Question - Solving and Simplifying Fractions in Math Problems
Solution:
The image shows two separate math problems, labeled A and B, asking for the calculation and simplification of fractions if possible, and to verify the solutions with a calculator. Let's solve them:**For A:**$$ A = \frac{2}{5} - \frac{3}{15} + \frac{2}{15} $$First, find a common denominator for the fractions, which is 15 in this case. Adjust the first fraction to have the same denominator by multiplying both the numerator and denominator by 3:$$ A = \frac{2 \cdot 3}{5 \cdot 3} - \frac{3}{15} + \frac{2}{15} $$$$ A = \frac{6}{15} - \frac{3}{15} + \frac{2}{15} $$Now, add and subtract the fractions using the common denominator:$$ A = \left( \frac{6 - 3 + 2}{15} \right) $$$$ A = \frac{5}{15} $$This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:$$ A = \frac{5 \div 5}{15 \div 5} $$$$ A = \frac{1}{3} $$**For B:**$$ B = \frac{9}{2} - \frac{5}{2} + \frac{15}{8} $$In this case, the common denominator for the first two fractions is already the same (2). The third fraction has a different denominator. The least common multiple (LCM) of 2 and 8 is 8, so we need to adjust the first two fractions to have the denominator of 8:$$ B = \frac{9 \cdot 4}{2 \cdot 4} - \frac{5 \cdot 4}{2 \cdot 4} + \frac{15}{8} $$$$ B = \frac{36}{8} - \frac{20}{8} + \frac{15}{8} $$Now, combine the fractions:$$ B = \left( \frac{36 - 20 + 15}{8} \right) $$$$ B = \frac{31}{8} $$There's no way to simplify the fraction $$ B = \frac{31}{8} $$ further since 31 is a prime number and not divisible by 8.To verify these calculations with a calculator, simply enter them as given in the simplified forms ($$ A = \frac{1}{3} $$, $$ B = \frac{31}{8} $$) and compare the decimal results if needed.
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