Question

Write the following integers in increasing order:
(i) -8, 5, 0, -12, 1, -9, 15
(ii) -106, 107, -320, -7, 185

Answer 1

Hint: Integers are numbers that can be positive, negative or zero. They cannot be a fraction, decimal or percentage. All the numbers on the number line at the left of zero will be negative and all the numbers to the right of zero will be positive. We can say that the numbers on the number line increases from left to right. The negative numbers will be small and positive numbers will be large. Of the negative numbers, the smallest numbers are those which are close to the leftmost part of the number line.

Complete step-by-step solution:
We have to arrange a given integer in increasing order. Let us recollect what integers are. Integers are numbers that can be positive, negative or zero. They cannot be a fraction, decimal or percentage. Let us consider a number line. We can say that all the numbers on this number line at the left of zero will be negative and all the numbers to the right of zero will be positive. We can say that the numbers on the number line increases from left to right. That is, negative numbers will be small and positive numbers will be large. Of the negative numbers, the smallest numbers are those which are close to the leftmost part of the number line. For example, let us consider a number line as shown below.

The smallest integer will be -5 and the largest will be 5. The numbers increase from left to right, that is, we can see that $-5<-4<-3<-1<0<1<2<3<4<5$ .
Now, let us consider the given set of numbers.
(i) We have to arrange -8, 5, 0, -12, 1, -9, 15 in increasing order. We can see that -12 is the smallest integer and 15 is the largest. We can arrange this set in increasing order as
-12, -9, -8, 0, 1, 5, 15
(ii) Let us arrange -106, 107, -320, -7, 185 in increasing order. Here, we can see that -320 is the smallest and 185 is the largest. We can write the increasing order of these integers as
-320, -106, -7, 107, 185
Hence, the increasing order of (i) -8, 5, 0, -12, 1, -9, 15 is -12, -9, -8, 0, 1, 5, 15 and that of (ii) -106, 107, -320, -7, 185 is -320, -106, -7, 107, 185.

Note: Students must not get confused with smallest integers. For example, between -12 and -7, They may get confused with the smallest integer by considering the same to be -7. In negative integers, when a negative sign comes with a large number, it will become the smallest. We know that 12 is greater than 7. But when a negative sign is present, -12 will be lesser than -7. There are a lot of rules associated with integers like addition, subtraction, multiplication and division. There are also properties associated with integers similar to the operations on positive numbers. We can conclude that all natural numbers are also integers that start from 1 and end at infinity and all whole numbers are also integers, starting from 0 and ending at infinity. We can also conclude that all integers are real numbers but not all real numbers are integers because real numbers also include rational and irrational numbers.