Sure, let's solve each part step-by-step.
### Part (a)
Subtract [tex]\( 7 \frac{1}{9} \)[/tex] from 14:
1. Convert [tex]\( 7 \frac{1}{9} \)[/tex] into an improper fraction:
[tex]\[
7 \frac{1}{9} = 7 + \frac{1}{9} = \frac{63}{9} + \frac{1}{9} = \frac{64}{9}
\][/tex]
2. Convert 14 into a fraction with a common denominator:
[tex]\[
14 = \frac{126}{9}
\][/tex]
3. Subtract the fractions:
[tex]\[
14 - 7 \frac{1}{9} = \frac{126}{9} - \frac{64}{9} = \frac{126 - 64}{9} = \frac{62}{9}
\][/tex]
4. Convert the result back to a mixed number:
[tex]\[
\frac{62}{9} = 6 \frac{8}{9} \approx 6.888888888888889
\][/tex]
### Part (b)
Subtract [tex]\( 2 \frac{6}{13} \)[/tex] from [tex]\( 1 \frac{7}{26} \)[/tex]:
1. Convert [tex]\( 2 \frac{6}{13} \)[/tex] into an improper fraction:
[tex]\[
2 \frac{6}{13} = 2 + \frac{6}{13} = \frac{26}{13} + \frac{6}{13} = \frac{32}{13}
\][/tex]
2. Convert [tex]\( 1 \frac{7}{26} \)[/tex] into an improper fraction:
[tex]\[
1 \frac{7}{26} = 1 + \frac{7}{26} = \frac{26}{26} + \frac{7}{26} = \frac{33}{26}
\][/tex]
3. Find a common denominator for [tex]\(\frac{32}{13}\)[/tex] and [tex]\(\frac{33}{26}\)[/tex]:
[tex]\[
\frac{32}{13} = \frac{32 \times 2}{13 \times 2} = \frac{64}{26}
\][/tex]
4. Subtract the fractions:
[tex]\[
1 \frac{7}{26} - 2 \frac{6}{13} = \frac{33}{26} - \frac{64}{26} = \frac{33 - 64}{26} = \frac{-31}{26} = -1 \frac{5}{26} \approx -1.1923076923076925
\][/tex]
### Part (c)
Subtract [tex]\( 1 \frac{6}{11} \)[/tex] from [tex]\( 7 \frac{18}{22} \)[/tex]:
1. Simplify [tex]\( 7 \frac{18}{22} \)[/tex]:
[tex]\[
7 \frac{18}{22} = 7 + \frac{9}{11} \quad \text{(since } \frac{18}{22} = \frac{9}{11})
\][/tex]
2. Convert [tex]\( 1 \frac{6}{11} \)[/tex] into an improper fraction:
[tex]\[
1 \frac{6}{11} = 1 + \frac{6}{11} = \frac{11}{11} + \frac{6}{11} = \frac{17}{11}
\][/tex]
3. Convert [tex]\( 7 \frac{9}{11} \)[/tex] into an improper fraction:
[tex]\[
7 \frac{9}{11} = 7 + \frac{9}{11} = \frac{77}{11} + \frac{9}{11} = \frac{86}{11}
\][/tex]
4. Subtract the fractions:
[tex]\[
7 \frac{9}{11} - 1 \frac{6}{11} = \frac{86}{11} - \frac{17}{11} = \frac{86 - 17}{11} = \frac{69}{11} = 6 \frac{3}{11} \approx 6.272727272727273
\][/tex]
So, the solutions are:
- (a) [tex]\( 6.888888888888889 \)[/tex]
- (b) [tex]\( -1.1923076923076925 \)[/tex]
- (c) [tex]\( 6.272727272727273 \)[/tex]
