Solving and Simplifying Fractions in Math Problems
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.
