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What Do We Understand By The Term Improper Fraction?

If the value of the numerator equals or exceeds the value of the denominator, then it is an improper fraction. It is usually written in mixed number form in a simplified manner since mixed fractions are easier to analyze than improper fractions. A fraction has two parts, a numerator, and a denominator. In mathematics, proper fractions and improper fractions can be distinguished by these two factors. 7/4 and 9/6 are improper fractions, for instance.

An Improper fraction is a fraction that equals or exceeds 1, while mixed fractions are fractions that are based on both natural numbers and proper fractions. A mixed fraction is the simplified form of an improper fraction. By following some basic steps, you will be able to convert any improper fraction to a mixed number or mix fraction to an improper fraction.

How can you Simplify an Improper Fraction?

  • Analyze whether the given fraction is improper or not
  • Take a look at the denominator and count how many parts are being divided by the numerator.
  • The common factor between numerator and denominator should be checked
  • In both the numerator and denominator, remove the like terms.

Conversion of Improper Fractions into Mixed Fractions:

When an “improper fraction” is converted into a mixed fraction, divide the numerator by the denominator. The quotient will become the whole number, the remainder the numerator, and the divisor will become the denominator.

Let us consider an example. Convert 19/4 to a mixed fraction.

When we divide 19 by 4, the quotient is 4 and the remainder is 3. So the mixed fraction is 4 ¾.

An improper fraction can be converted into a mixed fraction, but sometimes expressing fractions according to their improper form minimizes a lot of confusion, especially in calculations where fractions might be expressed.

For example, consider 3 + 4 ¾

Is it 3 + 4 + ¾ or 3 + 4 × ¾

This confusion can be removed by writing it as 3 + 19/4

Addition of Improper Fractions:

When adding improper fractions, there are two scenarios. If all fractions have the same denominator, then we can add all the numerators while keeping the same denominator.

For example, 19/4 + 5/4 + ¾

Since the denominator of all three fractions is equal, we just add all the numerators:

19+5+3= 27

Therefore, 19/4 + 5/4 + ¾= 27/4

Steps Involved:

  • Find the least common multiple of all the denominators given.
  • Add all of these fractions together and find the fraction that has the LCM (found in step 1) as the denominator.
  • Using the LCM, divide each denominator by the quotient, then multiply the quotient by the numerator.
  • In the next step, you will sum all the numbers you obtained in the previous step to make the new fraction.

Subtraction of Improper Fractions:

  • The first step is to check whether the denominators are the same.
  •  The second step is to rationalize the denominators.
  • The last step is to subtract the given fractions and simplify if necessary.

For example: Subtract 7/2 &9/4

LCM (2,4) = 4


(7/2 x 2/2) – (9/4 × 1/1)

= 14/4 – 9/4

= (14-9) / 4

= 5/4

Practice Problems:

  1. Convert 5 2/3 into an improper fraction.

Ans: Given, 5 2/3

Multiply 3 by 5 and 2

3 x 5 + 2 = 17

So, 17/3 is the required fraction.

  • Convert 9/8 into a mixed fraction.

Ans: Given, 9/8

9/8 = 8/8 + 1/8

= 1 + 1/8

= 1   1/8

Improper fractions are very easy to understand if learned from the best of the teachers and guides. You can learn the concept of fraction number in the same way with the help of Cuemath, your best online learning platform for mathematics.

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