Each portion has a selection of names the we may need to use in various scenarios. Because that example, the number 1 has a lot of unique names. Remember that the result of dividing any type of number (except 0) by itself is 1. Other names because that 1 incorporate 2/2, 6/6, 93/93, and also so on. Another property of the number 1 is that when any integer is multiply by 1, the initial number remains unchanged. This two attributes of the number 1 deserve to be used to rename fractions.

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By renaming fractions, it can be much easier to then transform fractions come decimals, as well as tackle concerns where you have to add, subtract, divide, or multiply fractions.

How come rename fractions

Fractions are typically renamed by students. When a college student renames a fraction, it transforms right into a mixed number, i m sorry is the fraction’s proper form. This makes it easier to transform fractions right into decimals. To transform a combined number into a fraction, you can rename it together an wrong fraction. If you should put the portion in its easiest form, you must additionally simplify it. 

Converting to an not correct Fraction

Let us take the portion 5 4/10. In this instance 5 is the whole number and also 4/10 is the ideal fraction. Come rename this together an wrong fraction, many the whole number (5) by the denominator (10):

5 x 10 = 50

Then, using this number, add the numerator. This will offer you the new numerator that the not correct fraction.

50 + 4 = 54

Therefore 5 4/10 change the name is 54/10.


Sometimes girlfriend may find that a question will ask the portion to be change the name in its simplest form. This method that once you have converted the combined number into an improper fraction, you must simplify it.

Here is an example: 

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

2 x 6 = 12

12 + 4 = 16

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

Now we must rename this fraction in a much easier form. To execute so we need to discover the greatest common factor (GCF) of the numerator and also denominator and divide. A aspect is a number that is produced when 2 numbers room evenly split. In this context, a aspect is additionally known together a divisor. The greatest typical factor of two or more numbers is the highest number shared by all the factors.

To find the GCF, you need to list the components of 16 and 6:

16: 1, 2, 4, 8, 166: 1, 2, 3, 6

Notice the both re-publishing 2 together a factor, together this is the highest common factor in the list so the the GCF. Utilizing this, we currently divide the numerator and also denominator by the Greatest common Factor:

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

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

Simplifying with prime numbers

Let united state look in ~ this example: 

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

To start, girlfriend should discover the new numerator:

1 x 4 = 4

4 + 3 = 7

Therefore 1 3/4 together an improper portion is 7/4.

The question likewise asks united state to rename the fraction in its simplest form. As such, let us list the determinants of 7 and 4:

4: 1, 2, 47 is a element number, an interpretation its only factors are 1 and 7

Since these numbers perform not re-publishing a typical factor, they can not be simplified. 7/4 is thus the simplest form of 1 3/4!

How perform you rename a portion as a combined number?

Any number have the right to be renamed as a blended number so long as the molecule is bigger than the denominator. 2/3, because that example, can not be expressed together a combined number!

Here is one example: 

Rename the wrong fraction: 19/7. To type the whole number, we need to discover out how many 7’s enter 19. To figure this out, you have to list the multiples of 7:

7, 14, 21, 28

As we have the right to see, 7 goes into 19 twice through a remainder of 5 (7×2 = 14, +5 = 19)

The number you main point the denominator by, i beg your pardon is 2 in this case, becomes the totality number, and also the remainder i do not care the brand-new numerator: 19/7 i do not care 2 5/7. 


In the same means that you deserve to simplify not correct fractions, you can also simplify blended numbers – in two various ways.

Method 1:

Let united state look at the example 28/8. 8 goes right into 28 three times through a remainder the 4, you can express this as such:

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

You may an alert that the fraction 4/8 is half, meaning you can simplify this as 1/2. Mental that together these are tantamount fractions, 4/8 and also 1/2 are exactly the same.

So, 28/8 can be renamed as 3 ½.

Method 2:

You can actually leveling the improper portion before you calculation it as a mixed number. This is especially valuable if you have a massive fraction with a molecule 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, 288: 1, 2, 4, 8

4 is the greatest common factor the these 2 numbers, so let united state divide both by 4:

28 / 4 = 78 / 4 = 2

Now the improper fraction is 7/2 i beg your pardon is a lot less complicated to work-related with. The answer, the course, will certainly be 3 1/2.

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