What Is an Improper Fraction With Formula and Solved Examples
A fraction is a numerical quantity that represents a part of a proportion or an amount of something or a collection. A fraction comprises a numerator and a denominator. For example, if one watermelon is cut into half, then the fraction for each of the halves will be represented as ½; where 1 is the numerator and 2 is the denominator. Improper fraction is more useful than mixed fractions when doing calculations. In this article, we will be discussing what are improper fractions and how they can be solved.
Improper Fraction
As defined above, a fraction with the numerator value greater than the denominator is known as an improper fraction. For instance, a fraction of 10/3 has 10 in the numerator which is greater than the denominator 3. Similarly, other examples of improper fractions are 100/3, 25/4, and 99/2. The main difference between proper and improper fraction is that the value of the numerator is higher than the denominator in the latter.
The two solutions of improper fractions provided below can further explain the steps involved.
Simplification of Improper Fractions
Different fractions have their own benefits and understanding. A mixed fraction is definitely easier to understand when referring to day to day items, quantities, or other comparisons. But in terms of doing mathematical calculations, a mixed fraction can be more confusing than any other types of fractions. Moreover, in order to attempt mathematical calculations, the first step involves simplifying these mixed fractions to a proper or improper fraction. An improper fraction is more useful than mixed fractions when doing calculations such as addition and subtraction.
Examples
1.Convert the Improper Fraction 7/4 Into a Mixed Fraction.
Answer
Following are the steps mentioned below to convert an improper fraction into a mixed fraction:
Step 1: Use the division method to solve the improper number to get a mixed fraction
Step 2: When we divide 7 by 4, we get 1 whole part and 3 as a remainder.
Step 3: The remainder, 3, becomes the numerator along with 4 as the denominator. ¾ is considered as a proper fraction when we look at the mixed fraction number obtained.
Step 4: The last step is to combine the whole number with the proper fraction, which in this case
is 1 and 3/4. These two-part together make the mixed fraction 1¾.
From here you can conclude, that the mixed fraction for the improper fraction 7/4 is 1¾.
2. Convert the Mixed Fraction 5⅗ Into an Improper Fraction.
Answer
Following are the steps mentioned below to convert a mixed fraction into an improper fraction:
Step 1: Unlike the above-mentioned example, the conversion of a mixed fraction to an improper fraction involves multiplication.
Step 2: The first multiplication has to take place between the denominator and the whole number. In the example given above, 5 is the whole number, as well as 5, is the denominator.
Therefore, the product of the two becomes 25.
Step 3: This product will then be added with the numerator, i.e, 25 +3 = 28.
Step 4: The product when added with the numerator value of the mixed fraction, becomes the new numerator for the improper fraction. That being said, it means, 28 is the numerator for the improper fraction.
Step 5: In the case of the denominator, the value remains the same for an improper fraction as given by the mixed fraction. Remember, not to change the value of the denominator when converting from mixed to an improper fraction. Therefore, in this case, the denominator remains 5.
Step 6: The last step is to combine the numerator and denominator together to get an improper fraction. 28/5 becomes the new improper fraction for the mixed fraction of 5⅗.
Note: The denominator value is lesser than the numerator and therefore it can easily be distinguished as an improper fraction.
FAQs on Improper Fraction Meaning and How to Solve
1. What is an improper fraction?
An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. This means the value of the fraction is equal to or greater than 1.
- Example: 7/4 is an improper fraction because 7 > 4.
- Example: 5/5 is also improper because the numerator equals the denominator.
- Improper fractions can always be written as mixed numbers.
2. 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. Follow these steps:
- Step 1: Divide the numerator by the denominator.
- Step 2: The quotient becomes the whole number.
- Step 3: The remainder becomes the new numerator over the same denominator.
- 9 ÷ 4 = 2 remainder 1
- Mixed number = 2 1/4
3. How do you convert a mixed number into an improper fraction?
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Steps:
- Step 1: Multiply the whole number by the denominator.
- Step 2: Add the numerator to the result.
- Step 3: Write the sum over the original denominator.
- (3 × 5) + 2 = 17
- Improper fraction = 17/5
4. What is the difference between a proper fraction and an improper fraction?
The difference is that a proper fraction has a numerator smaller than the denominator, while an improper fraction has a numerator greater than or equal to the denominator.
- Proper fraction example: 3/8
- Improper fraction example: 9/4
- Proper fractions are less than 1, while improper fractions are greater than or equal to 1.
5. Can an improper fraction be equal to 1?
Yes, an improper fraction equals 1 when the numerator and denominator are the same. For example:
- 6/6 = 1
- 10/10 = 1
6. How do you simplify an improper fraction?
To simplify an improper fraction, divide both the numerator and denominator by their greatest common divisor (GCD). Steps:
- Find the GCD of the numerator and denominator.
- Divide both by the GCD.
- GCD of 12 and 8 is 4.
- 12 ÷ 4 = 3, 8 ÷ 4 = 2
- Simplified fraction = 3/2
7. How do you add improper fractions?
To add improper fractions, make the denominators the same and add the numerators. Steps:
- Find a common denominator.
- Add the numerators.
- Simplify if needed.
- Same denominator, so add numerators: 5 + 4 = 9
- Result = 9/3 = 3
8. How do you multiply improper fractions?
To multiply improper fractions, multiply the numerators together and the denominators together. Formula:
- (a/b) × (c/d) = (ac)/(bd)
- Numerator: 7 × 2 = 14
- Denominator: 4 × 3 = 12
- Result = 14/12 = 7/6 (simplified)
9. How do you divide improper fractions?
To divide improper fractions, multiply by the reciprocal of the second fraction. Steps:
- Keep the first fraction the same.
- Flip the second fraction (reciprocal).
- Multiply the fractions.
- Reciprocal of 3/2 is 2/3.
- 9/4 × 2/3 = 18/12
- Simplified result = 3/2
10. What is an example of an improper fraction in real life?
An improper fraction appears in real life when a quantity is more than one whole, such as 9/4 pizzas. This means:
- 9/4 = 2 1/4 pizzas
- You have two whole pizzas and one quarter of another.
