Mixed number as improper fraction calculator: Mixed Number to Improper Fraction Calculator

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Mixed Numbers to Improper Fractions Calculator

This online mixed numbers to improper fractions calculator has been specially designed to turn mixed number to improper fraction. So if you are looking for accurate results regarding such conversions, scroll down the article below and start learning basics with us.

Stay focused!

What Is A Mixed Number?

In the light of mathematical contextual:

“A mixed number is the fraction that contains a whole number and a proper fraction”

For example:

$$ 2\frac{1}{3} \hspace{0.25in} 3\frac{3}{6} \hspace{0.25in} 6\frac{7}{9} $$

Steps Involved In Converting Mixed Numbers To Improper Fractions:

Below are the steps that you need to follow up in order to perform such conversions:

Step # 01:
Multiply the denominator with the whole number

Step # 02:
Now add the result of the step # 01 in the numerator

Step # 03:
Now write the result of step # 02 in the numerator and denominator will remain the same

All above steps are summarized in the following pictorial representation:

Our best mixed numbers to improper fractions calculator also uses the same process to generate accurate outputs with seconds.

How To Turn A Mixed Number Into An Improper Fraction?

Here we will be resolving a few examples to clear the difference between mixed numbers and the improper fractions. Keep scrolling!

Example # 01:
How to make an improper fraction from the mixed number given below:

$$ 2\frac{5}{6} $$

Solution:

By following the three steps discussed above, we get:

Step # 01:

$$ Denominator = 6 $$
$$ Whole Number = 2 $$

$$ Denominator * Whole Number = 6 * 2 $$

$$ = 12 $$

Step # 02:

$$ 12 + Numerator = 12 + 5 $$

$$ = 17 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{17}{6} $$

So we have:

$$ 2\frac{5}{6} = \frac{17}{6} $$

Example # 02:

What is 1 2 3 as an improper fraction?

Solution:

Here 1 2 3 means \(1\frac{2}{3}\)

So we have:

Step # 01:

$$ Denominator = 3 $$
$$ Whole Number = 1 $$

$$ Denominator * Whole Number = 3 * 1 $$

$$ = 3 $$

Step # 02:

$$ 3 + Numerator = 3 + 2 $$

$$ = 5 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{5}{3} $$

So we have:

$$ 1\frac{2}{3} = \frac{5}{3} $$

Example # 03:

How to change a mixed number into an improper fraction that is as follows:

$$ 9\frac{2}{3} $$

Solution:

Step # 01:

$$ Denominator = 3 $$
$$ Whole Number = 9 $$

$$ Denominator * Whole Number = 3 * 9 $$

$$ = 27 $$

Step # 02:

$$ 27 + Numerator = 27 + 2 $$

$$ = 29 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{29}{3} $$

So we have:

$$ 9\frac{2}{3} = \frac{29}{3} $$

Which is our required answer.

You can also verify all these results by fetching values in our best mixed numbers to improper fractions calculator.

Example # 04:

Write down 4 2 3 as an improper fraction?

Solution:

Here we have:
4 2 3 is actually \(4\frac{2}{3}\)

Step # 01:

$$ Denominator = 3 $$
$$ Whole Number = 4 $$

$$ Denominator * Whole Number = 3 * 4 $$

$$ = 12 $$

Step # 02:

$$ 12 + Numerator = 12 + 2 $$

$$ = 14 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{14}{3} $$

So we have:

$$ 4\frac{2}{3} = \frac{14}{3} $$

Which is our required answer.

Example # 05:

How to convert a mixed number into an improper fraction that is written down:

$$ 2\frac{7}{10} $$

Solution:

Step # 01:

$$ Denominator = 10 $$
$$ Whole Number = 2 $$

$$ Denominator * Whole Number = 10 * 2 $$

$$ = 20 $$

Step # 02:

$$ 20 + Numerator = 20 + 7 $$

$$ = 27 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{27}{10} $$

So we have:

$$ 2\frac{7}{10} = \frac{27}{10} $$

Which is our required answer.

Use our free online mixed number to improper fraction calculator if you feel any hurdle resolving these problems.

Example # 06:

How do you write 1 1 2 as an improper fraction?

Solution:

1 1 2 is actually a mixed number that is \(1\frac{1}{2}\)

Now:

Step # 01:

$$ Denominator = 2 $$
$$ Whole Number = 1 $$

$$ Denominator * Whole Number = 2 * 1$$

$$ = 2 $$

Step # 02:

$$ 2 + Numerator = 2 + 1 $$

$$ = 3 $$

The above number will be the final numerator

Step # 03:

The final improper fraction is as follows:

$$ \frac{3}{2} $$

So we have:

$$ 1\frac{1}{2} = \frac{3}{2} $$

Which is our required answer.

Some Important Conversions:

We have summarized most common and important mixed fraction to improper fraction in the following table:

MIXED NUMBER INTO IMPROPER FRACTION

Sr #

Mixed Numbers

As An Improper Fraction

1

$$ 2\frac{1}{2} $$ $$ \frac{5}{2} $$

2

$$ 2\frac{2}{3} $$ $$ \frac{8}{3} $$

3

$$ 1\frac{2}{5} $$ $$ \frac{7}{2} $$

4

$$ 5\frac{2}{3} $$ $$ \frac{17}{3} $$

5

$$ 3\frac{2}{5} $$ $$ \frac{17}{5} $$

6

$$ 2\frac{1}{4} $$ $$ \frac{9}{4} $$

7

$$ 4\frac{1}{2} $$ $$ \frac{9}{2} $$

8

$$ 3\frac{4}{5} $$ $$ \frac{19}{5} $$

9

$$ 3\frac{2}{3} $$ $$ \frac{11}{3} $$

10

$$ 3\frac{1}{3} $$ $$ \frac{10}{3} $$

11

$$ 3\frac{3}{4} $$ $$ \frac{15}{4} $$

12

$$ 2\frac{3}{5} $$ $$ \frac{13}{5} $$

13

$$ 1\frac{1}{3} $$ $$ \frac{4}{3} $$

14

$$ 2\frac{2}{5} $$ $$ \frac{12}{5} $$

15

$$ 4\frac{5}{6} $$ $$ \frac{29}{6} $$

16

$$ 3\frac{2}{9} $$ $$ \frac{29}{9} $$

17

$$ 5\frac{1}{3} $$ $$ \frac{16}{3} $$

18

$$ 7\frac{1}{2} $$ $$ \frac{15}{2} $$

19

$$ 3\frac{3}{5} $$ $$ \frac{18}{5} $$

20

$$ 2\frac{4}{12} $$ $$ \frac{28}{12} $$

21

$$ 4\frac{7}{8} $$ $$ \frac{39}{8} $$

22

$$ 5\frac{4}{7} $$ $$ \frac{39}{7} $$

23

$$ 7\frac{2}{4} $$ $$ \frac{30}{4} $$

24

$$ 5\frac{8}{13} $$ $$ \frac{73}{13} $$

25

$$ 1\frac{4}{5} $$ $$ \frac{9}{5} $$

26

$$ 4\frac{3}{5} $$ $$ \frac{23}{5} $$

27

$$ 2\frac{6}{8} $$ $$ \frac{22}{8} $$

28

$$ 1\frac{5}{5} $$ $$ \frac{10}{5} $$

29

$$ 6\frac{5}{6} $$ $$ \frac{41}{6} $$

30

$$ 3\frac{5}{5} $$ $$ \frac{20}{5} $$

31

$$ 2\frac{7}{9} $$ $$ \frac{25}{9} $$

32

$$ 12\frac{3}{5} $$ $$ \frac{63}{5} $$

33

$$ 1\frac{4}{23} $$ $$ \frac{27}{23} $$

34

$$ 9\frac{4}{5} $$ $$ \frac{49}{5} $$

35

$$ 4\frac{13}{24} $$ $$ \frac{109}{24} $$

36

$$ 3\frac{3}{12} $$ $$ \frac{39}{12} $$

37

$$ 8\frac{3}{51} $$ $$ \frac{411}{51} $$

38

$$ 2\frac{4}{6} $$ $$ \frac{16}{6} $$

39

$$ 4\frac{5}{7} $$ $$ \frac{33}{7} $$

How Mixed Numbers To Improper Fractions Calculator Works?

Let our free calculator convert mixed numbers to improper fractions in a single tap. Want to see how? Let’s go!

Input:

  • Enter the whole number, numerator, and the denominator in their designated fields
  • Tap the calculate button

Output:

The free mixed number to improper fraction calculator determines:

  • Corresponding improper fraction of the given mixed number
  • Steps involved during the calculations

FAQ’s:

What is 3 2 as a mixed number?

3 2 is actually \(\frac{3}{2}\) and its corresponding mixed number is \(1\frac{1}{2}\)
(For detailed calculations, tap  improper fractions to mixed numbers calculator)

Write down 7 2 as a mixed number.

Here:

7 2 = \(\frac{7}{2}\)

The corresponding mixed number is \(3\frac{1}{2}\)

Can an improper fraction be negative?

Yes, an improper fraction can definitely be negative. All you have to do is to treat this as a positive improper fraction and put the negative sign with the answer.

What is a proper fraction?

A particular fraction in which the denominator is greater than its numerator is called a proper fraction.

Conclusion:

The conversion between a mixed number and an improper fraction leads us to know the nature of the fractions. When you get an idea how small or large the fraction is, you can easily resolve it. And the best method to resolve such fractions is none other than an online mixed numbers to improper fractions calculator.

References:

From the source of Wikipedia: Mathematical fractions

From the source of Khan Academy: mixed numbers and improper fractions, review

From the source of Lumen Learning: Convert to an improper fraction

Mixed Number Fraction Calculator — Online Mixed Number Fraction Calculator

Mixed Number Fraction Calculator a free online tool that converts a mixed fraction to an improper fraction.

What is a Mixed Number Fraction Calculator?

A mixed number fraction calculator is a free online tool that converts a mixed fraction to an improper fraction. This calculator helps you to convert mixed fractions to improper fractions within a few seconds.

Mixed Number Fraction Calculator

How to Use the Mixed Number Fraction Calculator?

Follow the steps below and try to use the calculator.

  • Step 1: Enter the mixed fraction in the three respective input boxes.
  • Step 2: Click on «Calculate» to get the improper fraction form of the mixed fraction that was entered.
  • Step 3: Click on «Reset» to enter the new set of fractions.

How to Convert a Mixed Fraction to an Improper Fraction?

A mixed fraction is a mixture of a whole and a proper fraction. 

In order to convert a mixed fraction to an improper fraction, you need to multiply the denominator with the whole number part and then add the numerator to the product.

The resultant will be the new numerator, whereas, the denominator remains the same.

Want to find complex math solutions within seconds?

Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps.

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Solved Examples on Mixed Number Fraction Calculator

Example 1:

Convert \(4\dfrac{3}{5}\) to an improper fraction.

Solution:

The new numerator = (Denominator × Whole number) + Numerator

Numerator = (5 × 4) + 3 = 20 + 3 = 23

Denominator = 5

Therefore, the improper fraction = 23/5

Example 2:

Convert \(8\dfrac{7}{9}\) to an improper fraction.

Solution:

The new numerator = (Denominator × Whole number) + Numerator

Numerator = (9 × 8) + 7 = 72 + 7 = 79

Denominator = 9

Therefore, the improper fraction = 79/9

Example 3:

Convert \(6\dfrac{7}{11}\) to an improper fraction.

Solution:

The new numerator = (Denominator × Whole number) + Numerator

Numerator = (11 × 6) + 7 = 66 + 7 = 73

Denominator = 11

Therefore, the improper fraction = 73/11

Similarly,

Now, use the calculator and convert the following mixed fractions to improper fractions:

  • \(4\dfrac{2}{5}\)

  • \(2\dfrac{3}{7}\)

  • \(5\dfrac{1}{6}\)

☛ Related Articles:

  • Types of Fractions
  • Improper Fractions
  • Numerator
  • Denominator

☛ Math Calculators:

How to convert improper fractions to mixed numbers



How to convert improper fractions to mixed numbers


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3

We write down the number 142 and 3, as indicated above.

»
«

© Maxim Semenikhin, 2013-2014

Mixed Number Calculator — Mathcracker.

Com

Solvers

Algebra



Instructions:

Use this calculator to calculate mixed fractions. Enter the mixed fraction in the box below.

How to use this mixed number calculator

The mixed fraction calculator will help you calculate any algebraic expression with mixed numbers and fractions that you provide. For example, you can enter the mixed number ‘2 3/4’ and the calculator will convert it to a fraction and reduce it.

After you have entered the mixed number/fractional expression, you need to click «Calculate» and all the steps will be shown for you.


What is a mixed fraction

A

mixed fraction

it’s just an integer that goes along with the fraction. The format is as follows: first comes an integer, then a space, and then a fraction. For example, the following fraction is mixed:

\[2\,\,\frac{2}{3}\]

In this case, the integer is «2» and the fraction is «2/3». The presence of these two elements together in this case means that we add them. Thus, when we write a mixed fraction, we mean the following:

\[2\,\,\frac{2}{3} = 2 + \frac{2}{3}\]

How to calculate mixed numbers

The basic idea is to simply reduce a mixed number to a sum of fractions. That is, it is necessary to divide the integer and fractional parts of the mixed number and operate with them as ordinary fractions.

What are the steps for calculating mixed numbers

  • Step 1: Be clear about what mixed number we want to analyze
  • Step 2: Extracting the Integer and Fractional Parts of a Mixed Number
  • Step 3: Convert the integer part to a fraction and then simply operate on them as fractions

Why deal with mixed fractions?

The use of mixed fractions (also known as mixed numbers) is a kind of legacy notation. In fact, it has no noticeable significance and does not play any important role. But knowing how to operate with them is useful, since they appear in formulas from time to time.


Example: calculating a mixed number

Write as a fraction: \(1\,\,\frac{1}{3}\).

Solution:

We need to simplify the following given mixed fraction: \(\displaystyle 1 \,\, \frac{ 1}{ 3}\).

This results in the following calculation:

\( \displaystyle 1 \,\, \frac{ 1}{ 3}\)

This is the given mixed fraction

\( = \,\,\)

\(\displaystyle 1\,\,\frac{ 1}{ 3}\)

By definition, the mixed fraction can be written this way

\( = \,\,\)

\(\displaystyle 1+\frac1{ 3}\)

Using \(3\) as the common denominator

\( = \,\,\)

\(\displaystyle \frac{ 1 \times 3 + 1}{ 3}\)

This is a regular fraction obtained after expanding the denominator

\( = \,\,\)

\(\displaystyle \frac{ 4}{ 3}\)

which completes the calculation.

Example: Another Calculation of Mixed Fractions

Calculate the following mixed number \(3 + 2\,\,\frac{2}{3}\).

Solution:

First we need to simplify the following given mixed fraction: \(\displaystyle 2 \,\, \frac{ 2}{ 3}\).

This results in the following calculation:

\( \displaystyle 2 \,\, \frac{ 2}{ 3}\)

This is the given mixed fraction

\( = \,\,\)

\(\displaystyle 2\,\,\frac{ 2}{ 3}\)

By definition, the mixed fraction can be written this way

\( = \,\,\)

\(\displaystyle 2+\frac2{ 3}\)

Using \(3\) as the common denominator

\( = \,\,\)

\(\displaystyle \frac{ 2 \times 3 + 2}{ 3}\)

This is a regular fraction obtained after expanding the denominator

\( = \,\,\)

\(\displaystyle \frac{ 8}{ 3}\)

Now we need to evaluate and simplify the following expression: \(\displaystyle 3+\frac{8}{3}\).

This results in the following calculation:

\( \displaystyle 3+\frac{8}{3}\)

Amplifying in order to get the common denominator 3

\( = \,\,\)

\(\displaystyle 3\cdot\frac{3}{3}+\frac{8}{3}\)

Finding a common denominator: 3

\( = \,\,\)

\(\displaystyle \frac{3\cdot 3+8}{3}\)

Expanding each term: \(3 \times 3+8 = 9+8\)

\( = \,\,\)

\(\displaystyle \frac{9+8}{3}\)

Adding up the terms in the numerator

\( = \,\,\)

\(\displaystyle \frac{17}{3}\)

which completes the calculation.

By alexxlab

Similar Posts

142 3
028

Let’s start looking at the numbers formed by the digits of the number 142 in turn until we reach a number that is greater than or equal to 3.
Now the number is selected 1, it’s less than 3, so you need to continue moving to the right.

«,
«

142 3
0017

We have reached the number 14, which is greater than 3. The number 14 is an incomplete divisible of .

»
«

9002 8

Let’s determine by which digit we need to multiply the divisor of 3 in order to get the largest possible number less than or equal to the incomplete divisible 14.
Obviously, which is 4, because 3 &middot 4 = 12, which is less than 14, and 3 &middot 5 is already equal to 15, which is more than 14. Therefore, we write 4 as a private number.0003″
«

142 3
4
142 3
12 4 900 10

Now multiply 3 by 4 and write the result 12 under the partial divisible as shown above.

«,
«

142 3
12 4 900 10
2

Let’s subtract in columns 14 — 12 = 2.

«,
»

142 3
12 4
22

Subtract the next digit from the dividend 2.

«,
«

142 3
12 47 010
22

equal to the incomplete dividend 22.
Obviously 7, because 3 &middot 7 = 21, which is less than 22, and 3 &middot 8 is already equal to 24, which is greater than 22. Therefore, we write 7 in the private figure.

«,
«

142 3
12 47 010
22
21

as shown above.

«,
«

9000 5

142 3
12 47
22
21
1

22 — 21 \u003d 1.
So, the result: 142: 3 \u003d 47 (remainder 1) .

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Step 1 of

142 3

Let’s write the numbers 142 and 3 as shown above.

Let’s show how to divide with a remainder on the calculator:

1. Divide 142 by 3 on a calculator. We get 47.333333…
2. We discard the fractional part from the result. We get 47 — this will be a quotient, which is written in the integer part of the mixed number.
3. Multiply 47 back by 3. Get 141.
4. Subtract 141 from the original number 142. 142 — 141 = 1 — this will be the remainder. It is written in the numerator of a fraction of a mixed number.

So 142 : 3 = 47 (remainder 1)

Now, after the division is done, you only need to write the answer as a fraction:

Online calculator
conversion of improper fractions to mixed numbers

You can get a detailed explanation of how to convert your specific improper fraction to a mixed number. To do this, simply use the calculator at the top of the page: enter an improper fraction and press the «=» button.

You can use this calculator to add, multiply, subtract and divide mixed numbers: first convert mixed numbers to fractions, and then use the addition, subtraction, multiplication and division calculators for ordinary fractions.