Give the following in ascending order
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Rational Numbers in Ascending Order
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We will learn how to arrange the rational numbers in ascending order.
General method to arrange from smallest to largest rational numbers (increasing):
Step 1: Express the given rational numbers with positive denominator.
Step 2: Take the least common multiple (L.C.M.) of these positive denominator.
Step 3: Express each rational number (obtained in step 1) with this least common multiple (LCM) as the common denominator.
Step 4: The number having the smaller numerator is smaller.
Solved examples on rational numbers in ascending order:
1. Arrange the rational numbers
−7
10
,
5
−8
and
2
−3
in ascending order:
Solution:
We first write the given rational numbers so that their denominators are positive.
We have,
5
−8
=
5×(−1)
(−8)×(−1)
=
−5
8
and
2
−3
=
2×(−1)
(−3)×(−1)
=
−2
3
Thus, the given rational numbers with positive denominators are
−7
10
,
−5
8
,
−2
3
Now, LCM of the denominators 10, 8 and 3 is 2 × 2 × 2 × 3 × 5 = 120
We now write the numerators so that they have a common denominator 120 as follows:
−7
10
=
(−7)×12
10×12
=
−84
120
,
−5
8
=
(−5)×15
8×15
=
−75
120
and
−2
3
=
(−2)×40
3×40
=
−80
120
.
Comparing the numerators of these numbers, we get,
- 84 < -80 < -75
Therefore,
−84
120
<
−80
120
<
−75
120
⇒
−7
10
<
−2
3
<
−5
8
⇒
−7
10
<
2
−3
<
5
−8
Hence, the given numbers when arranged in ascending order are:
−7
10
,
2
−3
,
5
−8