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Comparison And Ordering Of Integers

Comparison of Integers (Same Sign)

  • We can compare integers. For comparison, we use greater than (>), less than (<) or equal to (=) symbols.
  • If two integers are negative, the integer closer to zero is greater than the other.
  • If two integers are positive, the larger number is greater.

For example: Compare \(-9\) and \(-13\).

\(-9\;\Box-13\)

\(-9\) is closer to zero than \(-13\).

  • So, \(-9\) is greater than \(-13.\)  

\(\therefore\;-9>-13\)

  • A larger negative number is always less than a smaller negative number.

Example: \(-125<-75\)

  • Zero is always greater than the negative integers.

Example: \(0>-100,\;0>-500\)

Illustration Questions

Which one of the following statements shows the correct comparison between \(-12\) and \(-6\) ?

A \(-12>-6\)

B \(-12<-6\)

C \(-12=-6\)

D \(-12\leq-6\)

×

\(-6\) is closer to zero than \(-12\).

image

So, \(-6\) is greater than \(-12\).

\(\therefore\;-6>-12\)

Hence, option (B) is correct.

Which one of the following statements shows the correct comparison between \(-12\) and \(-6\) ?

A

\(-12>-6\)

.

B

\(-12<-6\)

C

\(-12=-6\)

D

\(-12\leq-6\)

Option B is Correct

Comparison of Integers having Different Signs

  • When we compare negative and positive integers, we use greater than \((>)\), less than \((<)\) or equal to \((=)\) sign.
  • A positive number is always greater than a negative number.

Positive numbers > Negative numbers

For example: Compare \(-17\) and \(1\).

\(-17\,\Box\,1\)

\(-17\) is a negative number and \(1\) is a positive number, so \(-17\) is less than \(1.\)

Therefore, \(-17<1\)

Illustration Questions

Which one of the following statements shows the correct comparison between \(5\) and \(-50\) ?

A \(5\leq-50\)

B \(5=-50\)

C \(-50>5\)

D \(5>-50\)

×

A positive number is always greater than a negative number.

Here, \(5\) is a positive number and \(-50\) is a negative number.

Thus, \(5>-50\)

Hence, option (D) is correct.

Which one of the following statements shows the correct comparison between \(5\) and \(-50\) ?

A

\(5\leq-50\)

.

B

\(5=-50\)

C

\(-50>5\)

D

\(5>-50\)

Option D is Correct

Ordering of Integers having Same Signs

  • We can arrange the integers in the order of least to greatest or greatest to least.
  • For the arrangement from least to greatest, follow the given steps:
  1.  Use a number line.
  2.  Start with the integer which is smallest, i.e. the number furthest to the left on the number line.
  3. On a number line, any integer is greater than the number on its left side and is smaller than the number on its right side. 

For example: Arrange \(-6,\;-2,\;-10\) and \(-9\)  in the order of least to greatest.

First, draw a number line from \(-10\) to \(0\) and represent the numbers according to their places.

Now, arrange the plotted numbers as per the number line.

On a number line, any integer is greater than the number on its left side and is smaller than the number on its right side. 

Write the given numbers starting from furthest to the left and moving towards zero on the number line.

\(-10<-9<-6<-2\)

Now, arrange the given numbers according to the number line.

Write the given numbers starting from furthest to the left and moving towards zero on the number line.

\(-10<-9<-6<-2\)

Illustration Questions

Which one of the following lists shows the order from least to greatest of the given numbers \(-18,\;-2,\;-7,\;-15\)?

A \(-2<-7<-15<-18\)

B \(-18<-15<-7<-2\)

C \(-18>-15>-7>-2\)

D \(-2>-7>-15>-18\)

×

First, draw a number line from \(-18\) to \(0.\)

Plot the numbers on the number line according to their places.

image

Now, arrange the plotted numbers as per the number line.

We start with the integer which is least.

On a number line, any integer is greater than the number on its left side and is smaller than the number on its right side. 

Thus, the arrangement of least to greatest would be:

\(-18<-15<-7<-2\)

Hence, option (B) is correct.

Which one of the following lists shows the order from least to greatest of the given numbers \(-18,\;-2,\;-7,\;-15\)?

A

\(-2<-7<-15<-18\)

.

B

\(-18<-15<-7<-2\)

C

\(-18>-15>-7>-2\)

D

\(-2>-7>-15>-18\)

Option B is Correct

Ordering of Negative and Positive Integers

  • We can order negative and positive integers using a number line.
  • To arrange the negative and positive integers in the order of least to greatest, remember the following points:
  1. Positive integers are always greater than the negative integers.
  2. The integer furthest to the left on the number line is always less than the integer furthest to the right. In other words we can say that on a number line, any integer is greater than the number on its left side and is smaller than the number on its right side. 
  3. For ordering from least to greatest, write the integers placed on the number line from left to right.

For example: Arrange \(5,\;-4,\;2\,and-5\) in the order of least to greatest.

First, draw a number line from \(-5\) to \(5\) and plot the integers on it according to their places.

Now, arrange the plotted numbers as per the number line.

Start from the furthest to the left and move the way up to the right.

\(-5<-4<2<5\)

Now, arrange the given numbers according to the number line. Start from the furthest to the left and move the way up to the right.

\(-5<-4<2<5\)

Illustration Questions

Which one of the following list of integers is in the order of least to greatest?

A \(-8,\;4,\;1\)

B \(4,-8,\;1\)

C \(-8,\;1,\;4\)

D \(1,\;4,-8\)

×

First, we draw a number line from \(-8\) to \(4\) and plot the numbers according to their places.

image

Now, we arrange the plotted numbers as per the number line.

We start from furthest to the left and move our way up to the right.

On a number line, any integer is greater than the number on its left side and is smaller than the number on its right side.

\(-8<1<4\)

Hence, option (C) is correct.

Which one of the following list of integers is in the order of least to greatest?

A

\(-8,\;4,\;1\)

.

B

\(4,-8,\;1\)

C

\(-8,\;1,\;4\)

D

\(1,\;4,-8\)

Option C is Correct

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