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Question
Insert five rational number between:
`-(3)/(4) and -(2)/(5)`
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Solution
Since, `-(3)/(4) and -(2)/(5)`
Let a = `-(2)/(5), "b" = -(3)/(4) and "n" = 5`
∴ d = `"b - a"/("n" + 1)`
= `(-3/4 - (-2/5))/(5 + 1)`
= `((-3)/4 + 2/5)/(6)`
= `((-15 + 8)/(20))/(6)`
= `-(7)/(120)`
Hence, required rational numbers are :
a + d = `-(2)/(5) + (- 7/120)`
= `-(2)/(5) - (7)/(120)`
= `(-48 - 7)/(120)`
= `-(55)/(120)`
= `-(11)/(24)`
a + 2d = `(2)/(5) + 2 xx (- 7/120)`
= `(2)/(5) + (4)/(45)`
= `(18 + 4)/(45)`
= `(22)/(45)`
a + 3d = `(2)/(5) + 3 xx (- 7/120)`
= `(2)/(5) + (2)/(15)`
= `(6 + 2)/(15)`
= `(8)/(15)`
a + 4d = `(2)/(5) + 4 xx (- 7/120)`
= `(2)/(5) + (8)/(45)`
= `(18 + 8)/(45)`
= `(26)/(45)`
a + 5d = `(2)/(5) + 5 xx (- 7/120)`
= `(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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