What happens to a whole number when it is multiplied by a fraction greater than 1?

Numbers are mathematical figures or values that may be used to count, measure, or perform other arithmetic operations. These Numbers systems include integers, whole numbers, natural numbers, rational and irrational numbers, prime numbers, and so on. The number system is a standardized way of representing numbers in a variety of media, including figures and language. It contains a wide range of numbers, including prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. Depending on the number system employed, these numbers can be represented in a variety of ways.

There are several types of numbers in the number system, such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. These numbers may be expressed using these figures and words. Integers such as 50 and 35 expressed as figures, for example, can also be written as fifty and thirty-five.

Whole numbers 

Whole numbers are the subset of numbers that contains zero and all positive integers. The total number ranges from 0 to infinity. These numbers are commonly used in everyday calculations, mostly to quantify fundamental quantities. Natural numbers are just entire numbers, including zero. The subset is represented by the integers 0, 1, 2, 3, 4, 5,… Fractions, decimals, and negative integers are not included in the subset.

Positive integers, also known as counting numbers, are whole-number portions that contain zero, such as 0,1, 2, 3, 4, 5, and so on, whereas negative integers, fractions, and decimals are not included. Whole numbers include 10, 11, 24, 50, 100, 1000, and so on.

Fraction 

Fractions are defined as numerical figure that represents a portion of a whole. A fraction is a component or sector of any amount taken from a whole, where the whole might be any number, a specified value, or an object. All fractions have a numerator and a denominator, which are separated by a horizontal bar called the fractional bar.

What happens to a whole number when it is multiplied by a fraction greater than 1?

Solution:  

There are three conditions which give the different result when whole number is multiplied by fraction.

• First Case: If we multiply the whole number with a fraction greater than 1 then it will resultant value will become greater. Example: 5 Is a whole number and if multiplied it by fraction greater than 1,

 = 5 × 4/3 

 = 5 × 1.33

 = 6.6666

Here the whole number was 5 but after multiplying it by fraction greater than 1 then the resultant value becomes bigger.

• Second Case: If we multiply the whole number with a fraction less than 1 then it will resultant value will become lesser. Example: 5 Is a whole number and if we multiplied it by fraction lesser than 1.

= 5 × 2/4 

= 5 × 0.5

= 2.5

Here the whole number is 5 but after multiplying it by fraction less than 1 then the resultant value becomes lesser.

• Third Case: If we multiply the whole number with a fraction equal to 1 then it will resultant value will be same as there will be no change. Example: 5 Is a whole number and if we multiplied it by fraction equal to 1.

= 5 × 5/5

= 5 × 1

= 5 which is same as whole number.

Sample Questions

Question 1: Add 8 + 5/2 whole number with fraction?

Solution:

Given: 8 + 5/2 

Here we can write 8 as 8/1

= 8/1 + 5/2 

By taking LCM,

=  (8 + 5)/2  

= 13/2 

Question 2: Simplify 3/5 + 5/6

Solution:

Given: 3/5 + 5/6

Here by taking lcm of denominator 5 and 6 are 30

= (18 + 25)/30

= 43/30

Question 3: Simplify 6/2 + 5/8 + 2/9.

Solution:

Given: 6/2 + 5/8 + 2/9 

Here by taking lcm of denominator 2, 8, 9 are 72

= (216 + 45 + 16)/72

= 277/72

Question 4: Multiply 8 × 9/2?

Solution: 

Given: 8 × 9/2

= 8 × 9/2

= 72/2

= 36

Question 5: If we multiply the whole number 6 with a fraction greater than 2, what will be the result?

Solution: 

6 Is a whole number and if we multiplied it by fraction greater than 2,

= 6 × 7/3

= 6 × 2.33

= 13.998

So, If we multiply the whole number 6 with a fraction greater than 2 then the resultant value will become greater. 

Question 6: In a class of 50 students, 1/5^th of them watch cartoons. How many students don’t watch cartoons?

Solution: 

Total number of students = 50, 

The fraction of students who watch cartoons = 1/5

Number of students who watch cartoons = 1/5 × 50 = 10

So, the number of students who dont watch cartoons = 50 – 10 = 40

Therefore, the number of students who do not watch cartoons is 40.