Fraction as a part of a whole definition, rules, facts, and examples here. Get various problems and solutions involved in whole fractions. Know the tips to solve various problems and find the definition here. Follow the step-by-step procedure to solve part-whole fraction problems. Refer to the models that are present in whole fractions. Check the below sections to know the various concepts involved in fraction whole parts.

## What is a Fraction of a Whole?

In the interpretation of part-whole, the denominator value shows equal parts number in whole and the numerator represents the number of parts that are included in a particular fraction. The construct of the whole-part is often represented with the model area like dividing the shape into equal parts. The fraction represents the part of the object. Therefore, the fraction is the whole object part. It is a collection of objects or part of the collection. If the number is not a whole number, then it is a fraction number.

The fraction is a whole number part like 1, 2, 3, 4, 5, 6, ………. 200 …….. etc.

**Example of fraction numbers:** \(\frac { 1 }{ 3 } \), \(\frac { 1 }{ 5 } \), \(\frac { 1 }{ 7 } \), \(\frac { 1 }{ 9 } \), \(\frac { 1 }{ 11 } \), \(\frac { 1 }{ 13 } \), etc.

### How do you write a Fraction as a Whole?

The way to represent whole parts is a fraction. If the fraction is represented with a/b, then the numerator “a” represents the equal number of parts where the whole number is divided into parts. The denominator “b” represents the way that represents the whole number. The denominator value cannot be zero, as division by zero is the undefined value.

### Important Concepts of Whole Parts

**Property of one**

The number which is divided by itself and which is not divided by zero is called the property of one.

**Example:** 3/3 = 1 where 3 ≠ 0

**Mixed Numbers**

The mixed number is nothing but the whole number (a) along with the fraction value (b/c) where c ≠ 0 and it ca be written as a b/c where c ≠ 0

**Example:** 4¾ is the mixed fraction

**Proper and Improper Fractions**

If the proper fraction is ab, then a<b and if the improper fraction is ab, then a≥b

**Conversion of an improper fraction into a mixed fraction**

- The numerator has to be divided with denominator
- Check remainder, quotient, divisor
- Note down the mixed number as the quotient i.e., remainder/divisor

**Conversion of a mixed fraction into an improper fraction**

- The denominator has to be multiplied by the whole number
- The product we get in Step 1 has to be added to the numerator
- In the last step, add the final product and put the denominator as it is

**Fractions of equivalent property**

If the numbers are a, b and c where c ≠ 0, b ≠ 0 then a/b = a-c/b-c

Also, Check:

### Problems on Fraction as a Part of a Whole

**Problem 1:**

Mary had some stamps. She gave 7 stamps to her younger brothers. Mary then had 14 stamps. How many stamps did Mary have at first?

**Solution:**

As given in the question,

No of stamps she gave to her younger brother = 7

No of stamps she had = 14

To find the number of stamps at first, we have to add the values

Therefore 7 + 14 = 21

Thus, Mary had 21 stamps at first

**Problem 2:**

Rahul spent \(\frac { 3 }{ 4 } \) of an hour for 2 days working on his science project. Kite spent \(\frac { 1 }{ 4 } \)of an hour for 6 days working on his science project. Find the one who spent most f his time working on the science project?

**Solution:**

As given in the question,

Amount of time Rahul spent for an hour = \(\frac { 3 }{ 4 } \)

No of working days = 2

Amount of time Kite spent for an hour = \(\frac { 1 }{ 4 } \)

No of working days = 6

To find the total time they spent on the science project, we apply the law of multiplication here

Therefore, amount of time Rahul spent = \(\frac { 3 }{ 4 } \) * 2

It can be written as \(\frac { 3 }{ 4 } \) + \(\frac { 3 }{ 4 } \) = \(\frac { 6 }{ 4 } \) hours

Hence, Rahul takes \(\frac { 6 }{ 4 } \) hours to complete the science project

The amount of time Kite spent on his project = \(\frac { 1 }{ 4 } \) * 6

It can be written as \(\frac { 1 }{ 4 } \) + \(\frac { 1 }{ 4 } \) +\(\frac { 1 }{ 4 } \) +\(\frac { 1 }{ 4 } \) +\(\frac { 1 }{ 4 } \) +\(\frac { 1 }{ 4 } \) = \(\frac { 6 }{ 4 } \)

Hence, Kite takes \(\frac { 6 }{ 4 } \) hours to complete the science project

From, the above simplification, we came to know that both of them completes the project in some time.

Therefore, they both complete the science project in \(\frac { 6 }{ 4 } \) hours

**Problem 3:**

Baine worked 3\(\frac { 1 }{ 5 } \) hrs before work and 2\(\frac { 2 }{ 3 } \) hrs after lunch. How many hours did she work altogether? How many hours did she leave in her 8 days of work?

**Solution:**

As given in the question,

Baine worked before work = 3\(\frac { 1 }{ 5 } \) hrs

Baine worked after lunch = 2\(\frac { 2 }{ 3 } \)

Therefore, the total amount of time he worked = 3\(\frac { 1 }{ 5 } \) hrs + 2\(\frac { 2 }{ 3 } \)

We have to find the common denominator for 3 and 5

To find the no of hours she worked altogether, we have to add both the fraction values

3\(\frac { 1 }{ 5 } \) hrs + 2\(\frac { 2 }{ 3 } \)

The result is 5\(\frac { 13 }{ 15 } \) hours

To find the number of hours left in her day, we have to subtract the fraction values

Now, we just can’t drop 5\(\frac { 13 }{ 15 } \) as it is \(\frac { 0 }{ 15 } \)

The way we can write 8 is 7 plus 1 and \(\frac { 0 }{ 15 } \)

Thus, \(\frac { 0 }{ 15 } \) is 1 times 15 is 15, plus 0 is just 15

So, I have 7 and \(\frac { 15 }{ 15 } \) minus 5 and \(\frac { 13 }{ 15 } \)

Now, I am ready to subtract 15 minus 13 is 2, and 7 minus 5 is 2

She has two hours and \(\frac { 2 }{ 15 } \)

That is what she has left

Hence, she has worked so far is \(\frac { 2 }{ 15 } \)

Therefore, 5\(\frac { 13 }{ 15 } \) hours they work altogether

\(\frac { 2 }{ 15 } \) hours she left in her 8 days of work