\frac{5}{2} - \frac{1}{5}$$To combine these two fractions, we need a common denominator. The least common multiple of $$2$$ and $$5$$ is $$10$$. Convert both fractions to have the denominator of $$10$$:$$-\frac{5}{2} \times \frac{5}{5} = -\frac{25}{10}$$$$-\frac{1}{5} \times \frac{2}{2} = -\frac{2}{10}$$Now add the two fractions with a common denominator:$$-\frac{25}{10} - \frac{2}{10} = -\frac{27}{10}$$This gives us the final result: $$-\frac{27}{10}$$
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