Improper fractions, with the name, signifying that the fractions are not done in a proper manner for any number, object or element. In Maths, a fraction is a part of a whole. Fractions have two parts, numerator and denominator. If ⅓ is a fraction, then 1 is the numerator, and 3 is the denominator. An improper fraction has a numerator greater than the denominator. For example, 3/2 is an improper fraction, but 2/3 is a proper fraction, whose denominator is greater than the numerator. Show
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. Table of contents:
What are Improper Fractions?An improper fraction is defined as a fraction whose numerator is greater than the denominator. Suppose, x/y is an improper fraction, such that x > y. It is therefore, the improper fraction is always greater than one. Examples of Improper Fractions are:
How to Simplify Improper Fractions?We have understood what an improper fraction is. Now, let us discuss here how to simplify such fractions here.
The resulted fraction is the simplified fraction. Let us understand these steps with the help of examples. Example: 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 the numerator and denominator, we get; (2 x 2 x 3)/5 = 12/5 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 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 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 2/3. Is it 3 + 6 + 2/3 or 3 + 6 × 2/3 ? This confusion can be removed by writing it as 3 + 20/3. Mixed to Improper FractionLet us say 31/4 is a mixed fraction to be converted into an improper fraction. Another Method: Addition of Improper FractionsThe 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, (17/4) + (9/4) + (5/4) Since the denominator of all three fractions is equal, we add all the numerators by keeping the common denominator as 4. Hence, we get the following: (17/4) + (9/4) + (5/4) = (17 + 9 + 5) / 4 (17/4) + (9/4) + (5/4) = 31/4. The other case is that denominators of fractions are not equal. Here, the process is slightly different and involves the calculation of the least common multiple of the denominators. You can learn the calculation of the least common multiples here. Consider the example, (15/3) + (3/4) + (5/2) Here, the denominators of the fractions are different. (i.e., 3, 4, 2), and take the LCM of 2, 3, and 4. Hence, to add the given fractions, follow the below steps:
Therefore, (15/3) + (3/4) + (5/2) = (60/12) + (9/12) + (30/12) (15/3) + (3/4) + (5/2) = (60 + 9 + 30) / 12 (15/3) + (3/4) + (5/2) = 99/12. Now, the sum of fractions can be simplified as: (15/3) + (3/4) + (5/2) = 33/4 convert into mixed fractions, if required. Hence, the mixed fraction is: (15/3) + (3/4) + (5/2) = 8 1/4. Subtraction of Improper FractionsIn a similar manner, as we added the improper fractions, we can also subtract them.
Let us see an example: Subtract 5/2 – 7/3. LCM (2,3) = 6 Therefore, (5/2 x 3/3) – (7/3 x 2/2) = 15/6 – 14/6 = (15-14)/6 = 1/6. Related ArticlesSolved Examples of Improper FractionsExample 1: Multiply 3 by 9/7. Solution: Given: 3 x 9/7 3 x 9/7 = 27/7 Example 2: Convert the improper fraction 5/4 into a mixed fraction. Solution: Given, 5/4 To convert an improper fraction into a mixed fraction, first, divide the number 5 by 4. If we divide 5 by 4, we get the quotient as 1 and the remainder as 1. Hence, keep the quotient as the whole number part and the remainder as the fraction’s numerator part and the denominator as 4. Hence, 5/4 written in the mixed fraction is 1 1/4. i.e., 5/4 = 1 1/4. Example 3: Convert the mixed number 4 2/3 into an improper fraction. Solution: Given: Mixed fraction = 4 2/3 To convert the mixed fraction into an improper fraction, follow the below steps: Step 1: Multiply 3 by 4, and we get 12. Step 2: Now, add 12 and 2, we get 14 I,e 3(4) + 2 =14 Now, put the number 14 in the fraction’s numerator and keep the number 3 as the denominator. So, 14/3 is the required fraction. Example 4: Write 3 1/4 as an improper fraction. Solution: Given that 3 1/4 is a mixed number. Now, multiply denominator 4 by the whole number 3. 4 × 3 = 12 Now, add 12 to the numerator. 12 + 1 = 13 Hence, 13 is the new numerator of the improper fraction, whereas the denominator remains the same. So, 3 1/4 = 13/4 Video LessonPractice QuestionsConvert the given improper fractions into mixed numbers.
Convert into improper fractions.
Learning about fractions can be so much fun. Download BYJU’S – The Learning App and discover innovative ways to learn science and math. Frequently Asked Questions on Improper FractionA fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc. Divide the numerator by denominator. Write the whole number separately and put the remainder in the numerator. If 11/4 is a fraction, then; Multiply 3 by 1 and add 2 to get the denominator of the required fraction and keep the denominator common. A proper fraction has a numerator smaller than the denominator, but an improper fraction has a denominator smaller than the numerator. 3 ⅕ = (5 x 3 + 1)/5 = 16/5 How do you turn a mixed fraction into a improper fraction?To change an improper fraction to a mixed number, follow these steps: Divide the numerator by the denominator. Write down the whole number part of the quotient. Take the remainder and write it over the original denominator.
How do you convert mixed fractions?A mixed number is a whole number plus a fractional part.. Multiply the whole number by the denominator.. Add the answer from Step 1 to the numerator.. Write answer from Step 2 over the denominator.. |