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प्रश्न
Insert five rational number between:
`(2)/(5) and (2)/(3)`
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उत्तर
Since, `(2)/(5) < (2)/(3)`
Let a = `(2)/(5), "b" = (2)/(3) and "n" = 5`
∴ d = `(b - a)/("n" + 1)`
= `(2/3 - 2/5)/(5 + 1)`
= `((10 - 6)/(15))/(6)`
= `(4)/(90)`
= `(2)/(45)`
Hence, required rational numbers are :
a + d = `(2)/(5) + (2)/(45)`
= `(18 + 2)/(45)`
= `(20)/(45)`
= `(4)/(9)`
a + 2d = `(2)/(5) + 2 xx (2)/(45)`
= `(2)/(5) + (4)/(45)`
= `(18 + 4)/(45)`
= `(22)/(45)`
a + 3d = `(2)/(5) + 3 xx (2)/(45)`
= `(2)/(5) + (2)/(15)`
= `(6 + 2)/(15)`
= `(8)/(15)`
a + 4d = `(2)/(5) + 4 xx (2)/(45)`
= `(2)/(5) + (8)/(45)`
= `(18 + 8)/(45)`
= `(26)/(45)`
a + 5d = `(2)/(5) + 5 xx (2)/(45)`
= `(2)/(5) + (2)/(9)`
= `(18 + 10)/(45)`
= `(28)/(45)`
Thus, five rational numbers between `(2)/(5) and (2)/(3)` are
`(4)/(9), (22)/(45), (8)/(15), (26)/(45) and (28)/(45)`.
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