What does slash mean in math?

In order to perform various operations in math, we make use of many symbols such as + , – , x , ÷ etc. One such symbol that is commonly used in various branches of math is slash. So, what does slash mean in math? Slash is a symbol, represented as “ / “ which finds its use in various operations such as division and concepts such as fractions and set theory. Let us learn more about this symbol.

Slash in Division

We know that in order to show the division of two numbers, we use the symbol ÷ between them. For example, if we have two numbers, say “ a “ and “ b “, and we intend to divide “ a “  by “ b “, then we can write them as a ÷ b. Is there any other way of representing this division?

Instead of the symbol “ ÷ “ we can also use the symbol slash “ / “ when dividing one number from another. Let us take the same example, as above, where we want to divide “ a “  by “ b “. This division can now be represented as a / b.

Let us consider some more examples.

Example

Represent the division of 20 by 4 using symbols.

Solution

We have been given that the number 20 is to be divided by the number 4. We are now aware of two symbols that can be used to represent this division. The representation can thus be –

20 ÷ 4 or 20 / 4

Example

Represent the division of 15 by 7 using symbols.

Solution

We have been given that the number 15 is to be divided by the number 7. We are now aware of two symbols that can be used to represent this division. The representation can thus be –

15 ÷ 7 or 15 / 7

Check Our What does o mean in math?

Slash in Fractions

It is not only division, where we find the use of the symbol slash. Slash is commonly used to represent fractions as well. Let us recall that fractions are used to represent a part or a whole of a number. The general form of a fraction is p/q where q ≠ 0. Similar to the divisions, we can use a slash to fractions as well. The fraction, p/q can also be written as p / q, which would mean the same as its original form, i.e. part  “ p “ of the whole “ q “. Let us consider some examples.

Example

Represent the fraction 7 parts of 19 using symbols.

Solution

We have been given that the fraction 7 parts of 19. We are now aware of two methods to represent a fraction. The representation can thus be –

7/19 or 7 / 19

Example

Represent the fraction 13 parts of 21 using symbols.

Solution

We have been given that the fraction of 13 parts of 21. We are now aware of two methods to represent a fraction. The representation can thus be –

13/21 or 13 / 21

Check Our What is orientation in math?

Slash in Set Notations

Another branch of mathematics, where the symbol slash is extensively used is set theory. We know that a set is a group or a collection of numbers, objects or things. However, in set theory, the meaning of the symbol slash is different from what it means in the case of division and fractions.

So, what does slash mean in sets? In the case of sets, the symbol slash means “ such that “ or “ given that “. To understand its usage, we must first recall the representation of sets. We know that there are two ways, in which a set can be represented, namely –

• Roster form
• Set builder form

Roster form

The roster form is the form of representation where each element of a set is represented individually, separated by a comma. Let us take an example.

Example

Represent the set of the first seven natural numbers in roster form.

Solution

We know that the first seven natural numbers are 1, 2, 3, 4, 5, 6 and 7. Therefore, the representation in roster form would be { 1, 2, 3, 4, 5, 6, 7 }

Check Our What does origin mean in math?

Set Builder form

Set Builder form of sets is the method where we define the conditions on which the set has been formed.  Let us take the example that we discussed above, i.e. set of the first 7 natural numbers. Here we have been given two conditions –

• The numbers in the set are natural numbers. We can represent this symbolically as a number, say, x belongs to the set of natural numbers, i.e. x ∈ N, where N is the set of natural numbers.
• The first 7 numbers in order are part of the set. We can represent this symbolically as x ≤ 7.

Combining the conditions together, we have “ x “ is a natural number such that x is less than or equal to 7. Notice, the term “ such that ” in the condition that we have defined. This is where we use the symbol slash. So, the representation of this set ins et builder form would be –

{ x /   x ∈ N, x ≤ 7 }

In general, the set builder form is written as –

{ x | P ( x ) holds } which is read as x is a number or an object such as the condition P ( x ) holds true.

What does slash mean in math?: Examples

Represent the following set in set builder form.

A  = { 2, 4, 6, 8, 10 }

Solution

We have been given the set A  = { 2, 4, 6, 8, 10 }. We can observe that in the given set A, we have even numbers and the largest number is 10. Therefore, this set A can be defined as a set of even natural numbers which is less than or equal to 10. Symbolically, we have, x, is an element in the set A such that, 2x ∈ N and x ≤ 10. Using these conditions, we can now define the set A as –

A = { 2x / x ∈ N, x ≤ 10 }

Example

Represent the following set in set builder form.

A  = { 3, 4, 5, 6, 7, 8, 9, . . . . . . . . }

Solution

We have been given the set A  = { 3, 4, 5, 6, 7, 8, 9, . . . . . . . . }. We can observe that in the given set A, we have whole numbers, starting from 3 and going up to infinity. Since this set contains infinite numbers, it is called an infinite set and we need to define it accordingly. Therefore, this set A can be defined as a set of whole numbers such that x is greater than or equal to 3. Symbolically, we have, x, is an element in the set A such that, x ∈ W and x ≥ 3. Using these conditions, we can now define the set A as –

A = {x / x ∈ W, x ≥ 3 }

Example

Represent the following set in set builder form.

A  = { 1, 4, 9, 16, 25, 36, 49 }

Solution

We have been given the set A  = { 1, 4, 9, 16, 25, 36, 49 }. Observe the numbers carefully. We can see that the given numbers are perfect squares. We have,

Therefore, we can define the set as x2, where x is a natural number and x is less than or equal to 7. Using these conditions, we can now define the given set as

A = {x 2 / x ∈ N, x ≤ 7}

Check Our What does period mean in math?

What Does Slash Mean in Math?: FAQs