What Is An Improper Fraction? Definition & Examples

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If you are learning about fractions in mathematics, you may have come across the term “improper fraction”.

An improper fraction is a type of fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).

For example, \frac{5}{3} is an improper fraction because 5 is greater than 3 .

Improper fractions can be a bit confusing at first, but they are an important concept to understand in order to work with fractions effectively.

What Is An Improper Fraction?

An improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. In other words, it is a fraction that represents a value greater than one whole unit .

For example, \frac{3}{2} and \frac{7}{4} are improper fractions because the numerator is greater than the denominator.

Examples

Improper fractions can be contrasted with proper fractions, which have a numerator that is less than the denominator. For example, \frac{2}{3} and \frac{3}{4} are proper fractions.

Another type of fraction is a mixed number, which consists of a whole number and a proper fraction. For example, 2\frac{1}{2} is a mixed number because it represents two whole units and one half of another unit.

Improper fractions can also be converted into mixed numbers, and vice versa.

In summary, an improper fraction is a type of fraction where the numerator is greater than or equal to the denominator. Improper fractions can be contrasted with proper fractions and mixed numbers, and can be converted into mixed numbers and vice versa.

Converting Improper Fractions To Mixed Numbers

When you have an improper fraction, it means that the numerator is greater than or equal to the denominator.

A mixed number is a combination of a whole number and a proper fraction.

Converting an improper fraction to a mixed number can make it easier to understand and work with in certain situations.

Step-by-Step Guide

To convert an improper fraction to a mixed number, follow these steps:

  1. Divide the numerator by the denominator.
  2. Write down the whole number part of the result.
  3. Write down the remainder as the numerator of the fraction.
  4. Write down the original denominator as the denominator of the fraction.

Here’s an example: 

\frac{11}{3} = 11 \div 3 = 3 \ r2 = 3 \ \frac{2}{3}
  1. 11 \div 3 = 3
  2. The whole number part is 3 .
  3. Find the remainder 11 - (3 \times 3) = 2
  4. The original denominator is 3 .

So, \frac{11}{3} can be written as 3 \ \frac{2}{3} .

Examples

Let’s look at a few more examples:

Convert \frac{9}{4} into a mixed number?

  1. 9 \div 4 = 2
  2. The whole number part is 2 .
  3. Find the reminader 9 - (2 \times 4) = 1
  4. The original denominator is 4. 
\frac{9}{4} = 9 \div 4 = 2 \ r1 = 2 \ \frac{1}{4}

So, \frac{9}{4} can be written as 2 \ \frac{1}{4} .

What about \frac{16}{5} ?

  1. 16 \div 5 = 3
  2. The whole number part is 3.
  3. Find the remainder 16 - (3 \times 5) = 1
  4. The original denominator is 5.

So, \frac{16}{5} can be written as 3 \ \frac{1}{5} . 

\frac{16}{5} = 16 \div 5 = 3 \ r1 = 3 \frac{1}{5}

Converting an improper fraction to a mixed number is a simple process that can make it easier to work with fractions in certain situations. By following the step-by-step guide and practising with examples, you can become confident in your ability to make this conversion.

Converting Mixed Numbers to Improper Fractions

If you’re working with fractions, you’ll likely come across mixed numbers, which are numbers expressed as the sum of a whole number and a proper fraction.

However, improper fractions are often easier to work with mathematically. Fortunately, converting mixed numbers to improper fractions is a straightforward process.

Step-by-Step Guide

To convert a mixed number to an improper fraction, follow these simple steps:

  1. Multiply the whole number by the denominator of the fraction.
  2. Add the result to the numerator of the fraction.
  3. Place the sum over the original denominator.

Here’s an example to illustrate the process:

Convert 3 \frac{1}{4} to an improper fraction.

  1. Multiply the whole number 3 by the denominator of the fraction 4 as follows: 3 \times 4 = 12
  2. Add the result to the numerator of the fraction: 12 + 1 = 13
  3. Place the sum over the original denominator: \frac{13}{4}

So, 3 \frac{1}{4} is equivalent to \frac{13}{4} . 

3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}

More Examples

Let’s look at a few more examples to solidify the process of converting mixed numbers to improper fractions:

Convert 2 \frac{3}{5} to an improper fraction.

  1. Multiply the whole number by the denominator of the fraction: 2 \times 5 = 10
  2. Add the result to the numerator of the fraction: 10 + 3 = 13
  3. Place the sum over the original denominator: \frac{13}{5}

Therefore, 2 \frac{3}{5} is equivalent to \frac{13}{5} . 

2 \frac{3}{5} = \frac{(2 \times 5) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}

Convert 4 \frac{2}{3} to an improper fraction.

  1. Multiply the whole number by the denominator of the fraction: 4 \times 3 = 12
  2. Add the result to the numerator of the fraction: 12 + 2 = 14
  3. Place the sum over the original denominator: \frac{14}{3}

Therefore, 4 \frac{2}{3} is equivalent to \frac{14}{3} . 

4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}

Converting mixed numbers to improper fractions is a simple process that can be done quickly and easily with a little practice.

Improper Fractions Summary

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. This type of fraction can be expressed as a mixed number, which is a whole number and a proper fraction combined. Improper fractions are commonly used in mathematics and can be found in many real-life situations.

When dealing with improper fractions, it’s important to understand how to convert them into mixed numbers. To do this, you need to divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the proper fraction.

For example, \frac{11}{4} can be converted to 2\frac{3}{4} .

Improper fractions can also be added, subtracted, multiplied, and divided just like any other fractions. When adding or subtracting improper fractions, you need to find a common denominator. This can be done by multiplying the denominators together. Once you have a common denominator, you can add or subtract the numerators.

In summary, improper fractions are fractions where the numerator is greater than or equal to the denominator. They can be converted to mixed numbers, added, subtracted, multiplied, and divided, just like any other fractions.