Step-by-step explanation:
Required difference is 1\dfrac{7}{20}1
20
7
Step-by-step explanation:
Step 1 of 5.
[ Changing the mixed fractions into improper fractions ]
The given fractions are
3\dfrac{3}{5}=\dfrac{3\times 5+3}{5}=\dfrac{15+3}{5}=\dfrac{18}{5}3
5
3
=
5
3×5+3
=
5
15+3
=
5
18
2\dfrac{4}{7}=\dfrac{2\times 7+4}{7}=\dfrac{14+4}{7}=\dfrac{18}{7}2
7
4
=
7
2×7+4
=
7
14+4
=
7
18
\dfrac{19}{6}
6
19
\dfrac{18}{8}
8
18
Step 2 of 5.
[ Finding the LCM of the denominators of the given fractions ]
5 = 5
7 = 7
6 = 2 × 3
8 = 2 × 2 × 2
So, LCM = 2 × 2 × 2 × 3 × 5 × 7 = 840
Step 3 of 5.
[ Changing the denominators of the fractions into the obtained LCM ]
\dfrac{18}{5}=\dfrac{18\times 168}{5\times 168}=\dfrac{3024}{840}
5
18
=
5×168
18×168
=
840
3024
\dfrac{18}{7}=\dfrac{18\times 120}{7\times 120}=\dfrac{2160}{840}
7
18
=
7×120
18×120
=
840
2160
\dfrac{19}{6}=\dfrac{19\times 140}{6\times 140}=\dfrac{2660}{840}
6
19
=
6×140
19×140
=
840
2660
\dfrac{18}{8}=\dfrac{18\times 105}{8\times 105}=\dfrac{1890}{840}
8
18
=
8×105
18×105
=
840
1890
Step 4 of 5.
[ Writing the greatest and the smallest fractions ]
So, the greatest fraction is \dfrac{3024}{840}
840
3024
, that is, 3\dfrac{3}{5}3
5
3
and the smallest fraction is \dfrac{1890}{840}
840
1890
, that is, \dfrac{18}{8}
8
18
Step 5 of 5.
[ Finding the required difference ]
Now the required difference is
3\dfrac{3}{5}-\dfrac{18}{8}3
5
3
−
8
18
=\dfrac{18}{5}-\dfrac{18}{8}=
5
18
−
8
18
=\dfrac{18\times 8-18\times 5}{40}=
40
18×8−18×5
where LCM of 5 and 8 is 40
=\dfrac{144-90}{40}=
40
144−90
=\dfrac{54}{40}=
40
54
=\dfrac{27}{20}=
20
27
=1\dfrac{7}{20}=1
20
7
