Class-8 || Rational Numbers || Rational Numbers between Two Rational Numbers
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Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, they can be written in the form a/b, where "a" and "b" are integers and "b" is not equal to zero.
To describe rational numbers between two given rational numbers, let's assume we have two rational numbers, let's say p/q and r/s, where p/q is smaller than r/s.
To find rational numbers between p/q and r/s, we can follow the steps below:
Step 1: Find a common denominator for q and s. This will be the least common multiple (LCM) of q and s. Let's call it "d."
Step 2: Convert the fractions p/q and r/s to have the same denominator d. Multiply p/q by (d/q) and r/s by (d/s). This gives us the fractions pd/dq and rd/ds.
Step 3: Determine the numerators for the rational numbers between p/q and r/s. These numerators can be any integers between pd and rd (exclusive). For example, if pd = 2 and rd = 6, then the numerators for the rational numbers between p/q and r/s can be 3, 4, and 5.
Step 4: Write down the rational numbers using the numerators found in the previous step and the common denominator d. Each rational number will be of the form (numerator/denominator).
For example, let's say we have p/q = 1/3 and r/s = 1/2.
Step 1: The LCM of 3 and 2 is 6, so we take d = 6.
Step 2: Multiply 1/3 by 2/2 and 1/2 by 3/3. This gives us pd/dq = 2/6 and rd/ds = 3/6.
Step 3: The numerators between 2 and 3 (exclusive) are 2 + 1 = 3.
Step 4: The rational numbers between 1/3 and 1/2 are 3/6.
So, the rational numbers between 1/3 and 1/2 are 3/6.
Note: Depending on the given rational numbers, there may be more than one rational number between them. The process described above gives one possible set of rational numbers between the given pair.
Rational numbers
Fractions
Quotient
Integers
Numerator
Denominator
Common denominator
Least common multiple (LCM)
Equivalent fractions
Mixed numbers
Proper fractions
Improper fractions
Recurring decimals
Terminating decimals
Division
Decimal representation
Addition
Subtraction
Multiplication
Division algorithm
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