Mixed number to improper fraction worksheets: Grade 5 math worksheet — Fractions: convert mixed numbers to improper fractions

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Mixed Numbers and Improper Fractions

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Search Printable Mixed Numbers and Improper Fraction Worksheets

It’s easy to get mixed up in math class. Give your students some extra practice with our mixed numbers and improper fractions worksheets! Designed by teachers for third to fifth grade, these activities provide plenty of support in learning to convert mixed numbers and improper fractions. Take the stress out of their next math challenge with these mixed numbers and improper fractions worksheets!

Converting Mixed Numbers to Improper Fractions

Basic Math Operations | Building Fraction Sense | Math Worksheets

It’s time to start building new skills of  Converting Mixed Numbers to Improper Fractions. A full number and a certain fraction are combined to form a mixed number or mixed fraction.  For example, 2 1/7  is a mixed number where 2 is the whole number and 1/7 is the proper fraction.

An improper fraction is one in which the numerator is larger than the denominator and has an incorrect denominator. For example, 5/2 is an improper fraction.

Converting Mixed Numbers to Improper Fractions: Basic Idea

Parents can easily teach the idea of converting mixed numbers to improper fractions using simple steps.

The steps are given below:

1. Multiply the whole number by the denominator.

2. Add that number to the numerator.

3. Write that sum on top of the original denominator.

And we are done!

6 Unique Ideas for Converting Mixed Numbers to Improper Fractions

Converting mixed numbers to improper fractions is difficult for students of grade 4 or grade 6 and grade 7. Children can explore this idea clearly and practically by exploring the pdf of converting mixed numbers to improper fractions. This kind of education is essential if we want our right-brain students to acquire an idea in its entirety.

Introducing Shapes

Students understand shapes easily. Parents or teachers can teach them to convert mixed numbers to improper fractions through shapes.

Treasure Hunt Game

Everyone enjoys playing “treasure hunts.” During this procedure, parents or teachers make a question sheet like the one in the picture and give the dice to the students. They must change it into an improper fraction when the dice land on a mixed fraction.

They will receive 5 points if they choose the right answer; otherwise, they will lose 10 points for each incorrect response.


The word “BINGO” is written across the top of bingo scorecards, which include 25 fractions. Five of those squares must be filled in a row, either vertically, horizontally, or diagonally.

The player who declares mixed fractions, such as 12 1/8, is known as the caller, and the players will figure out the improper fractions.

A player will shout “Bingo” to the other players to let them know they have won when they have five covered squares in a row on their scorecard. The caller will stop creating new pairings if “Bingo” 

Gumball Mixed Fractions

I have a gumball machine at home.

I created some gumballs with mixed fraction printing. Then I tell them that if they want gumballs, they must find the improper fraction and take it.

If not, they won’t get any gum.

Word Problems

Students must have a variety of word-problem experiences in order to answer the questions with a lot of text. To learn converting mixed fractions into improper, word problems are important.


Quiz Time!

It’s time to select the right solution!

Math skills among children are enhanced and engaged by this kind of practice. A test like this can be created by teachers. Quizzes can be used in the classroom to repeat lessons and get students ready for the next level of learning.

Download Free Printables PDF

I  have gone over several methods for Converting Mixed Numbers to Improper Fractions during the discussion. I’m hoping that students can improve their problem-solving abilities by participating in these exercises of Converting Mixed Numbers to Improper Fractions. Listed below are a few exercises.

It is an excellent way to give kids an enjoyable way to practice Converting Mixed Numbers to Improper Fractions.

Download the attached PDF and have fun playing with the children. 




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«Addition and subtraction of mixed numbers». 6th grade





1) To develop the skills and abilities of students
in addition and subtraction of mixed numbers;

2) Develop logical thinking

3) To cultivate industriousness, perseverance,

Equipment: sheets — assignments
(Appendix 1) (for each student).

Course of the lesson

I. Organization of the lesson.

Motto: “If there was a hunt, they would argue
Any work».

( Write on the board ).

1) Cooked on the table
assignment sheets, on which you will write diaries.

2) On the left side of the sheet you see circles, on
them you will rate yourself, on one neighbor,
on the other teacher, if he sees fit.

– Today we have an open lesson, regular
lesson. Please answer all questions clearly

Guests not only from our school, but also from

II. Homework check:

1) Domino game.

III. Updating of basic knowledge.

1. What are fractions? What are
common fractions? name the correct and
improper fractions and mixed numbers.

2. Read an improper fraction and
represent it as a mixed number:

3. Express as incorrect

IV. Make block diagrams of the algorithm
adding mixed numbers.

(Appendix 2)


Setting the objectives of the lesson.

— Today we will look at more
difficult cases of adding mixed numbers and we will
practice skills.

VI. Formation of skills and abilities

– How to subtract a fraction from a whole number? 1)

2) Find the value of the expression:

Solve the equations:

— How to find the unknown first term?

– How to find the unknown minuend?

4) In the state farm «Spring» in one day, students
harvested carrots,
and less on the other. How many tons of carrots were harvested
students in two days?


VII. Independent work with verification.

1. «Computer» — a game.

Whose «computing machine» counts quickly
and right?

VIII. Summary of the lesson.

Homework: item 12, learn
rules, No. 400 (b, d, f, h),

No. 401 (f, g, h),

No. 404 (task).

Appendix 1

Appendix 2

Mixed numbers, converting a mixed number to an improper fraction and vice versa, how to convert an improper fraction to a proper one

In this material we will analyze such a thing as mixed numbers. We start, as always, with a definition and small examples, then we will explain the connection between mixed numbers and improper fractions. After that, we will learn how to correctly extract the integer part from a fraction and get an integer as a result.

The concept of a mixed number

If we take the sum n + ab, where the value of n can be any natural number, and ab is a proper ordinary fraction, then we can write the same thing without using a plus: nab. Let’s take specific numbers for clarity: for example, 28 + 57 is the same as 2857. Writing a fraction next to an integer is usually called a mixed number.

Definition 1

The mixed number is a number that is equal to the sum of a natural number n with a regular fraction ab. In this case, n is the integer part of the number, and ab is its fractional part.

It follows from the definition that any mixed number is equal to what will result from the addition of its integer and fractional parts. Thus, the equality nab=n+ab will be fulfilled.

It can also be written as n+ab=nab.

What are some examples of mixed numbers? So, 518 belongs to them, while five is its whole part, and one-eighth is a fractional one. More examples: 112, 2343453, 34000625.

Above, we wrote that the fractional part of a mixed number should contain only a proper fraction. Sometimes you can find entries like 5223, 7572. They are not mixed numbers, because their fractional part is wrong. They need to be understood as the sum of an integer and a fractional part. Such numbers can be reduced to standard mixed numbers by taking the integer part of the improper fraction and adding it to 5 and 75 in these examples, respectively.

Numbers like 0314 are also not mixed. The first part of the condition is not fulfilled here: the integer part must be represented only by a natural number, and zero is not.

How improper fractions and mixed numbers relate to each other

This relationship is easiest to follow with a specific example.

Example 1

Let’s take a whole cake and three more quarters of the same. According to the addition rules, we have 1 + 34 cakes on the table. This amount can be represented as a mixed number as 134 cakes. If we take a whole cake and also cut it into four equal parts, then we will have 74 cakes on the table. It is obvious that the quantity did not increase from cutting, and 134=74.

Our example proves that any improper fraction can be represented as a mixed number.

Let’s go back to our 74 cakes left on the table. Let’s put one cake back from its pieces (1 + 34). We will again have 134.

Answer: 74=134.

We figured out how to convert an improper fraction to a mixed number. If the numerator of an improper fraction contains a number that can be divided by the denominator without a remainder, then you can do this, and then our improper fraction will become a natural number.

Example 2

For example,

84=2 because 8:4=2.

How to convert a mixed number into an improper fraction

To successfully solve problems, it is useful to be able to perform the reverse action, that is, to make improper fractions from mixed numbers. In this paragraph, we will analyze how to do it correctly.

To do this, you need to reproduce the following sequence of actions:

1. To begin with, we represent the existing mixed number nab as the sum of the integer and fractional parts. It turns out n+ab

2. Next, replace the integer part with a fraction with a denominator equal to one (that is, write n as n1).

3. After that, we perform the already familiar action — we add two ordinary fractions n1 and ab. The resulting improper fraction will be equal to the mixed number given in the condition.

Let’s analyze this action using a specific example.

Example 3

Express 537 as an improper fraction.


We perform the steps of the above algorithm in sequence. Our number 537 is the sum of the integer and fractional parts, that is, 5 + 37. Now let’s write the five in the form 51. We got the sum 51 + 37.

The last step is to add fractions with different denominators:


The whole short form solution can be written as 537=5+37=51+37=357+37=387.

Answer: 537=387.

Thus, with the help of the above chain of actions, we can convert any mixed number nab into an improper fraction. We have obtained the formula nab=n b+ab, which we will use to solve further problems.

Example 4

Express 1525 as an improper fraction.


Take the indicated formula and substitute the required values ​​into it. We have n=15, a=2, b=5, so 1525=15 5+25=775.

Answer: 1525=775.

How to extract the integer part from an improper fraction

Usually we do not indicate an improper fraction as a final answer. It is customary to bring the calculations to the end and replace it with either a natural number (dividing the numerator by the denominator) or a mixed number. As a rule, the first method is used when it is possible to divide the numerator by the denominator without a remainder, and the second — if such an action is impossible.

When we extract the whole part from an improper fraction, we simply replace it with an equal mixed number.

Let’s see how exactly this is done.

Definition 2

Any improper fraction ab is a mixed number qrb. Here q is the partial quotient and r is the remainder of ab. Thus, the integer part of the mixed number is the incomplete quotient of the division of ab, and the fractional part is the remainder.

We present a proof of this assertion.

We need to explain why qrb=ab. To do this, the mixed number qrb must be represented as an improper fraction by following all the steps of the algorithm from the previous paragraph. Since is an incomplete quotient, and r is the remainder of dividing a by b, then the equality a=b q+r must hold.

So q b+rb=ab, so qrb=ab. This is the proof of our assertion. Let’s summarize:

Definition 3

Extraction of the integer part from improper fraction ab is carried out in the following way:

1) divide a by b with remainder and write the incomplete quotient q and remainder r separately.

2) Write the results as qrb. This is our mixed number, equal to the original improper fraction.

By alexxlab

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