Arrange the following rational number ascending order:a.23,(−4)7,(−8)3,6−9
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We shall represent the given numbers with positive denominators.
−9
4
and
−18
7
By multiplying both numerator and denominator by −1 we get,
−9
4
=
−9×−1
4×−1
=
9
−4
and
−18
7
=
−18×−1
7×−1
=
18
−7
Now let's take the LCM of 9,12,18,3 i.e. 36
By multiplying both numerator and denominator by 4 we get,
9
−4
=
9×4
−4×4
=
36
−16
By multiplying both numerator and denominator by 3 we get,
12
−5
=
9×3
−5×3
=
36
−15
By multiplying both numerator and denominator by 3 we get,
18
−7
=
18×2
−7×2
=
36
−14
By multiplying both numerator and denominator by 12 we get,
3
−2
=
3×12
−2×12
=
36
−24
Clearly by comparing the numerators i.e., −24<−16<−15<−14
∴
36
−24
<
36
−16
<
36
−15
<
36
−14
i.e.
3
−2
<
−9
4
<
12
−5
<
−18
7
.
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