How to rename mixed numbers in simplest form

Rename Mixed Numbers to Fraction Form with Circle Models

Follow the directions in the dialog box after pressing the button. The button may be pressed to see how to do the example.

Mixed Numbers to Fractions uses circle models to demonstrate how a number in mixed form can be renamed in fraction form .

The illustration below was made by Mixed to Fraction with Circles Designer . It shows the mixed number . You are to write in fraction form, with only a numerator and denominator.

In this example, you will notice that each of the two whole circles has 5 colored pieces and the part circle has 2 colored pieces, giving 12 colored pieces in all for a numerator of 12. The denominator is 5 because each circle has 5 equal parts, giving a fraction of

Multiply the whole number 2 by the denominator 5 and then add the numerator 2 for the numerator 12 in the fraction form.

Some textbooks call a fraction such as this improper, where the numerator is equal to or larger than the denominator. This is also known as the fraction form or a/b form of the number.

Another way to write the example is to think of each whole number as . So in the above example you would have:

For more instruction on renaming from mixed form to fraction form go to How to Rename from Mixed form to Fraction Form.

After you enter the fraction form answer you may press the button. The report will ask for your name but you may submit a code for your name. This report will give same results as on the dialog box. The report may be printed or e-mailed.

Number line models picture mixed numbers to fraction(improper) form with numerator and denominator.

Follow the directions in the dialog box after pressing the button. The button may be pressed to see how to do the example.

Mixed Numbers to Fractions uses number line models to demonstrate how a number in mixed form can be renamed in fraction form .

The illustration below was made by Mixed to Fraction Designer . It shows the mixed number. You are to write in fraction form, with only a numerator and denominator.

In this example, you will notice that the arrow is pointing to the 13th mark after 0, giving a numerator of 13. The number of parts between each whole unit is 5, giving a denominator of 5 for a fraction of 13/5. Some textbooks call a fraction such as this improper, where the numerator is equal to or larger than the denominator. This is also known as the fraction form or a/b form of the number.

Arrive at the numerator 13 by multiplying the whole number 2 by the denominator 5 and then add the numerator 3 as in thie above example.

Another way write the example, you can think of each whole unit as 5/5. So in the above example you would have:

For more instruction on renaming from mixed form to fraction form go to How to Rename from Mixed form to Fraction Form.

After you enter the fraction form answer you may press the button. The report will ask for your name but you may submit a code for your name. This report will give same results as on the dialog box. The report may be printed or e-mailed.

How to rename mixed numbers in simplest form

Each fraction has a variety of names that we may need to use in different scenarios. For example, the number 1 has a lot of distinct names. Remember that the result of dividing any number (except 0) by itself is 1. Other names for 1 include 2/2, 6/6, 93/93, and so on. Another property of the number 1 is that when any integer is multiplied by 1, the original number remains unchanged. These two features of the number 1 can be used to rename fractions.

By renaming fractions, it can be easier to then convert fractions to decimals, as well as tackle questions where you have to add, subtract, divide, or multiply fractions.

How to rename fractions

Fractions are frequently renamed by students. When a student renames a fraction, it transforms into a mixed number, which is the fraction’s proper form . This makes it easier to convert fractions into decimals. To convert a mixed number into a fraction, you can rename it as an improper fraction. If you need to put the fraction in its simplest form, you must also simplify it.

Converting to an Improper Fraction

Let us take the fraction 5 4/10. In this example 5 is the whole number and 4/10 is the proper fraction. To rename this as an improper fraction, multiple the whole number (5) by the denominator (10):

Then, using this number, add the numerator. This will give you the new numerator of the improper fraction.

Therefore 5 4/10 renamed is 54/10.

Simplifying

Sometimes you may find that a question will ask the fraction to be renamed in its simplest form. This means that once you have converted the mixed number into an improper fraction, you should simplify it.

Here is an example:

Rename 2 4/6 in its simplest form. Firstly, we must convert this to an improper fraction as we did in the previous section:

Therefore, 2 4/6 as an improper fraction is 16/6.

Now we must rename this fraction in a simpler form. To do so we need to find the greatest common factor (GCF) of the numerator and denominator and divide. A factor is a number that is generated when two numbers are evenly split. In this context, a factor is also known as a divisor. The greatest common factor of two or more numbers is the highest number shared by all the factors.

To find the GCF, you have to list the factors of 16 and 6:

  • 16: 1, 2 , 4, 8, 16
  • 6: 1, 2 , 3, 6

Notice that both share 2 as a factor, as this is the highest common factor in the list so it’s the GCF. Using this, we now divide the numerator and denominator by the Greatest Common Factor:

  • Numerator: 16 / 2 = 8
  • Denominator: 6 / 2 = 3

We can therefore rename the improper fraction 16/6 as 8/3. It is that simple!

Simplifying with prime numbers

Let us look at this example:

Rename 1 3/4 as an improper fraction in its simplest form.

To start, you should find the new numerator:

Therefore 1 3/4 as an improper fraction is 7/4.

The question also asks us to rename the fraction in its simplest form. As such, let us list the factors of 7 and 4:

  • 4: 1, 2, 4
  • 7 is a prime number, meaning its only factors are 1 and 7

Since these numbers do not share a common factor, they cannot be simplified. 7/4 is therefore the simplest form of 1 3/4!

How do you rename a fraction as a mixed number?

Any number can be renamed as a mixed number so long as the numerator is larger than the denominator. 2/3, for example, cannot be expressed as a mixed number!

Here is an example:

Rename the improper fraction: 19/7. To form the whole number, we need to find out how many 7’s go into 19. To figure this out, you should list the multiples of 7:

  • 7, 14, 21, 28

As we can see, 7 goes into 19 twice with a remainder of 5 (7×2 = 14, +5 = 19)

The number you multiply the denominator by, which is 2 in this case, becomes the whole number, and the remainder becomes the new numerator: 19/7 becomes 2 5/7.

Simplifying

In the same way that you can simplify improper fractions, you can also simplify mixed numbers – in two different ways.

Let us look at the example 28/8. 8 goes into 28 three times with a remainder of 4, you can express this as such:

  • Whole number: 8 x 3 = 24
  • Remainder: 28 – 24 = 4
  • Mixed Number: 3 4/8

You may notice that the fraction 4/8 is half, meaning you can simplify this as 1/2. Remember that as these are equivalent fractions, 4/8 and 1/2 are exactly the same.

So, 28/8 can be renamed as 3 ½.

You can actually simplify the improper fraction before you calculate it as a mixed number. This is especially useful if you have a massive fraction with a numerator in the hundreds.

Let us look again at 28/8. You should start by listing the factors of the numerator and denominator:

  • 28: 1, 2, 4, 7, 14, 28
  • 8: 1, 2, 4, 8

4 is the greatest common factor of these two numbers, so let us divide both by 4:

  • 28 / 4 = 7
  • 8 / 4 = 2

Now the improper fraction is 7/2 which is a lot simpler to work with. The answer, of course, will be 3 1/2.

Need help in maths?

Many children struggle with mathematics, and it’s difficult to catch up once you’ve fallen behind. Thankfully, students in elementary school, middle school, high school, and even university benefit from Tutorax’s in-home and online tutoring services. Tutoring is available in Math , English , geography , chemistry , French , and other subjects. Tutorax can help you with homework, exam preparation, and classroom support if you’re experiencing problems with arithmetic .

It is a fraction having the numerator (top number) greater than the denominator (bottom number). That’s why at times they are called top-heavy fractions.

Improper fractions represent more than one whole.

Example 1: The given picture shows an improper fraction, as there is more than one whole.

How to rename mixed numbers in simplest form

Mixed numbers

A combined form of a whole number and a fraction is called a mixed number.

So, mixed numbers are more than one whole too.

Example 1: 2 1 4 (two and a quarter) is a mixed number. This can be shown in the following picture.

How to rename mixed numbers in simplest form

Note:

While reducing a mixed number to the simplest form, we reduce the fraction part and not the whole number.

Improper fractions and mixed fractions are interchangeable. So, we can use either of them to show the same amount.

Example 1: In the following picture, 2 1 4 = 9 4 , as shown here

How to rename mixed numbers in simplest form

Simplifying mixed numbers

Following are the steps to simplify mixed fractions:

Find the highest common factor (HCF) of numerator and denominator of the fraction part.

Divide both the numerator and the denominator by HCF.

The whole number part will remain the same.

Example 1: Simplify the mixed number 2 9 15 .

Solution: Here, as we need to simplify the fraction part only, so the factors of the numerator are 1, 3, and 9.

Factors of the denominator are 1, 3, 5, and 15.

We can see that 3 is the highest common factor, so we divide the numerator and the denominator by 3.

9 ÷ 3 15 ÷ 3 = 3 5

3 5 is the simplest form of the fraction part 9 15 .

Hence, the simplified form of the given mixed number is 2 3 5 .

Fun Facts

Converting a mixed number into an improper fraction is just the addition of a whole number and the fraction part together.

A Mixed Fraction is a whole number and a proper fraction combined.

Such as 1 34

Examples

2 38 7 14 1 1415 21 45

See how each example is made up of a whole number and a proper fraction together? That is why it is called a “mixed” fraction (or mixed number).

Names

We can give names to every part of a mixed fraction:

Three Types of Fractions

There are three types of fraction:

Mixed Fractions or Improper Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 34 = 74 , as shown here:

1 34 74
How to rename mixed numbers in simplest formHow to rename mixed numbers in simplest form = How to rename mixed numbers in simplest formHow to rename mixed numbers in simplest form

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

  • Divide the numerator by the denominator.
  • Write down the whole number answer
  • Then write down any remainder above the denominator.

Example: Convert 114 to a mixed fraction.

Write down the 2 and then write down the remainder (3) above the denominator (4).

2 34

That example can be written like this:

Example: Convert 103 to a mixed fraction.

3 13

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

  • Multiply the whole number part by the fraction’s denominator.
  • Add that to the numerator
  • Then write the result on top of the denominator.

Example: Convert 3 25 to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

175

We can do the numerator in one go:

Example: Convert 2 19 to an improper fraction.

Are Improper Fractions Bad ?

NO, they aren’t bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction: What is: 1 + 2 14 ?
Is it: 1 + 2 + 14 = 3 14 ?
Or is it: 1 + 2 × 14 = 1 12 ?
Improper Fraction: What is: 1 + 94 ?
It is: 44 + 94 = 134

But, for everyday use, people understand mixed fractions better.

Example: It is easier to say “I ate 2 14 sausages”, than “I ate 94 sausages”

Enter the improper fraction in the fields below to convert it to a mixed number. The calculator shows all the work so you can follow along and learn the steps.

Solution:

Steps to Convert to a Mixed Number

On this page:

  • Calculator
  • How to Convert an Improper Fraction to a Mixed Number
  • Step One: Use Long Division
  • Step Two: Rewrite the Quotient and Remainder to the Mixed Number

You might also like our calculator to convert a mixed number to an improper fraction.

How to Convert an Improper Fraction to a Mixed Number

An improper fraction is a fraction with no whole number and has a larger numerator than the denominator. We can simplify these fractions to mixed numbers in a few simple steps.

How to rename mixed numbers in simplest form

Step One: Use Long Division

The first step in the conversion is to use long division to find the quotient and the remainder. These will be used in the next step.

When doing long division with a fraction, the numerator will be the dividend, and the denominator will be the divisor.

For example, let’s solve the quotient and remainder of 7 / 3 .

First, add the numerators:
7 / 3 = 7 ÷ 3
7 ÷ 3 = 2 R1

Thus, the quotient is 2, and the remainder is 1.

Step Two: Rewrite the Quotient and Remainder to the Mixed Number

The second step is to rewrite the fraction as a mixed number using the quotient and remainder from the previous step, along with the original denominator.

To convert, set the quotient as the whole number, the remainder as the numerator, and the original denominator as the denominator.

For example, let’s use the quotient and remainder from the previous step to rewrite 7 / 3 as a mixed number.

First, add the numerators:
quotient = 2
remainder = 1
original denominator = 3

Using these values, the rewritten mixed number is:
2 1 / 3

That’s it! You have now rewritten an improper fraction as a mixed number in two simple steps.

This method works great for converting a fraction to a mixed number, but you might also like our fraction simplifier to simplify fractions smaller than 1.

Subtracting Fractions and Mixed Numbers

Learning Objectives

· Subtract fractions with like and unlike denominators.

· Subtract mixed numbers without regrouping.

· Subtract mixed numbers with regrouping.

· Solve application problems that require the subtraction of fractions or mixed numbers.

Introduction

Sometimes subtraction, rather than addition, is required to solve problems that involve fractions . Suppose you are making pancakes and need cups of flour but you only have cups. How many additional cups will you have to get to make the pancakes? You can solve this problem by subtracting the mixed numbers.

Subtracting Fractions

The most simple fraction subtraction problems are those that have two proper fractions with a common denominator. That is, each denominator is the same. The process is just as it is for addition of fractions with like denominators, except you subtract! You subtract the second numerator from the first and keep the denominator the same.

Imagine that you have a cake with equal-sized pieces. Some of the cake has already been eaten, so you have a fraction of the cake remaining. You could represent the cake pieces with the picture below.

The cake is cut into 12 equal pieces to start. Two are eaten, so the remaining cake can be represented with the fraction . If three more pieces of cake are eaten, what fraction of the cake is left? You can represent that problem with the expression .

If you subtract 3 pieces, you can see below that of the cake remains.

You can solve this problem without the picture by subtracting the numerators and keeping the denominator the same:

Subtracting Fractions with Like Denominators

If the denominators (bottoms) of the fractions are the same, subtract the numerators (tops) and keep the denominator the same. Remember to simplify the resulting fraction, if possible.

Presentation on theme: “Lesson Menu Main Idea Example 1:Add Mixed Numbers Example 2:Subtract Mixed Numbers Example 3:Rename Mixed Numbers to Subtract Example 4:Rename Mixed Numbers.”— Presentation transcript:

2 Lesson Menu Main Idea Example 1:Add Mixed Numbers Example 2:Subtract Mixed Numbers Example 3:Rename Mixed Numbers to Subtract Example 4:Rename Mixed Numbers to Subtract Example 5:Real-World Example

3 Main Idea/Vocabulary Add and subtract mixed numbers.

4 Example 1 Add Mixed Numbers Find Write in simplest form. Add the whole numbers and fractions separately. Simplify. Estimate 3 + 15 = 18

5 Example 1 Add Mixed Numbers Answer: Check for Reasonableness: 18

6 Example 1 CYP FindWrite in simplest form. A. B. C. D.

7 Example 2 Subtract Mixed Numbers Find Write in simplest form. Simplify. Estimate 10 – 5 = 5 Rename the fraction using the LCD. Then subtract.

8 Example 2 Subtract Mixed Numbers Answer: Check for Reasonableness:

9 Example 2 CYP Find Write in simplest form. A. B. C. D.

10 Example 3 Rename Mixed Numbers to Subtract Find Since is less than, rename before subtracting. Estimate

11 Example 3 Rename Mixed Numbers to Subtract Change 1 to.

12 Example 3 Rename Mixed Numbers to Subtract Simplify. Subtract the whole numbers and then the fractions. Rename as. Check for Reasonableness Answer:

13 Example 3 CYP Find A. B. C. D.

14 Example 4 Find Rename Mixed Numbers to Subtract Using the denominator of the fraction in the subtrahend, 11 = Since is less than rename 11 before subtracting. Estimate 11 – 9 = 2

15 Example 4 Rename Mixed Numbers to Subtract Simplify. Subtract. Rename 11 as. Answer: Check for Reasonableness

16 Example 4 CYP Find A. B. C. D.

17 Example 5 CRAFTS Marlee is making necklaces and bracelets for a class craft sale. She uses feet of string for the necklaces and feet of string for the bracelets. What is the total length of string that Marlee used?

is anyone can answer this fraction below.

.Rename these improper fractions as mixed numbers:

16/5 18/6 19/4 24/5

sorry if it is line suppose but i typed slash pls.understand thanks

  1. ℹ️

To convert improper fractions into mixed numbers (a whole number + a fraction), we divide the numerator by the denominator. Write down the quotient. The remainder will form the fractional part.

Example: 16/5
Divide 16 by 5 to get the quotient 3 with a remainder of 1.
So the mixed number is
3 1/5
Sorry that is is not possible to write the fraction 1/5 in the proper way.

Respond to this Question

Similar Questions

How is adding and subtracting mixed numbers similar to adding and subtracting fractions? How is adding and subtracting mixed numbers different than adding and subtracting fractions? Give examples to explain your answer.

How do you turn an improper fraction into a mixed number?

arithmetic

a stock clerk had 600 pads on hand. He then issued 3/8 of his supply of pads to division X,1/4 to division Y and 1/6 to division Z. The number of pads remaining in stock is? I don’t get how to solve this problem. In arithmetic

mathematics

what are 3 mixed numbers between 3 and 4 but closer to 3? what are 3 improper fractions 3 and 4 but closer to 3?

Perform the indicated operations. Reduce the answers to lowest terms. 1.) 7 3/5 + 2 4/7 = _______________ 2.) 8 5/9 + 15 5/6 =________________ 3.) 14 5/10 + 8 3/5 = ________________ 4.) 5/6 x 3/4 = _____________________ Reduce

Solve the following problem and reduce to lowest terms (mixed number or improper fraction). 2/3 + 1/6 +11/12

write the mixed number as an improper fraction 6 2/3

write each mixed number as an improper fraction 1 7/8

i need some to explain how to turn 1.05 into a fraction Do you know how to add fractions? 1 + 0.05 equals 1.05. So if you can convert 1 to a fraction and 0.05 to a fraction, you can add the two fractions together. Your answer is

How to rename mixed numbers in simplest form

A mixed number is made up of a whole number and a fraction. For example:
How to rename mixed numbers in simplest form

An improper fraction is one that is ‘top-heavy’ so the numerator is bigger than the denominator. For example:
How to rename mixed numbers in simplest form

The relationship between mixed numbers and improper fractions can be best explained through the diagram above. These two shapes have been cut into four pieces. We can either express the amount of the shape we have as a mixed number: (1 3/4) or as an improper fraction (7/4).

How to rename mixed numbers in simplest form

Working with mixed numbers and improper fractions in KS2

In Years 5 and 6 children need to start to be able to see equivalence between mixed numbers and improper fractions.

In the diagram above 8/3 is equivalent to 2 2/3.

In the diagram above 10/3 is equivalent to 3 1/3.

Converting improper fractions into mixed numbers

What is 16/5 as a mixed number?

  • Divide the numerator by the denominator (16 ÷ 5 = 3 R 1).
  • Your answer is the whole number and your remainder becomes the numerator of the fraction next to the whole number, so your answer is 3 1/5.

Converting mixed numbers into improper fractions

What is 2 7/8 as an improper fraction?

  • Multiply the whole number by the denominator (2 x 8 = 16) and then add the numerator (16 + 7 = 23).
  • This answer becomes the numerator; the denominator stays the same: 23/8.

More like this

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

How to rename mixed numbers in simplest form

Shopping basket

JOIN OVER 250,000 PARENTS
& get FREE resources and activities for your child!

Start your 14-day trial

for FREE Click here

How to use TheSchoolRun

Testimonials

‘Thank you for providing a much-needed service for parents and one which really represented good value for money. I particularly loved your handwriting sections and the ‘Learning Journey’ links that you have created. There are not many services I would pay to subscribe to, and even less I would recommend, but yours is one which I did!’

‘I’m not on social media but just wanted to reach out and say I have been recommending you to everyone I know, with kids of course!

Your site has been fantastic. It’s not only teaching my little one things, it’s showing me how things should’ve been done when I was younger. I do wish you were around then, as your content is fantastic and my little boy looks forward to your daily worksheets. Learning definitely made fun.

People are so quick to moan these days, so I wanted to send an email to sing my praises. You’ve helped me become more organised with the schedule of things, but without the pressure I was putting myself under before. We have fun and learn.’

‘I’m finding your site an absolutely fantastic resource alongside the stuff being sent from my son’s school. We love being able to keep track of his progress on his Learning Journey checklist!’

‘Thank you so very much for all the help your site is giving myself to aid my daughter’s education at home. Truly, it makes her day enjoyable, structured and continuous.’