Question

22/（5 7/13+2 6/13）-（5 1/4-3 3/4）/5=

Answer 1

22/（5 7/13+2 6/13）-（5 1/4-3 3/4）/5= 2  9/20

22/ 8  - 3/10

2,75 - 3/10

11/4 - 3/10

49/20 = 2  9/20

Answer 2

Let's break down the given expression step by step:

1. Convert Mixed Numbers to Improper Fractions:

   • $5 \frac{7}{13} = \frac{5 \cdot 13 + 7}{13} = \frac{65 + 7}{13} = \frac{72}{13}$
   • $2 \frac{6}{13} = \frac{2 \cdot 13 + 6}{13} = \frac{26 + 6}{13} = \frac{32}{13}$
   • $5 \frac{1}{4} = \frac{5 \cdot 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}$
   • $3 \frac{3}{4} = \frac{3 \cdot 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$

2. Perform the Subtractions:

   • $\frac{72}{13} + \frac{32}{13} = \frac{72 + 32}{13} = \frac{104}{13}$
   • $\frac{21}{4} - \frac{15}{4} = \frac{21 - 15}{4} = \frac{6}{4} = \frac{3}{2}$

3. Calculate the Division:

   • $\frac{22}{\frac{104}{13}} = \frac{22 \cdot 13}{104} = \frac{286}{104} = \frac{143}{52}$
   • $\frac{\frac{3}{2}}{5} = \frac{3}{2} \cdot \frac{1}{5} = \frac{3}{10}$

4. Final Subtraction:

   • $\frac{143}{52} - \frac{3}{10} = \frac{143 \cdot 10}{52 \cdot 10} - \frac{3 \cdot 52}{10 \cdot 52} = \frac{1430}{520} - \frac{156}{520} = \frac{1430 - 156}{520} = \frac{1274}{520}$

Now, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it:

The GCD of 1274 and 520 is 26.

$\frac{1274}{520} = \frac{1274 \div 26}{520 \div 26} = \frac{49}{20}$

So, the simplified result of the expression is $\frac{49}{20}$.