Question

write down the all properties of rational number of operator

Answer 1

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Answer 2

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Property 1:

If a/b is a rational number and m is a nonzero integer, then

abab = a×mb×ma×mb×m

In other words, a rational number remains unchanged, if we multiply its numerator and denominator by the same non-zero integer.

For examples:

−25−25 = (−2)×25×2(−2)×25×2 = −410−410, (−2)×35×3(−2)×35×3 = −615−615, (−2)×45×4(−2)×45×4 = −820−820 and so on ……

Therefore, −25−25 = (−2)×25×2(−2)×25×2 = (−2)×35×3(−2)×35×3 = (−2)×45×4(−2)×45×4 and so on ……

Property 2:

If abab is a rational number and m is a common divisor of a and b, then

abab = a÷ma÷ma÷ma÷m

In other words, if we divide the numerator and denominator of a rational number by a common divisor of both, the rational number remains unchanged.

For examples:

−3240−3240 = −32÷840÷8−32÷840÷8 = −45−45



Property 3:

Let abab and cdcd be two rational numbers.

Then abab = cdcd ⇔ a×db×ca×db×c.










a × d = b × c

For examples:

If 2323 and 4646 are the two rational numbers then, 2323 = 4646 ⇔ (2 × 6) = (3 × 4).

Note:

Except zero every rational number is either positive or negative.

Every pair of rational numbers can be compared.



Property 4:

For each rational number m, exactly one of the following is true:

(i) m > 0 (ii) m = 0 (iii) m < 0

For examples:

The rational number 2323 is greater than 0.

The rational number 0303 is equal to 0.

The rational number −23−23 is less than 0.



Property 5:

For any two rational numbers a and b, exactly one of the following is true:

(i) a > b (ii) a = b (iii) a < b

For examples:

If 1313 and 1515 are the two rational numbers then, 1313 is greater than 1515.

If 2323 and 6969 are the two rational numbers then, 2323 is equal to 6969.

If −27−27 and 3838 are the two rational numbers then, −27−27 is less than 3838.



Property 6:

If a, b and c be rational numbers such that a > b and b > c, then a > c.

For examples:

If 3535, 17301730 and −815−815 are the three rational numbers where 3535 is greater than 17301730 and 17301730 is greater than −815−815, then 3535 is also greater than −815−815.



So, the above explanations with examples help us to understand the useful properties of rational numbers.



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