Rational Number between Two Rational Numbers

Reshma wanted to count the whole numbers between 3 and 10. From her earlier classes, she knew there would be exactly 6 whole numbers between 3 and 10. Similarly, she wanted to know the total number of integers between –3 and 3. The integers between –3 and 3 are –2, –1, 0, 1, 2. Thus, there are exactly integers between –3 and 3.

Thus, we find that number of integers between two integers are limited (finite). Will the same happen in the case of rational numbers also? Reshma took two rational numbers −35 and −13

So, we could find one more rational number between −35 and −13.

By using this method, you can insert as many rational numbers as you want between two different rational numbers.

Instruction

For example,

−35= −3×305×30

−35 = −3×305×30 =

and −13 = −1×503×50 =

We get 39 rational numbers between −90150 and −50150

1. Find five rational numbers between −57 and −38.

Convert the fractions to have the same denominator: −57 = −5x87x8 =

−38 = −3x78x7 =

Now we can identify five rational numbers between these two fractions from −4056 and −2156.

List three rational numbers between – 2 and – 1.

Solution:

Instruction

Let us write –1 and –2 as rational numbers with denominator 5. (Why?)

we, have -1 = −55 and -2 = −105

So, /5 < /5 < /5 < /5 < /5 < /5.

Or, -2 < /5 < /5 < /5 < /5 < -1.

The three rational numbers between –2 and –1 would be, -9/5 < -8/5 < -7/6.

Write four more numbers in the following pattern: −13 , −26 , −39 , −412....

Solution:

Instruction

We have, −26 = −1x23x2 , −39 = −1x33x3

−412 = −1x43x4

−1x13x1 = /3, −1x23x2 = /6.

Thus, we observe a pattern in these numbers.

Chapter 1: Rational Numbers

Glossary

Rational Number between Two Rational Numbers

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Chapter 1: Rational Numbers

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Glossary

Rational Number between Two Rational Numbers