Question

three rational number between 1/8 and 1/4

Answer 1

three rational numbers between 1/8 and 1/4 are 1/5, 1/6 and 1/7

Answer 2

Concept

If a and b are two rational numbers such that a < b, then, n rational numbers between a and b can be found as follows

• Multiply and divide a and b by (n+1) to get the corresponding equivalent fractions $\frac{a(n+1)}{(n+1)}$, and $\frac{b(n+1)}{(n+1)}$.

• n rational numbers between a and b are then $\frac{a(n+2)}{(n+1)}, \frac{a(n+3)}{(n+1)},..., \frac{a(2n+1)}{(n+1)}$.

Given

Two rational numbers: 1/8, 1/4.

Find

Three rational numbers between 1/8 and 1/4.

Solution

Equivalent fractions

Multiply and divide the two numbers by (3+1) = 4 to obtain equivalent fractions 4/32, 4/16.

We make the denominator of the two numbers same for better comparison.

Multiply and divide the second number by 2 to get 4/32, 8/32.

Numbers between 4/32 and 8/32

The second number is 8/32. We can write it as

                       $\frac{8}{32} = \frac{(4 + 4)}{32} = \frac{4}{32} + \frac{4}{32} = \frac{4}{32} + 4\times\frac{1}{32}.$

So, we see 8/32 is four 1/32-step greater than the first number 4/32.

The three numbers between 4/32 and 8/32 are:

• 4/32 + 1×(1/32) = 5/32.

• 4/32 + 2×(1/32) = 6/32.

• 4/32 + 3×(1/32) = 7/32.

The three required numbers are, this, 5/32, 6/32, 7/32.

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