Improper Fractions: Definitions, Conversions, Addition, Subtraction & Examples

A fraction is a numerical representation of a whole in parts. This whole can be a single object or a group of objects. A fraction has two parts a numerator and denominator which contribute as a whole. There are types of fractions; proper, improper and mixed fractions. In an improper fraction the numerator is equal or greater than the denominator like 5/5 or 12/10. The value of a numerator is always one or larger than one.

Read More: Linear Algebra

Key terms: Improper Fractions, Mixed Fractions, Denominator, Numerator, LCM

---

Improper Fractions and Mixed Fractions

[Click Here for Sample Questions]

Improper fraction can be defined as a fraction whose numerator value is greater than its denominator or equal to the denominator such as 8/10 or 9/9. A mixed fraction or mixed number has a whole number is a combination of a whole number and a fraction such as 5 1/7

Read More: LCM of Two Numbers

---

Simplification Of Improper Fraction

[Click Here for Sample Questions]

Improper fractions are easier to simplify compared to mixed fractions. There are 4 simple steps to follow:

• Step 1 – Identify the type of fraction, whether it is improper or not.
• Step 2 – Check the denominator and see how many parts it divides the numerator.
• Step 3 – Find the common factors in both numerator and denominator and multiply them to find GCF.
• Step 4 – Divide both the numerator and denominator by the GC. The final fraction is the simplified fraction.

Example: Simplify the improper fraction 24/9.

Solution: 24/9 is an improper fraction because numerator is greater than the denominator (24>9)

Let us factorize the numerator and denominator.

24=1x2x2x2x3

9=1x3x3

1 and 3 are the common factors for 24 and 9.

Now, multiply the common factors for GCF:

1x3=3

By dividing the numerator and denominator by GCF we get,

24/3=8 and 9/3=3

The simplified fraction is 8/3

(2x2x3)/5=12/5

Hence, 12/5 is the simplified fraction.

---

Improper Fractions To Mixed Fractions

[Click Here for Sample Questions]

To convert improper fraction into mixed fractions the numerator is divided by the denominator and the remainder and quotient is found out. The quotient obtained is the whole number of the mixed fraction and the remainder becomes the numerator. The denominator is the same as in the given improper fraction.

---

Mixed Fraction To Improper Fractions

[Click Here for Sample Questions]

Mixed fractions are a bit difficult to solve with other fractions. It is easier to solve when it is converted into an improper fraction. To convert a mixed fraction into an improper fraction there are 2 methods.

Method 1: By multiplication

• Step 1– Multiply the denominator with the whole number in the given mixed fraction.
• Step 2– Add the numerator with the product calculated from step 1. This added value becomes the numerator for improper fraction.
• Step 3– The denominator remains the same as of mixed fractions.

Method 2: By addition

• Step 1– Write the mixed fraction as sum of the whole number and the fraction part like 2+1/3
• Step 2– Rationalize the denominators: 6/3+1/3 (common denominators)
• Step 3– Addition of the fractions=7/3

---

Addition Of Improper Fractions

[Click Here for Sample Questions]

Addition of improper fractions is very simple. It is done in two ways depending upon the denominator whether it is equal or not. If the denominators are equal for all the fractions then all the numerators are added and the denominator remains the same.

For example, 15/2+3/2+5/2

These are the three improper fractions. All the fractions have the same denominator.

Now, adding all the numerators.

15+3+5=23

Therefore, the resultant fraction is 23/2

Now, if the denominators of all the fractions are different then they are added through LCM (Least Common Multiple) method.

For example, 15/3+3/4+5/2

Step 1– Take the LCM of all the denominators 3, 4, 2 which is 24. Now, 24 will be the common denominator for all the fractions.

Step 2– Divide the LCM with each denominator and multiply the quotient with the numerators.

For, 15/3 LCM 24 is divided by 3 and we get 8. Now, the numerator 15 is multiplied with 8 which is 120

Similarly for 3/4, 24/4=6 and 6x3=18

For 5/2, 24/2=12 and 12x5=60

Step 3– The numerators for the new fraction is the sum of all the numbers obtained in step 2.

Read More: Lines of Symmetry in a Parallelogram

---

Subtraction of Improper Fractions

[Click Here for Sample Questions]

Steps for subtracting improper fractions are the same as addition. If denominators are equal then the numerators are subtracted and the denominator remains the same and if the denominators are different then the LCM is considered.

For example,

5/2 – 7/3.

LCM of 2 and 3 is 6

Now, (5/2x3/3) – (7/3x2/2)

= 15/6 – 14/6

= (15-14)/6

= 1/6

---

Things to Remember

[Click Here for Sample Questions]

• When an improper fraction is simplified the resultant fraction is always an improper fraction.
• Numerically, a mixed fraction is always greater than 1 and any mixed fraction can be written as an improper fraction.
• For addition and subtraction of fractions if the denominators are different LCM is taken.
• In a proper fraction the denominator shows the number of parts and the numerator shows the number of parts which have been considered

Read More: Lines of Symmetry in a Rectangle

---