Improper Fractions

Improper fractions, with the name, signifies that the fractions are not done in a proper manner for any number, object or any element. In terms of Maths, an improper fraction has numerator bigger than the denominator whereas in a proper fraction the denominator is greater than the numerator. Fractions have two parts, numerator and denominator. For example, in β…“ fraction, 1 is the numerator and 3 is the denominator.

Fractions usually show, if any number or object is parted into n number of parts, which in combination gives a value of 1. Suppose, an apple is cut into two equal parts, then the half of the apple is represented as Β½ of apple, which means, its the fraction of apple. The table of contents given below shows the topics related to improper fractions which will be covered here in this article.

Table of contents:

Improper Fractions Definition

In arithmetic, there are three types of fractions. Proper fraction, improper fraction, and mixed fraction. In this article, you will find all the topics related to improper fractions. Also, we perform various arithmetic operations on these fractions, such as addition, division, multiplication, etc.

An improper fraction is defined as a fraction, whose numerator is greater than the denominator and therefore, the improper fraction is always greater than one.

Examples:

\(\frac{17}{5}\) \(\frac{9}{4}\) \(\frac{16}{3}\) \(\frac{5}{2}\)

Simplifying Improper Fractions

We have understood what an improper fraction is. Now, let us discuss here how to simplify such fractions here.

Step 1: Determine if the given fraction is improper or not.

Step 2: Now interpret the denominator and check for how many parts it is dividing the numerator.

Step 3: Check the common factors of numerator and denominator

Step 4: Cancel the like terms both from numerator and denominator.

The resulted fraction is the simplified fraction. Let us understand these steps with the help of examples.

Example

Q.1: Simplify the fraction 24/10.

Solution: Since we know 24>10, thus 24/10 is an improper fraction.

Let us factorise the numerator and denominator.

24 = 2 x 2 x 2 x 3

10 = 2 x 5

Since, we can see 2 is the common factor for 24 and 10, so after cancelling 2 from numerator and denominator we get;

(2 x 2 x 3)/5 = 12/5

Equivalent Mixed Fractions

To convert an improper fraction to a mixed fraction divide the denominator by the numerator. The quotient becomes the whole number, the remainder will be the numerator, and the divisor becomes the denominator.

Let us consider an example. Convert \(\frac{17}{4}\) to a mixed fraction.

When we divide 17 by 4, the quotient is 4 and the remainder is 1. So the mixed fraction is \(4\frac{1}{4}\).

Although an improper fraction can be converted to a mixed fraction, there are situations where expressing a fraction as an improper fraction minimizes a lot of confusion especially when the fractions are expressed in calculations.

For example, consider \(3 + 6 \frac{2}{3}\).

Is it \(3 + 6 + \frac{2}{3}\) or \(3 + 6 \times \frac{2}{3}\)?

This confusion can be removed by writing it as \(3 + \frac{20}{3}\)

However, an improper fraction cannot be used in everyday life. It makes far more sense to say β€œThe drive takes

Adding Improper Fractions

Addition of improper fractions can have two scenarios. If the denominators of all the fractions are equal, we can add all the numerators and keep the same denominator.

For example, \(\frac{17}{4}\) + \(\frac{9}{4}\) + \(\frac{5}{4}\)

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

17+9+5 = 31

Therefore,

\(\frac{17}{4}\) + \(\frac{9}{4}\) + \(\frac{5}{4}\) = \(\frac{31}{4}\)

If the denominators of fractions are not equal, the process is slightly different and involves calculation of least common multiple of the denominators.

You can learn the calculation of least common multiples here.

Consider the example,

\(\frac{15}{3}+\frac{3}{4}+\frac{5}{2}\)

The least common multiple of 3, 4, and 2 is 24.

Now the fraction we get by adding all these fractions will have 24 as the denominator.

Divide the LCM by each of the denominators and multiply the quotient by the numerators.

The numerator of the new fraction will be the sum of all the numbers obtained in the previous step.

Example, in the first fraction, the denominator is 3. LCM 24 divided by 3 is 8. The numerator is 15. 15 x 8 is 120. Similarly, for the other two fractions, the numbers are 18, and 60.

Therefore, \(\frac{15}{3}+\frac{3}{4}+\frac{5}{2}\)

= \(\frac{120+18+60}{24}\)

= \(\frac{198}{24}\)

= \(8\frac{1}{4}\)

Subtraction of improper fractions can be carried out similarly. If the previous example was a subtraction problem, instead of adding the numbers 120, 18, and 60, we subtract.

So 120 -18 – 60 = 42. The answer is \(\frac{42}{24}\).

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