Question

insert two rational numbers between 1/4 and 1/5

Answer 1

using formula 1/2(a+b)
a=1/4 b=1/5
1/2(1/4+1/5)
1/2(9/20)
9/40 is one rational no.
now for second
a=1/4 b= 9/40
1/2(1/4+9/40)
1/2(19/40)
19/80 is second required rational no.

Answer 2

CONCEPT:

Finding Rational numbers between any given two fractions.

Formula used: (a+b)/2

GIVEN:

Two Fractions: 1/4 and 1/5

FIND:

Two rational numbers between the given fractions, that is 1/4 and 1/5.

SOLUTION:

The formula for inserting rational numbers between a and b is (a+b)/2.

Inserting the First rational number:

Let a = 1/4 and b = 1/5

a + b = 1/4 + 1/5

= (5 + 4)/20

= 9/20

Now,

(a + b)/2 = (9/20)/2

= 9/40.

Therefore, the first rational number to be inserted is 9/40.

Inserting the Second rational number:

Let a = 1/4 and b = 9/40.

a + b = 1/4 + 9/40

= (10 + 9)/40

= 19/40

= 19/40

Now,

(a + b)/2 = (19/40)/2

= 19/80.

Therefore, the second rational number to be inserted is 19/80.

Hence, 9/40 and 19/80 are the two rational numbers that can be inserted between 1/4 and 1/5.

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