Question

Find the difference between the greatest and the smallest fraction 3 3/5, 2 4/7, 19/6 , 18/8

Answer 1

Required difference is $1\dfrac{7}{20}$

Step-by-step explanation:

Step 1 of 5.

[ Changing the mixed fractions into improper fractions ]

The given fractions are

$3\dfrac{3}{5}=\dfrac{3\times 5+3}{5}=\dfrac{15+3}{5}=\dfrac{18}{5}$

$2\dfrac{4}{7}=\dfrac{2\times 7+4}{7}=\dfrac{14+4}{7}=\dfrac{18}{7}$

$\dfrac{19}{6}$

$\dfrac{18}{8}$

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 ]

$\dfrac{18}{5}=\dfrac{18\times 168}{5\times 168}=\dfrac{3024}{840}$

$\dfrac{18}{7}=\dfrac{18\times 120}{7\times 120}=\dfrac{2160}{840}$

$\dfrac{19}{6}=\dfrac{19\times 140}{6\times 140}=\dfrac{2660}{840}$

$\dfrac{18}{8}=\dfrac{18\times 105}{8\times 105}=\dfrac{1890}{840}$

Step 4 of 5.

[ Writing the greatest and the smallest fractions ]

So, the greatest fraction is $\dfrac{3024}{840}$, that is, $3\dfrac{3}{5}$

and the smallest fraction is $\dfrac{1890}{840}$, that is, $\dfrac{18}{8}$

Step 5 of 5.

[ Finding the required difference ]

Now the required difference is

$3\dfrac{3}{5}-\dfrac{18}{8}$

$=\dfrac{18}{5}-\dfrac{18}{8}$

$=\dfrac{18\times 8-18\times 5}{40}$

• where LCM of 5 and 8 is 40

$=\dfrac{144-90}{40}$

$=\dfrac{54}{40}$

$=\dfrac{27}{20}$

$=1\dfrac{7}{20}$

#SPJ3

Answer 2

Answer:

this is the simplest form of ans of this question