# Improper Fractions Lesson

An improper fraction is a fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). In other words, it’s a fraction where the part is equal to or larger than the whole. In simpler terms, the top number is greater than or equal to the bottom number.

For example:

- is an
**8/5 improper fraction**because the numerator, 8, is greater than the denominator, 5.

- is an
**3/3 improper fraction**because the numerator, 3, is equal to the denominator, 3.

**Improper fractions** can always be converted to mixed numbers, which consist of a whole number part and a proper fraction part. For example , can be written as as a mixed number.

Every fraction has two parts the numerator and the denominator, and there are two main types of fractions: proper and improper fractions. Here are some examples of each.

**Improper fractions** are easier to add and subtract than mixed numbers, however, mixed numbers can be easier to interpret. To convert an improper fraction to a mixed number we follow three easy steps:

1) Divide the numerator by the denominator.

2) This gives you the value of the quotient (whole number part) and the remainder (numerator of the proper fraction part).

3) Now we arrange those values into the mixed number, in the following format:

Let’s practice converting the improper fraction 11/3, to a mixed number. The first step is to divide 11 by 3, we get 3 as the quotient and 2 as the remainder. Therefore, we will place 2 in the numerator of the proper fraction part, with 3 as the denominator. Hence, the mixed number is 3 2/3.

Similarly we can convert mixed numbers into improper fractions by doing the opposite and multiplying. In order to convert a mixed number to an improper fraction, we would follow the steps below:

1) Multiply the denominator by the whole number part.

2) Add the value from step 1 to the numerator.

3) Write the value from step 2 as the numerator of the improper fraction, and the denominator will remain the same.

Let’s practice converting the mixed number 4 2/5 to an improper fraction. The first step is to multiply the denominator by the whole number, 5 x 4 = 20, then add that value to the numerator, 20 + 2 = 22. Therefore the improper fraction is 22/5.

**Examples**

**Example 1:** Which of the following is not an improper fraction?

**Solution:** Since an improper fraction is defined by the numerator being greater than or equal to the denominator, we notice that the only fraction that does not meet this criteria is 5/6, because the numerator is 5, which is less than the denominator which is 6. Therefore, this is not an improper fraction, while all of the rest are because their numerator is greater than or equal to the denominator.

**The answer is 5/6.**

**Example 2: **Convert the improper fraction 9/2 to a mixed number.

**Solution:** We will start by dividing 9 by 2, which is 4 with a remainder of 1. This means that, 4 is the quotient, 1 is the remainder, and 2 is the divisor. Therefore the mixed number is 4 1/2.

**The answer is 4 1/2.**

**Example 3: **Convert the mixed number 3 7/8 to an improper fraction.

**Solution:** The first step is to multiply the denominator by the whole number, 8 x 3 = 24. Next, we will add that value to the numerator, 24 + 7 = 31. Lastly, we will write the value from the previous step over the given denominator to obtain the answer, 31/8.

The answer is 31/8.

**FAQs on Improper Fractions**

**1) What is an improper fraction?**

An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).

**2) How do you recognize an improper fraction?**

An improper fraction has a numerator that is greater than or equal to the denominator. For example, 7/4 or 5/5.

**3) Can improper fractions be simplified?**

Yes, improper fractions can be simplified just like proper fractions. Divide both the numerator and denominator by their greatest common factor to simplify.

For example, the improper fraction 12/8, has a greatest common factor of 4, therefore we would divide the numerator and denominator both by 4, and get a simplified improper fraction 3/2.

**4) How do you convert an improper fraction to a mixed number?**

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number part, and the remainder becomes the numerator of the proper fraction part.

**5) Are mixed numbers equivalent to improper fractions?**

Yes,every improper fraction can be expressed as a mixed number, and vice versa. They represent the same quantity.

**6) Can improper fractions represent values greater than 1?**

Yes, improper fractions can represent values greater than 1. For example, 9/5 is an improper fraction representing 1 whole and ⅘.

**7) In real-world situations, when might we encounter improper fractions?**

Improper fractions can be encountered in various real-world situations, such as when dealing with measurements, ratios, or division of quantities.

**8) Can you add or subtract improper fractions?**

Yes, you can add or subtract improper fractions by finding a common denominator and performing the operation as you would with any other fractions.

**9) How do you convert a decimal to an improper fraction?**

To convert a decimal to an improper fraction, write the decimal as a fraction with the decimal part as the numerator and an appropriate power of 10 as the denominator.