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Question

Determine by observation which of the numbers in each pair is the bigger one and which is smaller.

(1) −5, −1
(2) 0, -87
(3) 43, 0
(4) -32, 14
(5) -116, -76
(6) 2537, 2837
(7) 2537, -2837
(8) -710, -510

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Solution

(1) −5, −1
The number on the left is smaller than the number on the right on the number line.
We know that −5 lies on the left of −1 on the number line.
∴ −5 < −1

(2) 0, -87
All the negative numbers lie on the left of 0 on the number line.
-87 is on the left of 0.
And we know that a number on the left is smaller than a number on the right on the number line.
-87<0

(3) 43, 0
All the positive numbers lie on the right of 0 on the number line.
∴ 0 is on the left of43 .
And we know that a number on the left is smaller than a number on the right on the number line.
0<43

(4) -32, 14
All the positive numbers lie on the right of all the negative numbers on the number line.
-32 is on the left of14 .
And we know that a number on the left is smaller than a number on the right on the number line.
-32<14

(5) -116, -76
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −7 > −11 .
-116<-76

(6) 2537, 2837
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that 25 < 28 .
2537<2837

(7) 2537, -2837
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −28 < 25 .
-2837<2537

(8) -710, -510
If two numbers have the same denominator, then the one with the bigger numerator is the bigger number.
We know that −7 < −5 .
-710<-510

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