Answer:
a) [tex]\frac{5}{6}[/tex]is greatest fraction.
b) [tex]\frac{5}{12}[/tex] is greatest fraction.
c) [tex]\frac{19}{45}[/tex] is greatest fraction.
d) [tex]\frac{13}{14}[/tex] is greatest fraction.
Solution:
To compare two fraction we need to make denominator of both the fraction same.
a)Given fraction are [tex]\frac{5}{6}[/tex] and [tex]\frac{29}{36}[/tex]
[tex]\frac{5}{6}=\frac{5 \times 6}{6 \times 6}=\frac{30}{36}[/tex]
So [tex]\frac{30}{36}[/tex] is equivalent to [tex]\frac{5}{6}[/tex]
So [tex]\frac{30}{36}>\frac{5}{6}[/tex]
Hence [tex]\frac{30}{36}[/tex] that is [tex]\frac{5}{6}[/tex] is greater than [tex]\frac{29}{36}[/tex]
b)Given fraction are [tex]\frac{5}{12}[/tex] and [tex]\frac{3}{8}[/tex]
[tex]\frac{5}{12}=\frac{5 \times 2}{12 \times 2}=\frac{10}{24}[/tex]
Similarly we get [tex]\frac{3}{8}=\frac{3 \times 3}{8 \times 3}=\frac{9}{24}[/tex]
So [tex]\frac{10}{24}>\frac{9}{24}[/tex]
[tex]\frac{10}{24}>\frac{9}{24}[/tex]
That is [tex]\frac{5}{12}>\frac{3}{8}[/tex]
Hence [tex]\frac{5}{12}[/tex] is greater than [tex]\frac{3}{8}[/tex]
c) Given fraction are [tex]\frac{2}{5}[/tex] and [tex]\frac{19}{45}[/tex]
[tex]\frac{2}{5}=\frac{2 \times 9}{5 \times 9}=\frac{18}{45}[/tex]
So [tex]\frac{19}{45}>\frac{18}{45}[/tex]
That is [tex]\frac{19}{45}>\frac{2}{5}[/tex]
Hence [tex]\frac{19}{45}[/tex] is greater than [tex]\frac{2}{5}[/tex]
d)Given fraction are [tex]\frac{5}{7}[/tex], [tex]\frac{13}{14}[/tex] and [tex]\frac{19}{21}[/tex]
[tex]\frac{5}{7}=\frac{5 \times 6}{7 \times 6}=\frac{30}{42}[/tex]
[tex]\frac{13}{14}=\frac{13 \times 3}{14 \times 3}=\frac{39}{42}[/tex]
Similarly we get
[tex]\frac{19}{21}=\frac{19 \times 2}{21 \times 2}=\frac{38}{42}[/tex]
So [tex]\frac{39}{42}>\frac{38}{42}>\frac{30}{42}[/tex]
That is [tex]\frac{13}{14}>\frac{19}{21}>\frac{5}{7}[/tex]
Hence [tex]\frac{13}{14}[/tex] is greatest fraction.
