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, 2¹/₇
is a mixed fraction. Learn here all types of fractions in
detail.

Table of Contents: Definition Improper fraction to mixed fraction Mixed fraction to improper fraction Adding Mixed Fractions Subtracting Mixed Fractions Multiplying Mixed Fractions Mixed Equivalent Fractions FAQs

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 well-informed on the subject of
fractions. To become well-versed, 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.

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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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 step-wise 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 experience, I’m here to show you how to multiply fractions. To solve 8/6 multiplied by 4, simply multiply both the numerator and denominator by 4. So 8/6 x 4 = 32/24. Likewise, to solve 12/8 multiplied by 3, multiply both the numerator and denominator by 3. So 12/8 x 3 = 36/24. And there you have it – two fractions solved!
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 step-wise 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, and I know that if you want to multiply the numerator and denominator of 8/6 with 4 and 12/8 with 3, all you need to do is multiply the numerator of 8/6 by 4, and the denominator by 12. This will give you 32/72. On the other hand, to multiply 12/8 with 3, you need to multiply the numerator by 3 and the denominator by 8, thus giving you 36/24.
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 ten-year 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 2¹/₂.

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 = 2²/₄.

Hence, for both mixed fractions
2¹/₂ and 2²/₄, 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
depth, as well as providing practice exercises and tutorials. As a
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
date with the latest developments in the field. So, if you’re
looking to hone your mathematical skills, I highly recommend
downloading the BYJU’S app.

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say how to make an improper fraction into a mixed number, please
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