Which fraction is the least?

Question

3 1|4, 2 7|8, 2 3|5, 2 2|10? they are fractions

Answer 1

3 1/4, 2 7/8, 2 3/5, 2 2/10

Write mixed fraction as improper fraction.

13/4,112/8,13/5,22/10

L.C.M of 4,8,5,10 is 40.

13/4  (Multiply nominator and denominator by 10 is 130/40).

112/8 (Multiply nominator and denominator by 5 is 560/40)

13/8 (Multiply nominator and denominator by 8 is 104/40)

22/10 (Multiply nominator and denominator by 4 is 88/40)

130/40,560/40, 104/40,88/40

Equal  all the denominators.

So  88/40 is least fraction.

Answer 2

first convert the mixed numbers into improper fractions 
3 1|4 = 13/4
2 7|8 = 23/8
2 3|5 = 13/5
2 2|10 = 22/10

write the fractions with a common denominator
list the prime factors of each number

prime factors of 4 = 2 x 2
prime factors of 8 = 2 x 2 X 2
prime factors of 5 = 1 x 5
prime factors of 10 = 2 x 5

LCM is the product of each factor the greatest number of times it occurs in any number.
LCM = 2 * 2 * 2 * 5= 40

Least common multiple of 4, 8, 5, and 10 is 40

write the fractions with a common denominator
3 1|4 = 13/4 = 130 /40
2 7|8 = 23/8 = 115 / 40
2 3|5 = 13/5 = 104/40
2 2|10 = 22/10 = 88 / 40

the least to greatest order is
88/40 < 104/40 < 115/40 < 130/40
the least fractions is 2 2|10