Question

Which number in each of the following pairs is smaller?
i) $0, - 4$
ii) $ - 3,12$
iii) $8,13$
iv) $ - 15, - 27$

Answer 1

Hint: Numbers can be represented in a number line. When marked on a number line greater numbers lie toward right and smaller numbers lie towards left. If a number lies left with respect to another number we can say, the former number is smaller than the latter.

Complete step-by-step answer:
We are given four pairs of numbers.
From each pair, we have to find the smaller one.
We can use a number line to compare the numbers.
Zero can be considered as the centre in the number line.
Positive numbers are marked towards the right of the zero and negative numbers are marked towards the left of the zero.
The magnitude or absolute value of a number increases as the distance from zero increases.
If a number lies left with respect to another number we can say, the former number is smaller than the latter.

From the representation in the number line we can see, negative numbers increase in magnitude when distance from zero increases. So we can say that among two negative numbers the one with larger magnitude is the smaller number.
Now we can check each option one by one.
i) $0, - 4$
From the number line it is clear that $ - 4 < 0$ as $0$ is in the right of $ - 4$.
So the smaller number is $ - 4$.
ii) $ - 3,12$
Since every negative number is smaller than any positive number, we can say $ - 3 < 12$.
So $ - 3$ is the smaller number.
iii) $8,13$
For two positive numbers, we are clear about the smaller number. We can see from the number line that $13$ will be in the right of the number $8$.
So the smaller number is $8$.
iv) $ - 15, - 27$
As we said among two negative numbers the one with larger magnitude is the smaller number. Therefore here we can say $ - 27 < - 15$.
So the smaller number is $ - 27$.

Note: We are clear about the smaller and larger numbers in the case of positive numbers. But we may make mistakes in cases involving negative numbers. Especially if two negative numbers are given. Product of two negative numbers will result in a positive number. Product of two positive numbers will result in a positive number. Product of one negative number and one positive number gives a negative number.