Multiples

 What are Multiples ?

We know the numbers 1 , 2 , 3 , 4 , 5 ....... When these numbers are multiplied with the same number or another number , then we get the product of the numbers. This product of the numbers is the multiple of the numbers multiplied.

Example 1

Example 2

How can we find the multiples of a number ?

Finding multiples of any number seems very easy. We can follow the procedure mentioned below.

Example 1

Find out any five multiples of the number 15.

Any five multiples of 15 are as follows :

15 X 1 = 15      15 X 2 = 30     15 X 3 = 45      15 X 4 = 60     15 X 5 = 75

Hence, the five multiples of 15 are 15 , 30 , 45 , 60  and 75

Example 2

Find out any five multiples of 24.

Any five multiples of 24 are as follows :

24 X 1 = 24      24 X 5 = 120     24 X 8 = 192      24 X 10 = 240     24 X 15 = 360

Hence, the five multiples of 24 are 24 , 120 , 192 , 240  and 360

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Properties of Multiples

• We get multiple of a number by multiplying the given number with another number or the same number
• The lowest multiple of a number is the number itself.
• We can calculate infinite number of multiples.
• Any number is the multiple of itself. For example, 3 is the multiple of 3.
• All the numbers are the multiples of 1.

Exercise

Find any five multiples of the given numbers

12 , 25 , 48 , 26 , 6

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Least common Multiples ( LCM )

Conjunctions

 Conjunctions : and, but, or, so, because

What are Conjunctions ?

Conjunctions are words used to join two or more words or phrases or sentences.

• 10 and 12 are two digit numbers.
• It is raining , so I cannot go to school.
• I eat cake but I never eat biscuits.
• Would you like tea or coffee ?

Commonly used conjunctions include

Why do we need conjunctions ?

Conjunctions are used to give more information, give alternatives / choices, give reasons, give results.

These are also called as 'Connectors' or 'Joining words'.

List of Conjunctions

Use of Conjunctions

And

For example :

• They are very fond of bread.
• They are very fond of butter.

They are very fond of bread and butter.

• We went Shimla.
• We enjoyed a lot.

We went Shimla and enjoyed a lot.

• John likes Mathematics.
• John likes Science.

John likes Mathematics and Science.

But

For example :

• Tom is a boy.
• Mary is a girl.

Tom is a boy but Mary is a girl.

• Ice is cold.
• Fire is hot.

Ice is cold but fire is hot.

Or

For example :

• You may take this book.
• You may take that one.

You may take this book or that one.

• Would you like ice cream ?
• Would you like chocolate ?

Would you like ice cream or chocolate ?

So

For example :

• He studies a lot.
• He is the best student.

He studies a lot , so he is the best student.

( Reason )   → ( Result )

• I lost my car keys.
• I took a taxi.

I lost my car keys , so I took a taxi.

( Reason )   → ( Result )

Because

For example :

• He is the best student.
• He studies a lot.

He is the best student because he studies a lot.

( Result )   ← ( Reason )

• I didn't go to class.
• I was sick.

I didn't go to class because I was sick.

( Result )   ← ( Reason )

Exercises related to Conjunctions

The following exercises will help you gain greater understanding about how conjunctions work. Supply the best conjunction to complete each sentence.

• My brother loves animals , ______ he bought a puppy.
• I want to go for a hike _____ I want to study.
• I am getting good marks ______ I study everyday
• I have two puppies _____ a cat.
• You can have pista _____ vanilla flavour ice cream.
• Work hard ____ you will fail.
• Rahul was present ____ Ronit was absent in class.
• He failed _____ his brother passed.
• I honour her _____ she is a brave woman.
• I shall sit still _____ listen to her song.