﻿ Sign of greater than and less than — Math18

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Math18

# Sign of greater than and less than

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## What is a greater than sign?

A “greater than” symbol is represented by the “>” sign, it is a mathematical element to indicate that the number to the left of the sign is greater than the number to the right of it.

9 > 5
3 > 1
21 > 15

To be able to identify in a simple way it is considered that the opening of the sign expresses that the number is greater, in this case it would be the numbers on the left and the tip or closing of the sign indicates that it is smaller, corresponding to the number that is on the right of the sign.

Important: The opening always points to the largest element, and the tip or closure, to the smallest.

### How do you read the sign greater than?

The reading is very simple, for example:

• 15 > 12: Fifteen is greater than twelve.
• 7 > 3: Seven is greater than three.
• 2 > 1: Two is greater than one.

### Sign greater than or equal

Using the symbol indicates that the number is “greater than or equal”, that means that the number to the left of the sign is greater than or equal to the number on the left.

8 ≥ 5
6 ≥ 6
4 ≥ 3

## What is a sign less than?

A "less than" symbol is represented by the "<" sign, it is a mathematical element to indicate that the number to the left of the sign is less than the number to the right of it.

7 < 9
10 < 11
3 < 4

To be able to identify in a simple way it is considered that the tip or closure of the sign indicates that it is smaller, in this case it would be the numbers that are to the left of the sign and the opening of the sign expresses that the number is greater, in this case it would be The numbers on the right.

Important: The opening always points to the largest element, and the tip or closure, to the smallest.

### How do you read the sign less than?

The reading is very simple, for example:

• 5 < 9 Five is less than nine.
• 1 < 3 One is less than three
• 12 < 13: Twelve is less than thirteen

### Sign less than or equal

When using the symbol it indicates that the number is "less than or equal", that means that the number to the left of the sign is less than or equal to the number on the right.

3 ≤ 5
5 ≤ 5
5 ≤ 10

## Smaller or larger numbers on the line

When we place two numbers on the line, the number on the right is larger than the number on the left.

From the line it follows:

-1 > -2
2 > 1
0 < 2
2 > 1

## Comparison of numbers with decimals

In this case it is important to know the position value of the numbers, considering that the number on the left is always larger than the number on the right.

Some situations that may arise are:

• Assuming that you want to compare 0.56 and 0.43, first the comparison of the largest digit that corresponds to 5 tenths in 0.56 and 4 tenths in 0.43 is made, as 5 > 4 it follows that 0.56 > 0.43.
• Assuming that you want to compare 13,643 and 4,849, first the comparison of the largest digit that corresponds to 1 ten in 13,643 and 4 units in 4,849 is made, since the tens are larger values than the units it is possible to quickly deduce that 13,643 > 4,849.
• Assuming that you want to compare 12,439 and 12,434, by observation we see that the largest digits are equal (1 ten in 12,439 and 1 ten in 12,435), therefore, we move on to the next largest digit, since they are the same again (2 units in 12,439 and 2 units in 12,434) it is necessary to continue lowering position until finding different digits, in this case they are in the thousandths position with a position value of 9 thousandths in 12,439 and 5 thousandths in 12,435, as 9 > 5 deduces that 12,439 > 12,434

Some people prefer to make the comparison in the form of fractions, therefore, it is necessary to convert decimals to fractions.

## Comparison of fractions

For the comparison of fractions it is advisable to have everything in the form of a fraction, therefore, for mixed fractions the corresponding operation must be done to convert to a fraction.

### Comparison of fractions with the same denominator

When the fractions have the same denominator it is very simple to make the comparison, only the numerator values should be compared. For example:

5 / 3
and
8 / 3

The numbers to compare are 5 and 8, since 5 < 8 we have then:

5 / 3
<
8 / 3

### Comparison of fractions with different denominator

When the fractions have a different denominator, it is necessary to convert the fractions to their corresponding equivalent, so you would have the same denominator to be able to make a comparison in a simple way. For example:

4 / 3
and
5 / 2

It is necessary to convert to equivalent fractions, we only multiply the numerator by the denominator of the opposite fraction and also denominator by denominator.

4 x 2 = 8
5 x 3 = 15
3 x 2 = 6
Now we must rearrange, considering the new denominator of the two fractions (3 x 2 = 6):

8 / 6
and
15 /
6

Therefore, comparing the values of numerator 8 and 15, we have to 8< 15:

8 / 6
<
15 /
6