Presentation on common fractions. What is a share

Topics: Lesson 1 “Shares” and “What is a fraction” Lesson 1 Lesson 2 “The basic property of a fraction” and “Reducing fractions to a common denominator” Lesson 2 Lesson 3 “Comparison of fractions” and “Addition of fractions” Lesson 3 Lesson 4 “Subtraction, multiplication and division of fractions »Lesson Ordinary fractions

Lesson 1 Shares Mom bought a watermelon and cut it into 6 equal parts: grandma, grandpa, dad, mom, two children. These equal parts are called shares, since the watermelon was divided into 6 equal parts, each received one sixth of the watermelon, it is written like this

What is a fraction Ordinary fractions A rectangle is divided into 3 equal parts, two thirds of this rectangle is shaded. To designate such a record, a special “two-story” record is used. Such a record is called a fraction.

The number below, under the line, shows how many equal parts were divided. It is called the denominator. The number above, above the line, shows how many of these parts were taken. It is called the numerator of a fraction. Ordinary fractions 5

A fraction whose numerator is less than the denominator is called a proper fraction. A fraction whose numerator is greater than or equal to the denominator is called an improper fraction. Ordinary fractions 6

Fix: The circle is divided into 6 equal parts, each part makes up a circle. How many parts of the circle are shaded? What part of the square is shaded? Common fractions 7

Lesson 2 The main property of a fraction Ordinary fractions Divide the circle into 4 equal parts and paint 3 of them. The shaded part is a circle. If now every fourth circle is divided into 2 more equal parts, then the circle will be divided into 8 equal parts and 6 of them will be painted over. So now the circle is painted over.

In both cases, the same part of the circle is shaded, which means that the fractions express the same value. Such fractions are called equal. REMEMBER: If the numerator and denominator of a fraction are multiplied or divided by the same non-zero number, the result is a fraction equal to the given one. To reduce a fraction, its numerator and denominator must be divided by their common divisor Common Fractions

Ordinary fractions Bringing fractions to a common denominator When solving problems, fractions that have different denominators have to be replaced by equal fractions with the same denominators, while trying to choose the smallest common denominator.

For example, consider the common denominator of a fraction. The larger denominator - the number 24 - is divisible by the smaller one, so it can be taken as a common denominator of these fractions. Now we need to bring the fraction to the denominator 24. Let's find an additional factor 24:8=3. So ordinary fractions

Ordinary fractions IMPORTANT! as a common denominator of fractions, you can always take the product of their denominators FIXED Bring to the common denominator of the fraction: = ; = Back to top

Ordinary fractions Lesson 3 Comparing fractions Compare 2 unequal fractions - this means to establish which of them is greater and which is less. If we divide an apple into 5 equal parts, then 2 parts will make up a smaller part of the apple than 3 equal parts. Means

Ordinary fractions The considered example allows us to conclude: of two fractions with the same denominator, the one with the larger numerator is larger, and the one with the smaller numerator is smaller. IMPORTANT! To compare fractions with different denominators, they must first be reduced to a common denominator.

Ordinary fractions Check yourself: Compare fractions:

Ordinary fractions Adding fractions With fractional numbers, as well as with natural numbers, you can perform arithmetic operations. Consider first the addition of fractions

Ordinary fractions To add fractions with the same denominators, you need to add their numerators, and leave the denominator the same. To add fractions with different denominators, they must first be reduced to a common denominator.

Ordinary fractions Fix it Add fractions: i) To the beginning

Ordinary fractions Lesson 4 Subtracting fractions Subtracting fractional numbers, like natural numbers, is determined on the basis of addition operations: subtracting another from one number means finding a number that, when added to the second, gives the first. For example:

Common Fractions Remember! To find the difference between fractions with the same denominators, subtract the numerator of the second fraction from the numerator of the first fraction, and leave the denominator the same. Important! To find the difference between fractions with different denominators, they must first be reduced to a common denominator. Common fractions Multiplication of fractions Remember! To multiply a fraction by a fraction, you need to multiply the numerator by the numerator and the denominator by the denominator.

Division of fractions The product of reciprocal fractions is Ordinary fractions

This explains the rule for dividing fractions: To divide a fraction by a fraction, you need to multiply the dividend by the reciprocal of the divisor. For example, ordinary fractions
Ordinary fractions Thank you for your attention The presentation was created according to the textbook MATHEMATICS Grade 5 (edited by G.V. Dorofeev, I.F. Sharygin, 12th edition Moscow “Enlightenment”) Author of the presentation: Almukhametova D.Sh.

The use of ICT in mathematics lessons

Equipment:

1. the teacher has a computer, a multimedia projector;
2. students have notebooks, textbooks, pencils, colored pencils, rulers.

During the classes

Organization of the class for the lesson.

(self-check on the slide).

Work in notebook No. 868.

Read the assignment. What needs to be done? (You need to draw a square with a side of 6 cells, divide it into 3 parts and paint over two thirds). In how many ways can a square be divided into three equal parts? (A square can be divided into three equal parts in two ways). Students complete the task on their own. Self-test byslide 24.

How did fractional numbers appear?

It was not always possible to express the result of measurement or the cost of goods in natural numbers. This is how fractions were born. At first, people used the simplest fractions, , .Thus, fractional numbers have joined the family of natural numbers.

In Russian, the word fraction appeared in the 8th century, it came from the word “crush” to break into pieces, to break.

In the first mathematics textbooks of the 17th century, fractions were called “broken” numbers. The line in fraction writing began to be used about 300 years ago.

In the old days in Russia, coins with a denomination of less than one kopeck were used: a penny -pennies and pennies - pennies.

An interesting system of fractions was in ancient Rome. It was based on a division into 12 parts of a unit of weight, which was called ass.

And for the fractions obtained by splitting the twelfths into smaller ones, there were special names. Even now, sometimes they say: “He scrupulously studied this issue,” which means that the issue has been studied to the end. And a strange word comes scrupulously from the Roman nameassa - "scrupulus".

Summary of the lesson.

What is a share? (Share - each of the equal parts of the unit)

What determines the name of the share? (The name of the share depends on how many equal parts the unit was divided into)

What are common fractions? Give examples of ordinary fractions. (Records of the form, called common fractions)

What is the name of the number that is written above the fractional bar? What is the name of the number that is written under the fractional bar? (The number that is written above the line is called the numerator, below the line is the denominator)

What do the numerator and denominator of a fraction show? (The denominator shows how many shares are divided, and the numerator shows how many such shares are taken)

Slides captions:

Come on, check my friend, are you ready to start the lesson? Is everything in place, Is everything in order, Pen, book and notebook? Is everyone seated correctly? Is everyone watching closely? Everyone wants to receive only a mark of five.

Shares Ordinary fractions

Goals and objectives: Introduce the concept of a fraction, half, third, quarter, ordinary fraction, numerator and denominator of a fraction Develop the ability to read and write an ordinary fraction by numerator and denominator Cultivate a respectful attitude towards others, attention

Questions to consider: Share Half, third, quarter Ordinary fraction What the numerator and denominator of a fraction show From the history of fractions

Mom bought a watermelon. I cut it into 6 equal parts:

grandmother, grandfather, father, two children and myself.

What is a share? A fraction is each of the equal parts of a unit. Since the watermelon was cut into 6 equal parts, then it was divided into 6 shares and each received "one sixth" of the watermelon, or, in short, "one sixth of the watermelon."

How are shares recorded? A horizontal line is used to record any beat. It is called a fractional line. They write:

What does the number below the line show? The number under the line shows how many equal parts (shares) the unit was divided into 5 equal parts (shares)

Think and answer. How shares are formed When one object or unit of measurement is divided into equal parts. What the number under the line shows The number under the line shows how many equal parts the unit was divided into.

Half. The most famous share is, of course, half. Words with the prefix "floor" can often be heard: half an hour, half a kilometer ... They divided the whole into two parts - "half". The share is called half.

Third. The name of the share depends on how many equal parts the unit is divided into. Divided into three parts - "third". The share is called "third"

Quarter. If the whole is divided into 4 parts, then it turns out or in another way they say "quarter".

What are the other shares called? And if you divide it into five parts, then what is “five”, into six - “six”? There are no such funny words in Russian. To name the shares use the words "fifth", "sixth"

Complete the tasks. Read the shares How else can you call the shares a quarter, a third, a half.

We were overwhelmed by drowsiness, Reluctance to move Well, do this exercise with me: One - got up, stretched, Two - bent over, straightened, Three - three claps in your hands Three nods with your head.

Solve the puzzle and find out what we are going to get acquainted with now. "Fractions"

Ordinary fraction. Entries of the form are called ordinary fractions ... Numerator of a fraction Bar of a fraction (fractional bar) Denominator of a fraction

Ordinary fractions. Everyone can see a fractional line from a mile away. Above the line - the numerator, you know, Below the line - the denominator. Such a fraction, of course, must be called ordinary. Name the numerator and denominator of each fraction

When reading fractions, one must remember: the numerator of a fraction is a quantitative feminine numeral (one, two, eight, etc.), and the denominator is an ordinal number (seventh, hundredth, two hundred and thirtieth, etc.) For example: - one fifth; - two sixths; - eighty three hundred fifty second

What do the numerator and denominator of a fraction show? The denominator shows how many shares are divided, and the numerator shows how many such shares are taken. Read fractions. What does the numerator and denominator of each fraction show?

Write it as an ordinary fraction. Two sevenths Four ninths One hundredth Six eighths Three twenty-fifths Half

Think and answer. What part of the figure is shaded?

Work in a notebook. No. 868.

Homework: Make assignments on the topic of ordinary fractions, p. 23, No. 901, 902 The lesson is over. And again a change. And the noise in the corridor again. We must have time to each other without fail Tell about everything as soon as possible