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Question
Write three rational numbers that lie between the two given numbers.
`7/8, (-5)/3`
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Solution
The given numbers are `7/8 "and" - 5/3`
Let us convert each of the given numbers into fractions with equal denominators.
`7/8 = (7 xx 3)/(8 xx 3) = 21/24`
`- 5/3 = (-5 xx 8)/(3 xx 8) = (-40)/24`
We know that,
-40 < −39 < .....< −13 < −12 < .....< 11 < 12 < ....<17 < .... 21
`therefore - 40/24 < - 39/24 < .....< -13/24 < -12/24 < ......<11/24 < 12/24 < .....< 17/24 < .....< 21/24`
`=> (-5)/3 < (-39)/24 < ....< (-13)/24 < (-12)/24 < .....< 11/24 < 12/24 <.....< 17/24 <.....< 7/8`
Hence, 3 rational numbers between `7/8 "and" (-5)/3` are:
`(-13)/24, 11/24` and `17/24`
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