Finding a fraction of a number - examples for solving. How to find a fraction from a number. Finding a number by its fraction

Finding a fraction from a number is performed when a certain number is known, but the part of the number, which is expressed by the number of fractions of the whole, is not known.

Since a fraction is a part of a number, and a number is a natural or named number, then finding a fraction of a number is the calculation of that part of a number that is determined only by a fraction.

Part of a number is found by multiplication.

Rule. To find a fraction of a number, you need to multiply the number by that fraction.

If part of a number is a proper fraction, then the result of the calculation is less than the given number.

If part of a number is a mixed or improper fraction, then the result of the calculation is greater than the given number .

Finding a number by its fraction is performed when the number is unknown, but part of the number is known, which is expressed as fractions of the whole.

A number by its part is found by division.

Rule. To find a number by its fraction, you need to divide the number representing the fraction by that fraction

If part of the number is expressed as a proper fraction, then the result of the calculation is greater than the given number (24).

If part of a number is represented by a mixed or improper fraction, then the result of the calculation is less than the given number (2 > 1, 96 Timur says:

In some school textbooks, as well as on your website, the topic “finding a number from its fraction” appears. This formulation of the question is incorrect. And if, reading a 6th grade textbook, one can assume that the word “fraction” does not correctly replace the concept of fraction or part, then after reading this topic on your website it becomes clear that the very concept of a fraction is given incorrectly. A fraction is not part of a number at all, a fraction is a part (or several parts) of a UNIT.

How to find a fraction from a number

Let's look at the rule that explains how to find a fraction of a number and its application with examples.

To find a fraction of a number, you need to multiply the number by this fraction.

Find a fraction from a number:

To find a fraction of a number, you need to multiply the number by that fraction. We multiply them according to the rule for multiplying a number by a fraction: we multiply the numerator by the number, and leave the denominator unchanged. We reduce 30 and 6 by 6. Thus,

To find a fraction of a number, multiply the number by the fraction. 48 and 8 are reduced by 8.

To find four sevenths of 28, multiply the fraction by the number. We reduce 28 and 7 by 7 and multiply.

How to find the decimal fraction of a number? Likewise, multiplying a fraction by a number. For example,

www.for6cl.uznateshe.ru

Finding a fraction from a number
finding a number from the known magnitude of its fraction

There are a number of problems in which you need to find a part or fraction of a certain number. Such problems are solved by multiplication based on the following rule:

To find a fraction of a given number, you need to multiply that number by the fraction.

Exercise. Find from 40.

Solution. In the example under consideration, 40 is a given number, a fraction that specifies the required part. Then, according to the rule, we have:

So, we found that 40 equals 14 - the required part of this number.

Answer. 40 equals 14.

Sometimes it is necessary to determine the entire number using a known part of a number and the fraction that expresses this part. Such problems are solved by division.

To find a number based on the known value of its fraction, you need to divide the given value by the fraction.

Exercise. There are 12 boys in the class, which makes up a portion of the entire class. How many people are in the class?

Solution. Required number of students

Answer. There are 15 people in the class in total.

14. Finding a fraction from a number. Rules

There are 20 apples in a basket. Petya took

from this amount.
How many apples did Petya take?

Divide all apples by 5 and get one fifth of all apples:

Answer: Petya took 8 apples.

To find a fraction of a number, you need to multiply the number by that fraction.

By finding a fraction of a number we mean
finding that part of a number that is expressed as a fraction.

The tourists covered 60 km in a day. Moreover

part of the way they moved on
bicycles, and the rest on foot. How far did the tourists travel?

Answer: tourists traveled 55 kilometers.

Problems on the topic “Finding a fraction from a number”

These vehicles are passenger cars, the rest are trucks.
How many times were there fewer trucks in the car dealership than cars?

Igor prepared for the city math Olympiad for a month. During this time he needed to solve 120 problems. In the first 10 days (decade) he solved 4/15 of these problems, in the second decade - 5/8 of the remaining problems. How many problems must Igor solve in the last 10 days?

A train ticket for an adult costs 720 rubles. The cost of a ticket for a student is 1/3 of the cost of an adult ticket. How much are tickets for a group of 2 adults and 10 schoolchildren?

The wholesale price of a jar of cucumbers is 50 rubles. The retail price is 18% more than the wholesale price. How much does 4 jars of cucumbers cost at retail?

City N has 200,000 inhabitants. Among them, 15% are children and adolescents. Among adult residents, 9/20 do not work (pensioners, students, housewives). How many adult residents work?

school-assistant.ru

Finding a number by its fraction

If you know how much a part of the whole is, then from the known part you can “restore” the whole.

To do this, we use the rule of finding a whole (number) from its fraction (part).

To find a number by its part expressed as a fraction, you need to divide this number by the fraction.

Example. Let's consider the problem.

The train traveled 240 km, which amounted to

all the way. Which route should the train take?

Solution. 240 km is part of the entire journey. These same kilometers are expressed as a fraction of 15/23 of the entire journey. The denominator of the fraction indicates that the entire path is divided into 23 parts, and 15 such parts make up 240 km (the numerator of the fraction is 15).
So, you can find how much is

This means that to find the entire path (23 parts, each of which is 16 km) you need:

Briefly recording the solution to such a problem can be done as follows.

Answer: the train must travel 368 km.

Complex problems to find a number from its part

Often problems of this type are more complex than the problem discussed above, and more complex tasks have to decide in several steps.

In preparation for the dictation English language Olya learned a quarter of all the words assigned by the teacher. If she had learned 4 more words, then a third of all words would have been learned. How many words did Ole need to learn?

Solution. As usual, we emphasize all the important data in the problem statement.

As can be seen from the condition, four unlearned words are the part of all words that can be found in the form of a difference of fractions.

The rule for finding a number by its fraction:

To find a number by given value its fractions, you need to divide this value by the fraction.

Let's look at how to find a number by its fraction, using specific examples.

Examples.

1) Find a number whose 3/4 are equal to 12.

To find a number by its fraction, divide the number by that fraction. To do this, you need to multiply this number by the inverse of the fraction (that is, by an inverted fraction). To do this, you need to multiply the numerator by this number and leave the denominator unchanged. 12 and 3 by 3. Since we got one in the denominator, the answer is an integer.

2) Find a number if 9/10 of it equals 3/5.

To find a number given the value of its fraction, divide this value by this fraction. To divide a fraction by a fraction, multiply the first fraction by the inverse of the second (inverted). To multiply a fraction by a fraction, multiply the numerator by the numerator, and the denominator by the denominator. We reduce 10 and 5 by 5, 3 and 9 by 3. As a result, we get the correct irreducible fraction, which means this is the final result.

3) Find a number whose 9/7 are equal

To find a number by the value of its fraction, divide that value by that fraction. Mixed number and multiply it by the inverse of the second number (inverted fraction). We reduce 99 and 9 by 9, 7 and 14 by 7. Since we received an improper fraction, we need to separate the whole part from it.

So, let us be given some integer a. We need to find, for example, a fifth of this number. This can be done using ordinary fractions:

• Since we need to find a fifth of a number, we are looking for 1/5 of a.
• To find 1/5 of the number a, we must multiply the number a by the part that we need to find, that is, perform the action: a * 1/5 = a/5. That is, a fifth of the number a is a/5.
• Moreover, if we are looking for a part of a whole number, then the result will be less than the original number.

There may be different problems in finding a part of a whole: if you need to find, for example, a tenth of the number a, then you need a * 1/10 = a/10. If you need to find 1/8 of the number a, then you need a * 1/8 = a/8.
Finding any part of a whole is done by multiplying the given integer by the part that needs to be found.
Let's consider a specific example to further memorize the solution.

How to find the sixth part of the number 36

We are given an integer - the number 36. We need to find the sixth part of it, otherwise we need to find 1/6 of the number 36. Let us perform the operation of multiplying the whole by the part: 36 * 1/6 = 6. So the sixth part of the number 36 is the number 6. You can also say the following: the number 36 is exactly six times greater than the number 6, or the number 6 is exactly six times less than the number 36.

To find a part of any number, it must be divided by the size of that part. The steps involved will vary depending on the form in which the fraction is written;

With an ordinary fraction:

If the numerator of a common fraction is divisible by a given size of the part without a remainder, then it is sufficient to simply divide the numerator by this given size;

If the numerator cannot be divided without a remainder into a given part, then the denominator must be multiplied by the size of this part; With a mixed fraction: We do the same as with an ordinary fraction, but first we need to convert the mixed fraction into an ordinary fraction. With a decimal: The calculation will consist of a single division operation. A decimal fraction can be divided into a given part size into a column.

To solve this task, let’s remember what a fraction of a number is equal to and use an example to show how to find a fraction of a number.

Finding a fraction from a number

Fractions in mathematics are used to denote part of a quantity. This value is the whole number from which the part was taken. Knowing what a whole quantity is equal to, you can find its part. In order to find a fraction, that is, a part of a number, you need to multiply this number by this fraction.

Finding a fraction from a number using an example

Problem: There are 30 students in the class. 1/3 of all students are girls. Calculate the number of girls in the class.

In this problem, the integer value is the number of students in the class - 30, and the fraction, that is, the part - 1/3. In order to calculate the number of girls in a class, we must multiply the fraction 1/3 by the total value - 30.

30 * 1/3 = 30/1 * 1/3 = 30 * 1 / 1 * 3 = 30 / 3 = 10 students.

To multiply a whole number by a fraction:

• represent an integer as a fraction (30 = 30/1).
• Multiply the numerator of the first fraction by the numerator of the second fraction.
• multiply the denominator of the first fraction by the denominator of the second fraction.
• Write the first product in the numerator of the new fraction, and the second in the denominator.

In the process of solving problems 149–156, it is necessary to bring students to an understanding of the rule for finding part of a number:

To find the part of a number expressed as a fraction, you can divide this number by the denominator of the fraction and multiply the resulting result by its numerator.

Of course, students can formulate this rule only for specific situations: to find 3 / 4 number 24, you can divide this number by the denominator fractions 4 And multiply the resulting result by the numerator 3.

149 . a) 12 birds were sitting on a branch; 2/3 of their number flew away. How many birds flew away?

b) There are 32 students in the class; 3/4 of all students skied. How many students skied?

150 . a) The cyclists covered 48 in two days. km. On the first day they covered 2/3 of the entire route. How many kilometers did they travel on the second day?

b) Someone, having 350 rubles, spent 5/7 of his money. How much money does he have left?

c) The notebook has 24 pages. The girl wrote 5/8 of all pages of the notebook. How many unwritten pages are left?

151 . An ancient problem. Having bought a chest of drawers for 36 R., I was then forced to sell it for 7/12 of the price. How many rubles did I lose on this sale?

152 . Autotourists drove 360 ​​in three days km; on the first day they traveled 2/5, and on the second day - 3/8 of the entire journey. How many kilometers did the motor tourists travel on the third day?

153 . 1) There are 24 girls and several boys in the drama club. The number of boys is 3/8 the number of girls. How many students are in the drama club?

2) The collection contains 45 anniversary ruble coins. The number of 3 and 5 ruble coins is 2/9 of the number of ruble coins. How much in total commemorative coins in 1, 3 and 5 rubles in the collection?

Students must solve problems 154–156 by first finding the indicated part of a quantity, and then increasing or decreasing this quantity by the found part. Another solution will be shown later.

154 . 1) Reduce 90 rubles by 1/10 of this amount.

2) Increase 80 rubles by 2/5 of this amount.

155 . Last month the price of the product was 90 R. Now it has dropped by 3/10 of this amount. What is the price of the product now?

156 . Last month the salary was 400 R. Now it has increased by 2/5 of this amount. What is the salary now?

In the process of solving problems 157–158 and the following problems, it is necessary to lead students to understand and correctly apply the rule for finding a number by its part:

To find a number by its part expressed as a fraction, you can divide this part by the numerator of the fraction and multiply the resulting result by its denominator.

The formulation of this rule is complex due to the need
somehow call the number that we have named « part » . The authors of textbooks are forced to overcome this difficulty. So in the textbook I.V. Baranova and Z.G. Borchugova’s rule is formulated only for specific cases: to find a number, 3 / 5 which is 90 km, you need to divide 90 km by the numerator of the fraction 3 and multiply the resulting result by the denominator of the fraction 5.

This is how students can use it. True, when talking about number, it is better not to use names, since number and magnitude are not the same thing. Later in the same textbook on p. 226 is formulated general rule, in which the term we use « Part » corresponds to turnover « the number corresponding to it » , which is hardly easier.

157 . a) 120 R. constitute 3/4 of the available amount of money. What is this amount?

b) Determine the length of the segment, 3/5 of which is equal to 15 cm.

158 . a) My son is 10 years old. His age is 2/7 of his father's age. How old is father?

b) Daughter is 12 years old. Her age is 2/5 of her mother's age. How old is the mother?

The housewife spent 6 to buy vegetables R., which amounted to 1/6 of the money she had. Then she bought 2 kg apples 7 each R. per kilogram. How much money does she have left after these purchases?

160 . Father bought his son a suit for 24 R., on which I spent 1/3 of my money. After that he bought several books and had 39 left. R. How much did the books cost?

161 . The son is 8 years old, his age is 2/9 of his father's age. And the father’s age is 3/5 of the grandfather’s age. How old is grandpa?

162 .* From the Ahmes papyrus (Egypt, c. 2000 BC).

A shepherd arrives with 70 bulls. He is asked:

How many do you bring from your numerous flock?

The shepherd answers:

I bring two-thirds of a third of the cattle. Count it!

How many bulls are there in the herd?