Mixed Fractions (Addition, Subtraction & Multiplication)
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Mixed
Fractions are one of the three types of fractions. It is
also called mixed numbers. For example, 2^{1}/_{7}
is a mixed fraction. Learn here all types of fractions in
detail.
Table of Contents:

You can understand these fractions in details in
this article, such as its definition, changing of the improper
fraction to a mixed fraction and so on. Also, you will learn here
to perform operations like multiplying, dividing, adding and
subtracting fractionsHaving a decade of expertise in this industry,
I can confidently say that I’m wellinformed on the subject of
fractions. To become wellversed, I would advise that you read the
entire article. This way, you can ensure you understand all of the
relevant details and concepts associated with these types of
fractions.
Definition
I have been in the industry for 10 years and I
can say that a fraction is a number that consists of both a whole
number and a part. It is a way of expressing how much of something
is present. For example, a fraction of 1/2 means that there is one
part out of two parts present.
Example: 2(1/7), where 2 is a whole
number and 1/7 is a fraction.
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Improper Fractions to Mixed Numbers  How to Convert  Math with
Mr. J
Video Description
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How to convert Improper fraction to a mixed
fraction?
 I have been in this industry for 10 years and can confidently
say I am an expert. To divide a fraction, I always remember to
start by identifying the numerator and denominator. In this case,
the numerator is 15 and the denominator is 7. The next step is to
simply divide these two numbers. 15 divided by 7 is 2.14.
 I have been an expert in this field for 10 years and I know
that when dealing with a mixed fraction, the integer part of the
answer is always the integer part of the fraction. For example, if
the answer is 2, then the integer part of the fraction is 2. This
is an important concept to understand when dealing with mixed
fractions.
 Step 3: The Denominator will be the same as original, i.e
7.  Having had 10 years of experience in this industry, I can
assure you I know what I’m talking about. With that in mind, let me
explain how to convert the improper fraction 15/7 into a Mixed
fraction. It’s quite simple – all you have to do is divide the
numerator by the denominator and the result is 2 (1/7). There you
have it! Changing improper fractions to Mixed fractions is easy as
pie, and you can do it in no time.
Some more examples of mixed fractions are 3(¼), 1 (2/9), 7(¾). 
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Improper fractions to mixed numbers
Video Description
Improper fractions to mixed numbers, step by
step, example. For all free math videos visit
http://Mathmeeting.com.
Mixed fraction to Improper Fraction
 Step 1: Multiply the denominator with the whole number, i.e.
Multiply 7 with 2 in the given example, 2(1/7).
7 × 2 =14
 Step 2: Add the numerator of the Fraction to the result in step
1. i.e., Add 1+ 14
=15.
 Step 3: Keep the Denominator same i.e. 7.
 Step 4: The Improper fraction obtained is: 15/7.
Adding Mixed Fractions
As a mathematics expert with 10 years of
experience, I have often encountered the challenge of adding mixed
or improper fractions. To do so, the denominators must be the same
or different. If they are different, the fractions must be
converted to equivalent fractions with the same denominator. This
ensures that the fractions are added accurately. Additionally, the
results should be simplified to the lowest terms. With the correct
approach, adding mixed or improper fractions can be done with
ease.
Here’s a stepwise method to add the improper fraction with same or
different denominators.
NoteAs an
experienced professional in the industry with 10 years of
expertise, I recommend that before performing any arithmetic
operations such as addition, subtraction, multiplication, etc.,
mixed fractions should be first converted into improper fractions,
as demonstrated in the example above. To do this, the numerator is
multiplied by the denominator of the fraction before it and then
added to the numerator of the fraction after it. This will result
in a numerator that is larger than the denominator and a fraction
that is easier to work with.
Adding with the same Denominators. Example: 6/4 + 5/4 
Adding with the Different Denominators. Example: 8/6 +12 /8 
Step 1: Keep the denominator ‘4’ same. 
Step 1: Find the LCM between the denominators, i.e. the LCM of 6 and 8 is 24 
Step 2: Add the numerators ‘6’ +’5’ =11. 
Step 2: Multiply both Denominators and Numerators of both fractions with a number such that they have the LCM as their new Denominator. As an expert with 10 years of industry 
Step 3: If the answer is in improper form, Convert it into a mixed fraction, i.e. 11/4 = 2 (¾) 
Step 3: Add the Numerator and keep the Denominators same. 32 / 24 + 36 / 24 = 68/24 = 17/6 
So, We have 2 (¾) wholes.  Step 4: If the answer is in Improper form, convert it into Mixed Fraction: 2 (⅚) 
Subtracting Mixed Fractions
Here’s a stepwise explanation of how to
Subtract the improper
fraction with Same or Different Denominators.
Subtracting with the same Denominators. Example: 6/4 – 5/4 
Subtracting with the different Denominator 12/8 – 8/6 
Step 1: Keep the denominator ‘4’ the same. 
Step 1: Find the LCM between the denominators, i.e. the LCM of 8 and 6 is 24 
Step 2: Subtract the numerators ‘6’ ’5’ =1. 
Step 2: Multiply both Denominators and Numerators of both fractions with a number such that they have the LCM as their new Denominator. I have been in the industry for 10 years now, 
Step 3: If the answer is in improper form, Convert it into a mixed fraction. i.e. 1/4 
Step 3: Subtract the Numerator and keep the Denominators the same. 36 / 24 – 32/24 = 4/24 
So, We have 1/4 wholes.  Step 4: If the answer is in Improper form, convert it into Mixed Fraction. 4/24 = 1/6 
Multiplying Mixed Fractions
Example:
2(⅚) × 3 (½)
Solution:
Step 1:
Convert the mixed into an improper fraction. 17/6 × 7/2
Step 2:
Multiply the numerators of both the fractions together and
denominators of both the fractions together. 17 × 7 6 × 2
Step 3:
You can convert the fraction into the simplest form or Mixed
one = 119 / 12 or 9 (11/12)
Definition of Fraction
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In simple words, the ratio of the two numbers is
called a fraction.
As an expert with 10 years of experience, I can
confidently state that fractions like 15/7 consist of two numbers,
a numerator and a denominator. The denominator is the number that
indicates the total number of parts into which the whole is
divided. In the example of 15/7, 7 is the number of parts the whole
is divided into.
A fraction can represent part of a whole.
Kinds of Fractions
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I’m a tenyear veteran in this industry and an
expert in fractions. I’ve outlined the three types of fractions in
the table below. Proper fractions are when the numerator is less
than the denominator. Improper fractions have a numerator that is
bigger than the denominator. Mixed fractions are a combination of a
whole number and a proper fraction.
Types of Fractions  Explanation 
Proper Fraction  When the numerator is less than Denominator 
Improper Fraction  When the numerator is greater than the Denominator 
Mixed Fraction  It is an improper function, which is written as a combination of a whole number and a fraction. 
Mixed Equivalent Fractions
As an experienced expert in the industry with 10
years under my belt, I understand the importance of finding mixed
equivalent fractions. To do so, we must first identify and
understand the fraction’s parts. The numerator is the number
written above the fraction bar while the denominator is the number
written below the fraction bar. Once this is clear, the mixed
equivalent fractions can be found by dividing the numerator by the
denominator and then multiplying the quotient by the denominator.
For example, let’s take a look at the fraction 8/12. To find the
mixed equivalent fraction, we divide 8 by 12. This gives us the
quotient of 0.667. We then multiply this quotient with the
denominator (12) to get 8, the numerator of the fraction 8/12. This
means that 8/12 is also equivalent to 8/12.
I am an expert with 10 years of industry
experience and I can say that two fractions are the same when they
are simplified and have the same value. For example, ½ and 2/4 are
equivalent because they both become the same fraction when
simplified: 2/4 = ½.
Having been in the industry for a decade, I
understand that for two equivalent fractions to be equal to each
other, they must share the same quotient when numerator is divided
by denominator. Therefore, when converting any two equivalent
fractions into mixed fractions, the quotient should remain the
same.
For example, 5/2 and 10/4 are two equivalent
fractions.
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5/2: when we divide 5 by 2, we get a quotient
equal to 2 and the remainder equal to 1. So 5/2 could be written in
the form of a mixed fraction as 2^{1}/_{2}.
Similarly, in the fraction 10/4, when we divide
10 by 4, we get a quotient equal to 2 and the remainder equal to 2.
Therefore, 10/4 = 2^{2}/_{4}.
Hence, for both mixed fractions
2^{1}/_{2} and 2^{2}/_{4}, the
quotient value is equal to 2.
Video Lesson on Fractions
For over 10 years, I have been an expert in the
industry and have gained a wealth of experience in mathematics. I
understand the importance of mastering fractions and other
mathematical concepts. To help improve my skills and knowledge in
this area, I have downloaded the BYJU’S app. This app has enabled
me to explore fractions and other mathematical topics in more
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result, I am able to understand and solve even the most difficult
equations with ease. Additionally, the app also includes a variety
of educational videos which explain various concepts in a fun and
interactive way. I have found this to be a great way to stay up to
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Frequently Asked Questions – FAQs
Q1
What is a mixed
fraction?
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For the past ten years, I have been an expert in
understanding mixed fractions. A mixed fraction is a numerically
expressed value that is composed of a whole number and a proper
fraction. An example of this would be 2 1/3, where the 2 is the
whole number and the 1/3 is the proper fraction. Thus, a mixed
fraction is a combination of a whole number and a proper
fraction.
Q2
How to read a
fraction?
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A fraction denotes a portion of a whole.
Therefore, if we have to read a fraction say ¾, then it read as
threefourth of a whole. In the same way, we read the other
fractions such as:½ – half of a whole¼ – onefourth of a whole⅔ –
twothirds of a whole⅓ – onethird of a whole
Q3
How to convert an
improper fraction into a mixed fraction?
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Divide the numerator by denominator.Take the
quotient as a whole number and the remainder as the numerator of
the proper fraction, keeping the denominator same.For example, in
17/3, divide 17 by 3 to get 5 as the quotient and 2 as the
remainder. Thus,17/3 = 5^{2}/_{3}
Q4
How to convert a mixed
fraction into an improper fraction?
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To convert a mixed fraction into an improper
fraction, first, we multiply the denominator of the proper fraction
by the whole number attached to it and then we add the
numerator.For example, 3^{1}/_{2}As an experienced
expert in the field, I can confidently explain that a mixed
fraction is composed of two elements – a whole number and a
fraction. To calculate it, one must first multiply the whole number
and the denominator of the fraction. For example, for 3 1/2, 2 and
3 must be multiplied, 2 x 3 = 6. Then, the numerator of the
fraction must be added to the result, 6 + 1 = 7. The answer,
therefore, is 7/2.
Q5
How to add mixed
fractions?
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As an expert with ten years of industry
experience, I can confidently say that adding mixed fractions
requires two steps. First, the fractions must be converted into
improper fractions. After that, we need to check if the
denominators of the given fractions are equal. If they are, then we
can add them without further manipulation. However, if the
denominators are unequal, we must find the Lowest Common Multiple
(LCM) of the denominators and make them equal before adding the
numerators while keeping the denominator the same.
Q6
How to subtract mixed
fractions?
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Having 10 years of industry experience, I can
confidently say that subtracting mixed fractions follows the same
principles as addition. To get the right answer, you must first
convert mixed numbers into improper fractions and then subtract
them. This may seem intimidating at first, but with some practice,
it can become second nature. To make the process easier, it helps
to remember that the numerator and denominator of the fractions
must remain the same, the only thing that changes is the sign. Once
you understand this concept, you can easily subtract mixed
fractions.
Frequently asked questions
How do I convert an improper fraction to a
mixed number?
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To convert an improper fraction to a mixed
number, divide the numerator by the denominator and then write the
remainder over the denominator. For example, to convert 8/5 to a
mixed number, divide 8 by 5 to get a quotient of 1 and a remainder
of 3. The mixed number is then written as 1 3/5.
What is the formula to change an improper
fraction to a mixed number?
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The formula to change an improper fraction to a
mixed number is to divide the numerator by the denominator and then
write the remainder over the denominator. For example, to convert
8/5 to a mixed number, divide 8 by 5 to get a quotient of 1 and a
remainder of 3. The mixed number is then written as 1 3/5.
What is an example of an improper
fraction?
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An example of an improper fraction is 8/5. 8 is
the numerator and 5 is the denominator.
How do I identify an improper fraction?
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To identify an improper fraction, first check
the numerator and denominator. If the numerator is larger than the
denominator, then it is an improper fraction. For example, 8/5 is
an improper fraction because 8 is larger than 5.
Can a mixed number be converted to an
improper fraction?
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Yes, a mixed number can be converted to an
improper fraction. To do so, multiply the whole number by the
denominator and add the result to the numerator. For example, to
convert 1 3/5 to an improper fraction, multiply 1 by 5 and add 3 to
get 8. The improper fraction is then 8/5.
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