Answer :
Let's solve these arithmetic questions step by step:
11. [tex]\(\left( -\frac{1}{5} \right) + \left( \frac{3}{5} \right)\)[/tex]
Since they have the same denominator, we can combine the numerators:
[tex]\[ \frac{-1 + 3}{5} = \frac{2}{5} = 0.4 \][/tex]
So, [tex]\( \left( -\frac{1}{5} \right) + \left( \frac{3}{5} \right) = 0.4 \)[/tex]
### [tex]\(\boxed{0.39999999999999997}\)[/tex]
---
12. [tex]\( \frac{12}{13} + \frac{1}{13} + \frac{5}{13} \)[/tex]
Again, they have the same denominator, so combine the numerators:
[tex]\[ \frac{12 + 1 + 5}{13} = \frac{18}{13} = 1.3846153846153846 \][/tex]
So, [tex]\( \frac{12}{13} + \frac{1}{13} + \frac{5}{13} = 1.3846153846153846 \)[/tex]
### [tex]\(\boxed{1.3846153846153846}\)[/tex]
---
13. [tex]\( \frac{9}{16} - \frac{7}{16} \)[/tex]
Since they have the same denominator, subtract the numerators:
[tex]\[ \frac{9 - 7}{16} = \frac{2}{16} = \frac{1}{8} = 0.125 \][/tex]
So, [tex]\( \frac{9}{16} - \frac{7}{16} = 0.125 \)[/tex]
### [tex]\(\boxed{0.125}\)[/tex]
---
14. [tex]\( \frac{5}{8} - \frac{1}{2} \)[/tex]
Convert [tex]\( \frac{1}{2} \)[/tex] to a fraction with the same denominator, [tex]\( \frac{1}{2} = \frac{4}{8} \)[/tex], then subtract:
[tex]\[ \frac{5 - 4}{8} = \frac{1}{8} = 0.125 \][/tex]
So, [tex]\( \frac{5}{8} - \frac{1}{2} = 0.125 \)[/tex]
### [tex]\(\boxed{0.125}\)[/tex]
---
15. [tex]\( (5 \% 2) - (4 \% 4) \)[/tex]
Calculate the modulo operations:
[tex]\[ 5 \% 2 = 1 \][/tex]
[tex]\[ 4 \% 4 = 0 \][/tex]
Then subtract the results:
[tex]\[ 1 - 0 = 1 \][/tex]
So, [tex]\( (5 \% 2) - (4 \% 4) = 1 \)[/tex]
### [tex]\(\boxed{1}\)[/tex]
---
16. [tex]\( \left( \frac{2 \pi}{4} \right) - \left( \frac{1}{2} \right) \)[/tex]
Calculate each term and then subtract:
[tex]\[ \frac{2 \pi}{4} = \frac{\pi}{2} \][/tex]
[tex]\[ \frac{\pi}{2} - \frac{1}{2} \][/tex]
This simplifies to:
[tex]\[ \frac{1.5707963267948966 - 0.5} = 1.0707963267948966 \][/tex]
So, [tex]\( \left( \frac{2 \pi}{4} \right) - \left( \frac{1}{2} \right) = 1.0707963267948966 \)[/tex]
### [tex]\(\boxed{1.0707963267948966}\)[/tex]
---
17. [tex]\( \left( \frac{5}{7} \right) \left( \frac{7}{8} \)[/tex] \)
Multiply the fractions:
[tex]\[ \frac{5 \times 7}{7 \times 8} = \frac{35}{56} = \frac{5}{8} = 0.625 \][/tex]
So, [tex]\( \left( \frac{5}{7} \right) \left( \frac{7}{8} \)[/tex] = 0.625 \)
### [tex]\(\boxed{0.625}\)[/tex]
---
18. [tex]\( \left( \frac{3}{4} \right) \left( \frac{3}{5} \right) \left( \frac{4}{7} \)[/tex] \)
Multiply the fractions:
[tex]\[ \frac{3 \times 3 \times 4}{4 \times 5 \times 7} = \frac{36}{140} = \frac{18}{70} = \frac{9}{35} = 0.2571428571428571 \][/tex]
So, [tex]\( \left( \frac{3}{4} \right) \left( \frac{3}{5} \right) \left( \frac{4}{7} \)[/tex] = 0.2571428571428571 \)
### [tex]\(\boxed{0.2571428571428571}\)[/tex]
---
19. [tex]\( \frac{6}{12} \div \frac{1}{2} \)[/tex]
Rewrite the division as multiplication by the reciprocal:
[tex]\[ \frac{6}{12} \times \frac{2}{1} = \frac{6 \times 2}{12 \times 1} = \frac{12}{12} = 1.0 \][/tex]
So, [tex]\( \frac{6}{12} \div \frac{1}{2} = 1.0 \)[/tex]
### [tex]\(\boxed{1.0}\)[/tex]
---
20. [tex]\( \frac{1}{4} \div \frac{1}{4} \)[/tex]
Rewrite the division as multiplication by the reciprocal:
[tex]\[ \frac{1}{4} \times \frac{4}{1} = 1.0 \][/tex]
So, [tex]\( \frac{1}{4} \div \frac{1}{4} = 1.0 \)[/tex]
### [tex]\(\boxed{1.0}\)[/tex]
11. [tex]\(\left( -\frac{1}{5} \right) + \left( \frac{3}{5} \right)\)[/tex]
Since they have the same denominator, we can combine the numerators:
[tex]\[ \frac{-1 + 3}{5} = \frac{2}{5} = 0.4 \][/tex]
So, [tex]\( \left( -\frac{1}{5} \right) + \left( \frac{3}{5} \right) = 0.4 \)[/tex]
### [tex]\(\boxed{0.39999999999999997}\)[/tex]
---
12. [tex]\( \frac{12}{13} + \frac{1}{13} + \frac{5}{13} \)[/tex]
Again, they have the same denominator, so combine the numerators:
[tex]\[ \frac{12 + 1 + 5}{13} = \frac{18}{13} = 1.3846153846153846 \][/tex]
So, [tex]\( \frac{12}{13} + \frac{1}{13} + \frac{5}{13} = 1.3846153846153846 \)[/tex]
### [tex]\(\boxed{1.3846153846153846}\)[/tex]
---
13. [tex]\( \frac{9}{16} - \frac{7}{16} \)[/tex]
Since they have the same denominator, subtract the numerators:
[tex]\[ \frac{9 - 7}{16} = \frac{2}{16} = \frac{1}{8} = 0.125 \][/tex]
So, [tex]\( \frac{9}{16} - \frac{7}{16} = 0.125 \)[/tex]
### [tex]\(\boxed{0.125}\)[/tex]
---
14. [tex]\( \frac{5}{8} - \frac{1}{2} \)[/tex]
Convert [tex]\( \frac{1}{2} \)[/tex] to a fraction with the same denominator, [tex]\( \frac{1}{2} = \frac{4}{8} \)[/tex], then subtract:
[tex]\[ \frac{5 - 4}{8} = \frac{1}{8} = 0.125 \][/tex]
So, [tex]\( \frac{5}{8} - \frac{1}{2} = 0.125 \)[/tex]
### [tex]\(\boxed{0.125}\)[/tex]
---
15. [tex]\( (5 \% 2) - (4 \% 4) \)[/tex]
Calculate the modulo operations:
[tex]\[ 5 \% 2 = 1 \][/tex]
[tex]\[ 4 \% 4 = 0 \][/tex]
Then subtract the results:
[tex]\[ 1 - 0 = 1 \][/tex]
So, [tex]\( (5 \% 2) - (4 \% 4) = 1 \)[/tex]
### [tex]\(\boxed{1}\)[/tex]
---
16. [tex]\( \left( \frac{2 \pi}{4} \right) - \left( \frac{1}{2} \right) \)[/tex]
Calculate each term and then subtract:
[tex]\[ \frac{2 \pi}{4} = \frac{\pi}{2} \][/tex]
[tex]\[ \frac{\pi}{2} - \frac{1}{2} \][/tex]
This simplifies to:
[tex]\[ \frac{1.5707963267948966 - 0.5} = 1.0707963267948966 \][/tex]
So, [tex]\( \left( \frac{2 \pi}{4} \right) - \left( \frac{1}{2} \right) = 1.0707963267948966 \)[/tex]
### [tex]\(\boxed{1.0707963267948966}\)[/tex]
---
17. [tex]\( \left( \frac{5}{7} \right) \left( \frac{7}{8} \)[/tex] \)
Multiply the fractions:
[tex]\[ \frac{5 \times 7}{7 \times 8} = \frac{35}{56} = \frac{5}{8} = 0.625 \][/tex]
So, [tex]\( \left( \frac{5}{7} \right) \left( \frac{7}{8} \)[/tex] = 0.625 \)
### [tex]\(\boxed{0.625}\)[/tex]
---
18. [tex]\( \left( \frac{3}{4} \right) \left( \frac{3}{5} \right) \left( \frac{4}{7} \)[/tex] \)
Multiply the fractions:
[tex]\[ \frac{3 \times 3 \times 4}{4 \times 5 \times 7} = \frac{36}{140} = \frac{18}{70} = \frac{9}{35} = 0.2571428571428571 \][/tex]
So, [tex]\( \left( \frac{3}{4} \right) \left( \frac{3}{5} \right) \left( \frac{4}{7} \)[/tex] = 0.2571428571428571 \)
### [tex]\(\boxed{0.2571428571428571}\)[/tex]
---
19. [tex]\( \frac{6}{12} \div \frac{1}{2} \)[/tex]
Rewrite the division as multiplication by the reciprocal:
[tex]\[ \frac{6}{12} \times \frac{2}{1} = \frac{6 \times 2}{12 \times 1} = \frac{12}{12} = 1.0 \][/tex]
So, [tex]\( \frac{6}{12} \div \frac{1}{2} = 1.0 \)[/tex]
### [tex]\(\boxed{1.0}\)[/tex]
---
20. [tex]\( \frac{1}{4} \div \frac{1}{4} \)[/tex]
Rewrite the division as multiplication by the reciprocal:
[tex]\[ \frac{1}{4} \times \frac{4}{1} = 1.0 \][/tex]
So, [tex]\( \frac{1}{4} \div \frac{1}{4} = 1.0 \)[/tex]
### [tex]\(\boxed{1.0}\)[/tex]
