Mathematicians use three categories to describe fractions: proper, improper, and also mixed.

You are watching: Fractions that are greater than 1

Fractions that are higher than 0 however less 보다 1 are dubbed proper fractions. In appropriate fractions, the numerator is less than the denominator. As soon as a portion has a numerator that is higher than or equal to the denominator, the portion is an improper fraction. An improper portion is constantly 1 or higher than 1. And, finally, a An expression in which a whole number is merged with a suitable fraction. For example 5

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is a combined number.


")">mixed number
is a combination of a totality number and also a suitable fraction.

Identifying Proper and also Improper Fractions


In a ideal fraction, the numerator is always less 보다 the denominator. Instances of proper fractions include

*
 and
*
.

In an wrong fraction, the molecule is constantly greater than or equal to the denominator. Instances of improper fractions encompass

*
 and
*
.

Identify  as a proper or wrong fraction.

A) proper

B) improper


Show/Hide Answer

A) proper

Incorrect. In the fraction, the numerator is higher than the denominator, so it is an wrong fraction. The correct answer is improper.

B) improper

Correct. The fraction is higher than 1, and the molecule is greater than the denominator, so  is an not correct fraction.

Changing Improper fountain to mixed Numbers


An improper portion can likewise be composed as a mixed number. Blended numbers save on computer both a entirety number and a suitable fraction. Instances of mixed numbers incorporate

*
 and
*
.

Let’s look at a rapid example. Below are three entirety pizzas that are each cut into 4 pieces. A fourth pizza is there together well, but someone has taken one piece, leaving only three pieces.

*

You deserve to use fountain to to compare the variety of pieces you have to the variety of pieces that make up a whole. In this picture, the denominator is the total variety of pieces that comprise one whole pizza, which is 4. The total variety of all piece of pizza, i m sorry is 15, to represent the numerator.

You have the right to use the improper fraction  to represent the full amount the pizza here. Think: “Each whole pizza is cut into 4 equal pieces, and there room 15 piece total. So, the full amount of entirety pizzas is .”

As you looked in ~ the picture of the pizzas, however, you more than likely noticed best away the there to be 3 full pizzas and also one pizza through a item missing. If you have the right to use the improper portion  to stand for the complete amount of pizza, the makes an ext sense right here to usage a combined number – a fraction that consists of both a entirety number and also a spring part. For this pizza scenario, you can use the portion .

*

The combined number  can be less complicated to understand than the improper portion . However, both forms are legitimate ways to stand for the variety of pizzas.

Rewriting an improper fraction as a mixed number deserve to be helpful, due to the fact that it help you see more easily about how plenty of whole items girlfriend have.

Let’s look at again at the pizzas above.

The improper fraction  means there space 15 full pieces, and 4 pieces renders a totality pizza. If girlfriend didn’t have the picture, girlfriend could adjust  into a mixed fraction by determining:

– How many groups the 4 pieces space there in 15 pieces? since 15 ÷ 4 = 3 with a remainder, there are 3 entirety pizzas.

– What is the remainder? The remainder is 3. So, there room 3 pieces of the critical pizza left, out of the 4 that would certainly make a totality pizza. So,

*
 of a pizza is left.

Now, put the variety of whole pizzas with the fraction of a pizza that is left over. The combined number is .

Writing Improper fountain as blended Numbers

Step 1: division the denominator into the numerator.

Step 2: The quotient is the entirety number component of the mixed number.

Step 3: The remainder is the molecule of the fractional part of the blended number.

Step 4: The divisor is the denominator that the fractional part of the blended number.


Example

Problem

Write the improper fraction as a mixed number.

47 ÷ 7 = 6, remainder 5

*

Divide the denominator into the numerator.

The quotient, 6, i do not care the entirety number.

The remainder, 5, i do not care the numerator.

The denominator, i m sorry is also used as the divisor, continues to be as 7.

Answer   =

*
 


Change  from one improper portion to a mixed number.

A)

B)

C)

D)


A)

Incorrect. You probably puzzled the numerator v the totality number. This is much higher than . The correct answer is .

B)

Correct. The improper fraction  can be thought of together 12 ÷ 5 = 2, with a remainder that 2. So,  is the correct answer.

C)

Incorrect. To discover the mixed number, you must divide the denominator into the numerator. The correct answer is .

D)

Incorrect. Girlfriend probably mixed up the numerator and also the denominator. The exactly answer is .

Mixed numbers can additionally be readjusted to wrong fractions. This is sometimes helpful when law calculations with combined numbers, specifically multiplication.

Let’s begin by considering the idea that one totality as an not correct fraction. If you division a cake into 5 equal slices, and also keep every the slices, the one totality cake is equal to the 5 slices. So, 1 cake is the very same as

*
 cake.

*

Had you cut the cake right into 4 piece or 3 pieces, as shown below, you might have used the fountain

*
 or
*
 to stand for the entirety cake. The fountain may change depending top top the number of cuts you do to the cake, but you room still dealing with only one cake.


*

*

 


Let’s check out how to write a straightforward mixed number, , together an improper fraction. The blended number is stood for below. Each complete circle represents one whole.



To create an wrong fraction, you require to understand how countless equal sized piece make one whole. You additionally need to understand how numerous of those piece you have. Since you have actually

*
, you should divide up all of the circles right into 3 pieces.



Each totality circle has 3 pieces. You deserve to multiply the variety of whole circles, 2, by 3 to uncover how numerous one-third pieces room in the two whole circles. Climate you include 1 for the one-third item in the final, incomplete circle. As you deserve to see from the diagram, there space 7 individual one-third pieces. The improper fraction for  is

*
.

Writing blended Numbers together Improper Fractions

Step 1. Main point the denominator that the portion by the entirety number.

Step 2. Include this product come the molecule of the fraction.

Step 3. The amount is the numerator of the wrong fraction.

Step 4. The denominator of the improper fraction is the very same as the denominator that the fractional component of the combined number.


Example

Problem

Write

*
 as an not correct fraction.

4 • 4 = 16

16 + 3 = 19

Multiply the denominator that the fraction by the whole number.

Add this an outcome to the molecule of the fraction.

This answer becomes the molecule of the not correct fraction.

Notice that the denominator of the improper fraction is the same as the denominator that remained in the fractional part of the blended number.

Answer =


Change

*
 from a combined number to an not correct fraction.

A)

B)

C)

D)


A)

Incorrect. You most likely multiplied the totality number by the molecule of the fraction instead the the denominator, and then included it to the 5 that was at first at the top. The correct answer is .

B)

Incorrect. You more than likely put the totality number 3 in the tens location of the molecule without adhering to the exactly process. The correct answer is .

C)

Correct.

*
. The denominator continues to be the same, for this reason  is the wrong form.

D)

Incorrect. You most likely reversed the numerator and also denominator after finding your answer. The correct answer is .

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A portion can be established as proper or improper by to compare the numerator and also the denominator. Fractions that are much less than one are known as appropriate fractions, and the numerator (the top number) is much less than the denominator (the bottom number). A portion with a numerator that is greater than or same to the denominator is well-known as an wrong fraction. It represents a number higher than or same to one. Numbers that space not entirety numbers, however are better than one, can be created as improper fractions or mixed numbers. A mixed number has actually a entirety number component and a portion part.