How to Convert Between Improper Fractions and Mixed Numbers
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 What Is an Improper Fraction? Definition & Examples
1. What is an improper fraction? Explain with examples.
An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). This indicates that the value of the fraction is either 1 or more than 1. For instance, 5/4, 11/7, and 8/8 are all examples of improper fractions.
2. What are the main types of fractions students learn in the CBSE syllabus?
In mathematics, as per the CBSE curriculum, students primarily learn about three main types of fractions:
- Proper Fractions: The numerator is smaller than the denominator (e.g., 3/5, 7/10). The value is always less than one whole.
- Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 9/5, 6/6). The value is always one or greater than one.
- Mixed Fractions: These are a combination of a whole number and a proper fraction (e.g., 1 ¾, 3 ½). They are another way of representing an improper fraction.
3. What is the key difference between proper, improper, and mixed fractions?
The main difference between these fractions lies in their value relative to the number one. A proper fraction always represents a value less than 1. An improper fraction represents a value of 1 or more. A mixed fraction is simply a more intuitive way to write an improper fraction that is greater than 1, showing the whole units and the remaining fractional part separately (e.g., the improper fraction 7/3 is written as the mixed fraction 2 ⅓).
4. How do you convert an improper fraction into a mixed fraction?
To convert an improper fraction to a mixed fraction, follow these steps:
- Step 1: Divide the numerator by the denominator.
- Step 2: The whole number part of your answer (the quotient) becomes the whole number of the mixed fraction.
- Step 3: The remainder from the division becomes the new numerator.
- Step 4: The denominator does not change.
For example, to convert 11/4, divide 11 by 4. The quotient is 2, and the remainder is 3. Therefore, 11/4 is equal to the mixed fraction 2 ¾.
5. Why is the value of an improper fraction always 1 or more?
The value of an improper fraction is always 1 or more because it represents at least one complete whole. A fraction like 4/4 means you have all four parts of a whole that was divided into four, which equals exactly 1. A fraction like 5/4 means you have more parts than are needed to make one whole (you have one full whole and one extra part). This is because the numerator (the number of parts you have) is greater than or equal to the denominator (the number of parts in one whole).
6. How can you explain an improper fraction like 5/3 using a real-world example?
Imagine you are sharing chocolates, and each chocolate bar has 3 blocks. The fraction 5/3 means you have a total of 5 blocks. Since one whole chocolate bar has only 3 blocks, you would have one complete bar (which is 3/3) plus 2 extra blocks from a second bar (which is 2/3). So, 5/3 represents having more than one whole chocolate bar; specifically, it's the same as having 1 and ⅔ chocolate bars.
7. Can an improper fraction have the same numerator and denominator, like 7/7?
Yes, it can. The definition of an improper fraction states that the numerator must be greater than or equal to the denominator. A fraction like 7/7 perfectly fits this rule because 7 is equal to 7. Any fraction where the numerator and denominator are the same is an improper fraction that is always equal to 1, representing one complete whole.
