Video lesson “Isolating the whole part from an improper fraction. Representing a mixed number as an improper fraction. Mixed fractions How to get a whole part from a regular fraction

How to separate the whole part from an improper fraction? and got the best answer

Answer from Katy[active]
In order to convert a number, you need to divide the numerator by the denominator with the remainder, i.e. find out how many “integer” times it contains. And this incomplete quotient will be a whole part. Then the remainder (if there is one) is given by the numerator, and the divisor is the denominator of the fractional part (to make it clearer, you need to multiply the denominator by the integer that you received earlier, and then subtract from the NUMERATOR what you now received)
For example: 136/28 = 4 whole 24/28, this is a reducible fraction = 4 whole 6/7
I divided 136 by 28 and got 4. Then, to find out the numerator, I multiplied 28 by 4 to get 112, and subtracted 112 from 136. To reduce, you need to divide both the numerator and the denominator by the same number (in this case it is 4)
Good luck!

Answer from Andrey Polyakov[newbie]
25/22, 22/22 is one whole, and that leaves 3/22, and then 1 whole and 3/22

Answer from CINEMAholic[guru]
divide the numerator by the denominator, the number before the decimal point is the whole part, then multiply the whole part by the denominator and subtract it from the original numerator. This figure will be the numerator.
for example: 88/16=5.5
16*5=80
88-80=8
5 8/16=5 1/2

Answer from Vadim Kulpinov[guru]

Answer from Anna[newbie]
for example 1000/9.... you easily divide 1000 by 9... you get 111, which is an integer and the remainder goes to the numerator and the denominator remains the same 9....

Answer from Єranche[newbie]
try to calculate it on a calculator))
Divide the numeral by the denominator and write the number to the left of the decimal point.
if you need to select the fractional part:
You multiply the selected integer part by the denominator and subtract the resulting number from the numerator. That is:
79/3
1. select the whole part: 26
2. multiply the selected integer part by the denominator: 26*3
3. subtract the resulting number from the numerator 79-(26*3)
yay.

Answer from Alexey Laukhtin[guru]
Divide the numerator by the denominator and write the resulting number as an integer and the remainder as the numerator and the denominator remains the same.

Answer from Yoman Geiko[expert]
Damn, I learned how to do this first. Only then did the Internet appear, I learned how to use it correctly and it was not long before I found this site)

Answer from _DaFNa_[active]
for example, 23/3 - divide the numerator by the denominator using a calculator (if you have one nearby), take the first number, multiply by the denominator and get the whole part of this fraction. From the numerator you subtract the number that was obtained when multiplied by the denominator, and you get a proper fraction. In your answer, write the whole part and the proper fraction next to it.
If there is no calculator nearby, then you divide a little intuitively and then do the same.
The best fractions are those whose denominator is 2, 5 or 10 :)

Answer from Le chiffre[expert]
You highlight how many times the denominator fits in the numerator, then subtract the denominator from the numerator, the denominator remains unchanged.

Answer from Alexey Antoshechkin[newbie]
233 divide by the number and we know, take the first number and multiply

Answer from Mi S Slonopotam[guru]
Divide the numerator by the denominator - you get the whole part and the remainder (fraction)

Answer from Elena[active]
It seems correct about 3/2. You just need to divide the numerator by the denominator with the remainder. Then the quotient is the whole part, the remainder is the numerator, and the divisor is the denominator (i.e., it remains as it was). For example
48/13. Divide 48 by 13 to get 3 and the remainder is 9. So 48/13=3 whole 9/13
Source: mathematics

Answer from Pavel Chuprakov[newbie]

Answer from Sergei Nesterenko[newbie]
1) To convert an improper fraction into a mixed fraction, you need to: divide the numerator by the denominator with a remainder using a column, the incomplete quotient is the whole part, the remainder is the numerator and the denominator is the same.
2) To turn a mixed fraction into an improper one, you need to: multiply the whole part by the denominator and add the numerator, the resulting number goes into the numerator, but the denominator remains the same.

Answer from tanyusha lint[newbie]
To isolate the whole part from an improper fraction, you need to divide the resulting numerator by the denominator
write the number as an integer part, and the remainder as the numerator, and the denominator is the same.

has a numerator greater than the denominator. Such fractions are called improper.

Remember!

An improper fraction has a numerator equal to or greater than its denominator. That's why improper fraction

or equal to one or greater than one.

Any improper fraction is always greater than a proper fraction.

How to select an entire part

An improper fraction can have a whole part. Let's look at how this can be done.

1. To isolate the whole part from an improper fraction, you need to:
2. divide the numerator by the denominator with the remainder;
3. we write the resulting incomplete quotient into the whole part of the fraction;
4. write the remainder into the numerator of the fraction;

We write the divisor into the denominator of the fraction.

11

2

.

Remember!

Example. Select the whole part from the improper fraction The resulting number above, containing an integer and a fractional part, is called.

We got a mixed number from an improper fraction, but we can also do the opposite operation, that is represent a mixed number as an improper fraction.

To represent a mixed number as an improper fraction:

1. multiply its integer part by the denominator of the fractional part;
2. add the numerator of the fractional part to the resulting product;
3. write the resulting amount from point 2 into the numerator of the fraction, and leave the denominator of the fractional part the same.

Example. Let's represent a mixed number as an improper fraction.

§ 1 Isolating the whole part from an improper fraction

In this lesson you will learn how to convert an improper fraction into a mixed number by highlighting the whole part, and also vice versa to obtain an improper fraction from a mixed number.

First, let's remember what a mixed number and an improper fraction are.

A mixed number is a special form of writing a number that contains an integer and a fractional part.

An improper fraction is a fraction whose numerator is greater than or equal to its denominator.

Let's consider the problem:

We will divide 8 candies among three children. How much will each person get?

To find out how many candies each child will receive, you need to

But it is not customary to write an improper fraction in the answer. It is first replaced either by an equal natural number (when the numerator is divisible by the denominator), or by the so-called separation of the whole part from the improper fraction (when the numerator is not divisible by the denominator).

Isolating an integer part from an improper fraction is replacing the fraction with an equal mixed number.

To separate the whole part from an improper fraction, you need to divide the numerator by the denominator with a remainder. In this case, the incomplete quotient will be the whole part, the remainder will be the numerator, and the divisor will be the denominator.

Let's return to the task.

So, we divide 8 by 3 with a remainder, we get 2 in the incomplete quotient and 2 in the remainder.

§ 2 Representation of a mixed number as an improper fraction

Let's do the following task:

Divide 49 by 13, we get 3 in the incomplete quotient (this will be the integer part) and the remainder 10 (we will write this in the numerator of the fractional part).

To perform various operations with mixed numbers, the skill of representing mixed numbers as improper fractions is useful. It's time to figure out how such a translation is carried out.

To represent a mixed number as an improper fraction, you need to multiply the denominator of the fraction by the whole part and add the numerator to the resulting product. As a result, we get a number that will be the numerator of the new fraction, and the denominator remains unchanged.

The first step is to multiply the whole part of 5 by the denominator 7, we get 35.

The second step is to add the numerator 4 to the resulting product 35, it will be 39.

Now let's write 39 in the numerator and leave 7 in the denominator.

Thus, in this lesson you learned how to convert an improper fraction into a mixed number; to do this, you need to divide the numerator by the denominator with a remainder. Then the incomplete quotient will be the integer part, the remainder will be the numerator, and the divisor will be the denominator of the fractional part of the mixed number.

You also learned about representing a mixed number as an improper fraction. In order to represent a mixed number as an improper fraction, you need to multiply the denominator of the fractional part of the mixed number by the whole part and add the numerator to the resulting product.

List of used literature:

1. Mathematics 5th grade. Vilenkin N.Ya., Zhokhov V.I. and others. 31st ed., erased. - M: 2013.
2. Didactic materials for mathematics grade 5. Author - Popov M.A. - year 2013
3. We calculate without errors. Work with self-test in mathematics grades 5-6. Author - Minaeva S.S. - year 2014
4. Didactic materials for mathematics grade 5. Authors: Dorofeev G.V., Kuznetsova L.V. - 2010
5. Tests and independent work in mathematics grade 5. Authors - Popov M.A. - year 2012
6. Mathematics. 5th grade: educational. for general education students. institutions / I. I. Zubareva, A. G. Mordkovich. - 9th ed., erased. - M.: Mnemosyne, 2009

Lesson summary in 5th grade

“Mixed numbers. Isolating the whole part from an improper fraction"

During the classes

Organizing time. Greetings.

We will conduct an oral count and break all the records.

Verbal counting.

Find the mistakes

Proper fractions.

b)

Let's write down on the board what we can't compare yet.

2. Perform division:

45: 9=5 ; 0: 67=0; 234: 1=234;

567: 567=1; 34:17=2; a:a=1;

3. Perform division with remainder:

6 = 2 (remaining 2)

3 = 8 (remaining 1)

48: 9 = 5 (remaining 3)

Follow these steps:

We can't solve the last example, so let's write it out.

Explanation of new material

What is shown in the picture? How many parts was the cake divided into? How many parts did you take? Express it as a fraction.

What's in this picture? You can see that the cake is on different trays. How many pieces are on the first tray? Second?

Can be expressed as a number like this:

1 – integer part, - fractional part.

The sum of the integer and fractional parts is calledThe resulting number above, containing an integer and a fractional part, is called .

Determine from the picture which mixed number is equal to the fraction?

That is, we saw the connection between an improper fraction and a mixed number.

Let's draw conclusions: we can turn an improper fraction into a mixed number, i.e. as they say in mathematics, to separate the whole part from an improper fraction.

The rule for separating the whole part from an improper fraction:

Divide the numerator by the denominator with the remainder

The incomplete quotient will be the whole part

The remainder is the numerator, and the divisor is the denominator of the fraction.

Work on the topic of the lesson.

Select the whole part from an improper fraction (along with class):

Select the whole part from an improper fraction (at the board)

Compare

Historical information.

In the old days, coins in denominations of less than one kopeck were used in Rus':

penny - k. Andhalf - k.

Other coins also had names:

3 k. - altyn, 5 k. - nickel, 15 k. - five altyn,

10 kopecks - ten kopecks, 20 kopecks - two kopecks,

25 k. - a quarter, 50 k. - fifty kopecks.

Independent work

How can you imagine

1 hryvnia, 1 altyn, three half rubles .

Reflection

What's your mood?

Write the fraction that best matches your knowledge:

2 (can not understand anything)

2 (it was interesting, but not clear)

3 (difficult, the topic is not interesting)

3 (it was difficult, but I will definitely make an effort to study the topic)

4 (some examples caused difficulties)

4 (everything is clear, but I can’t help)

5 (everything is clear, I can help others)

I hope your grade will only increase with each lesson! And to get a grade of 5, you need to work not only in class, but also at home.

Homework.

Mathematics lesson in 4th grade topic: Isolating the whole part from an improper fraction Lesson topic: Isolating the whole part from an improper fraction. Didactic goal: to create conditions for the formation of new educational information. Therefore, we will start with repetition. Oral arithmetic Updating knowledge and skills Practical answers are written down in a column, we check the answers on the slides. pronounce in class Be able to sequence actions (Regulatory UUD). Be able to transform information from one form to another (Cognitive UUD). Be able to express your thoughts orally and in writing (Communicative UUD). Blitz survey: What rules did you use when: 1. Finding the sum of fractions. 2. Find the difference of fractions. 3. Find the number by part. 4. Find the part by number. They tell the rules. Participate in a conversation with the teacher. Be able to express your thoughts orally (Communicative UUD). Be able to navigate your knowledge system: distinguish the new from the already known with the help of a teacher (Cognitive UUD). The ability to self-assess on the criterion of success in educational activities (Personal UUD). based on the whole part of the fraction; write the remainder into the numerator of the fraction; write the divisor into the denominator of the fraction. 16:5 = 3 (rest. 1)) 3 – integer 1 – numerator 5 – denominator 16/5 = 3 1/5 Reading the rule in the textbook on P. 26, No. 3 – 1 example with explanation at the board. The rest with comments. No. 4 (a, b, c) - independently. Peer review. m is an integer, n and b are parts. In a fraction, the integer is always the numerator. The guys say the rule: to find a whole you need to multiply 6. Formulation of new knowledge. Let’s confirm our statement with a rule in the textbook. 7. Primary consolidation 8. Physical education lesson 9. Repetition of what has been learned Writing on the board: m/n = b Highlight where in the fraction the whole and the parts? How to find the whole? Applying the rule, we solve the equation. parts P. 28, task 10.