Fractions, fractions, definitions, notations, examples, operations with fractions. Math lesson summary: "Coordinate ray. Image of ordinary fractions on a coordinate ray"

Date of: 13/02/2017 ___________

Class: 5

Item: mathematics

Lesson No.: 129

Lesson topic: " Image of decimal fractions on coordinate ray.».

Goals and objectives of the lesson:

Educational:

Develop the ability to represent decimal fractions with points on a coordinate beam, find the coordinates of points depicted on a coordinate beam;

Educational:

– continue to work on developing: 1) skills to observe, analyze, compare, prove, and draw conclusions; 2) mathematical and general outlook; 3) evaluate your work;

Educational:

– develop the ability to express one’s thoughts, listen to others, conduct dialogues, defend one’s point of view; develop self-esteem skills.

During the classes

I. Organizing time , greetings, wishes for fruitful work.

Check if you have prepared everything for the lesson.

II. Setting lesson goals.

Guys, look carefully at the topic of today's lesson. What do you think we will do in class today? Let's try to formulate the goals of the lesson together.

III. Updating knowledge.All students write in notebooks, one student behind a closed board. The teacher checks the work on the board, after which all students compare and correct mistakes.

1) Mathematical dictation.

1. Three point one tenth.

2. Five point eight.

3. One point five.

4. Zero point seven.

5. Seven point twenty-five hundredths.

6. Zero point sixteen.

7. Three point one hundred twenty-five thousandths.

8. Five point twelve.

9. Ten point twenty four hundredths.

10. One point three.

Answers:

7. 3,125

9. 10,24

2) Oral work

(1) Read the decimals:

3) Let's remember!

To mark a point on a coordinate ray, you need...

What letter marks a point on a coordinate ray?

How is the coordinate of a point written?

3. Studying new material.

Decimal fractions on a coordinate ray are depicted in the same way as ordinary fractions.

(2) 1) Let us depict on the coordinate ray decimal 3,2.

The number 3.2 contains 3 whole units and 2 tenths of a unit. First, mark a point on the coordinate ray corresponding to the number 3. Then divide the next unit segment by ten equal parts and count two such parts to the right from the number 3. So we get point A on the coordinate ray, which represents the decimal fraction 3.2. The distance from the origin to point A is equal to 3.2 unit segments (A = 3.2).

Let us depict the decimal fraction 3.2 on the coordinate ray.

2) Let us depict the decimal fraction 0.56 on the coordinate ray.

4. Consolidation of the studied material.

(3) 1. The road from Karatau to Koktal is 10 km. Petya walked 3 km. How far along the road did he walk?

1. How many equal parts is the entire path divided into? ( into 10 parts)

2. What will one part of the path be equal to? (1/10 or 0.1)?

3. What will the three parts of such a path be equal to? (0.3)?

1. What numbers are marked by dots on the coordinate line.

(6) 4. Draw a coordinate ray. For a single segment, take 5 cells of the notebook. Find points A (0.9), B (1.2), C (3.0) on the coordinate ray

(7) Working with the textbook

(8)5. Physical education, attention exercise.

Differentiated work with students(work with gifted and low-achieving students).

6. Summing up the lesson.

Guys, what new did you learn in class today?

Do you think we managed to achieve our goals?

Reflection.

What do you guys think, have we achieved our goal?

What did you learn in the lesson? - What did you learn in the lesson?

What did you like about the lesson? What difficulties did you encounter?

(9)7. Homework :

Support sheet for the lesson "Image of decimal fractions on a coordinate ray».

1. Read the decimals:

0,2 1,009 3,26 8,1 607,8 0,2345 0,001 3,07 27,27 0,24 100,001 3,08 3,89 71,007 5,0023

2. Let us depict the decimal fraction 3.2 on the coordinate ray.

a) The number 3.2 contains 3 whole units and 2 tenths of a unit.

b) Let us depict the decimal fraction 0.56 on the coordinate ray.

3. The road from Karatau to Koktal is 10 km. Petya walked 3 km. How far along the road did he walk?

1. How many equal parts is the entire path divided into?

2. What will one part of the path be equal to?

3. What will the three parts of such a path be equal to?

4. What numbers are marked by dots on the coordinate line.

5. On a coordinate line, some points are designated by letters. Which point corresponds to the number 34.8; 34.2; 34.6; 35.4; 35.8; 35.6?

6. Draw a coordinate ray. For a single segment, take 5 cells of the notebook. Find points A (0.9), B (1.2), C (3.0) on the coordinate ray

7. Working with the textbook: open the textbook on page 89, perform the number: No. 1254 (ingenuity task).

8. Count the shapes like this: “First triangle, first corner, first circle, second corner, etc.”

9. Homework:

1. Task number on the board

2. Come up with a fairy tale that should begin like this: In a certain kingdom, in a certain state called the “State of Numbers,” there lived fractions: ordinary and decimal

This article is about common fractions. Here we will introduce the concept of a fraction of a whole, which will lead us to the definition of a common fraction. Next we will dwell on the accepted notation for ordinary fractions and give examples of fractions, let’s say about the numerator and denominator of a fraction. After this, we will give definitions of proper and improper, positive and negative fractions, and also consider the position of fractional numbers on the coordinate ray. In conclusion, we list the main operations with fractions.

Page navigation.

Shares of the whole

First we introduce concept of share.

Let's assume that we have some object made up of several absolutely identical (that is, equal) parts. For clarity, you can imagine, for example, an apple cut into several equal parts, or an orange consisting of several equal slices. Each of these equal parts that make up the whole object is called parts of the whole or simply shares.

Note that the shares are different. Let's explain this. Let us have two apples. Cut the first apple into two equal parts, and the second into 6 equal parts. It is clear that the share of the first apple will be different from the share of the second apple.

Depending on the number of shares that make up the whole object, these shares have their own names. Let's sort it out names of beats. If an object consists of two parts, any of them is called one second part of the whole object; if an object consists of three parts, then any of them is called one third part, and so on.

One second share has a special name - half. One third is called third, and one quarter part - a quarter.

For the sake of brevity, the following were introduced: beat symbols. One second share is designated as or 1/2, one third share is designated as or 1/3; one fourth share - like or 1/4, and so on. Note that the notation with a horizontal bar is used more often. To reinforce the material, let’s give one more example: the entry denotes one hundred and sixty-seventh part of the whole.

The concept of share naturally extends from objects to quantities. For example, one of the measures of length is the meter. To measure lengths shorter than a meter, fractions of a meter can be used. So you can use, for example, half a meter or a tenth or thousandth of a meter. The shares of other quantities are applied similarly.

Common fractions, definition and examples of fractions

To describe the number of shares we use common fractions. Let us give an example that will allow us to approach the definition of ordinary fractions.

Let the orange consist of 12 parts. Each share in this case represents one twelfth of a whole orange, that is, . We denote two beats as , three beats as , and so on, 12 beats we denote as . Each of the given entries is called an ordinary fraction.

Now let's give a general definition of common fractions.

The voiced definition of ordinary fractions allows us to give examples of common fractions: 5/10, , 21/1, 9/4, . And here are the records do not fit the stated definition of ordinary fractions, that is, they are not ordinary fractions.

Numerator and denominator

For convenience, ordinary fractions are distinguished numerator and denominator.

Definition.

Numerator ordinary fraction (m/n) is a natural number m.

Definition.

Denominator common fraction (m/n) is a natural number n.

So, the numerator is located above the fraction line (to the left of the slash), and the denominator is located below the fraction line (to the right of the slash). For example, let's take the common fraction 17/29, the numerator of this fraction is the number 17, and the denominator is the number 29.

It remains to discuss the meaning contained in the numerator and denominator of an ordinary fraction. The denominator of a fraction shows how many parts one object consists of, and the numerator, in turn, indicates the number of such parts. For example, the denominator 5 of the fraction 12/5 means that one object consists of five shares, and the numerator 12 means that 12 such shares are taken.

Natural number as a fraction with denominator 1

The denominator of a common fraction can be equal to one. In this case, we can consider that the object is indivisible, in other words, it represents something whole. The numerator of such a fraction indicates how many whole objects are taken. Thus, an ordinary fraction of the form m/1 has the meaning of a natural number m. This is how we substantiated the validity of the equality m/1=m.

Let's rewrite the last equality as follows: m=m/1. This equality allows us to represent any natural number m as an ordinary fraction. For example, the number 4 is the fraction 4/1, and the number 103,498 is equal to the fraction 103,498/1.

So, any natural number m can be represented as an ordinary fraction with a denominator of 1 as m/1, and any ordinary fraction of the form m/1 can be replaced by a natural number m.

Fraction bar as a division sign

Representing the original object in the form of n shares is nothing more than division into n equal parts. After an item is divided into n shares, we can divide it equally among n people - each will receive one share.

If we initially have m identical objects, each of which is divided into n shares, then we can equally divide these m objects between n people, giving each person one share from each of the m objects. In this case, each person will have m shares of 1/n, and m shares of 1/n gives the common fraction m/n. Thus, the common fraction m/n can be used to denote the division of m items between n people.

This is how we got an explicit connection between ordinary fractions and division (see the general idea of ​​​​dividing natural numbers). This connection is expressed as follows: the fraction line can be understood as a division sign, that is, m/n=m:n.

Using a common fraction, you can write the result of dividing two natural numbers, for which integral division is not performed. For example, the result of dividing 5 apples by 8 people can be written as 5/8, that is, everyone will get five-eighths of an apple: 5:8 = 5/8.

Equal and unequal fractions, comparison of fractions

A fairly natural action is comparing fractions, because it is clear that 1/12 of an orange is different from 5/12, and 1/6 of an apple is the same as another 1/6 of this apple.

As a result of comparing two ordinary fractions, one of the results is obtained: the fractions are either equal or unequal. In the first case we have equal common fractions, and in the second – unequal ordinary fractions. Let us give a definition of equal and unequal ordinary fractions.

Definition.

equal, if the equality a·d=b·c is true.

Definition.

Two common fractions a/b and c/d not equal, if the equality a·d=b·c is not satisfied.

Here are some examples of equal fractions. For example, the common fraction 1/2 is equal to the fraction 2/4, since 1·4=2·2 (if necessary, see the rules and examples of multiplying natural numbers). For clarity, you can imagine two identical apples, the first is cut in half, and the second is cut into 4 parts. It is obvious that two quarters of an apple equals 1/2 share. Other examples of equal common fractions are the fractions 4/7 and 36/63, and the pair of fractions 81/50 and 1,620/1,000.

But ordinary fractions 4/13 and 5/14 are not equal, since 4·14=56, and 13·5=65, that is, 4·14≠13·5. Other examples of unequal common fractions are the fractions 17/7 and 6/4.

If, when comparing two common fractions, it turns out that they are not equal, then you may need to find out which of these common fractions less different, and which one - more. To find out, the rule for comparing ordinary fractions is used, the essence of which is to bring the compared fractions to a common denominator and then compare the numerators. Detailed information on this topic is collected in the article comparison of fractions: rules, examples, solutions.

Fractional numbers

Each fraction is a notation fractional number. That is, a fraction is just a “shell” of a fractional number, its appearance, and all the semantic load is contained in the fractional number. However, for brevity and convenience, the concepts of fraction and fractional number are combined and simply called fraction. Here it is appropriate to paraphrase a well-known saying: we say a fraction - we mean a fractional number, we say a fractional number - we mean a fraction.

Fractions on a coordinate ray

All fractional numbers corresponding to ordinary fractions have their own unique place on, that is, there is a one-to-one correspondence between the fractions and the points of the coordinate ray.

In order to get to the point on the coordinate ray corresponding to the fraction m/n, you need to set aside m segments from the origin in the positive direction, the length of which is 1/n fraction of a unit segment. Such segments can be obtained by dividing a unit segment into n equal parts, which can always be done using a compass and a ruler.

For example, let's show point M on the coordinate ray, corresponding to the fraction 14/10. The length of a segment with ends at point O and the point closest to it, marked with a small dash, is 1/10 of a unit segment. The point with coordinate 14/10 is removed from the origin at a distance of 14 such segments.

Equal fractions correspond to the same fractional number, that is, equal fractions are the coordinates of the same point on the coordinate ray. For example, the coordinates 1/2, 2/4, 16/32, 55/110 correspond to one point on the coordinate ray, since all the written fractions are equal (it is located at a distance of half a unit segment laid out from the origin in the positive direction).

On a horizontal and right-directed coordinate ray, the point whose coordinate is the larger fraction is located to the right of the point whose coordinate is the smaller fraction. Similarly, a point with a smaller coordinate lies to the left of a point with a larger coordinate.

Proper and improper fractions, definitions, examples

Among ordinary fractions there are correct and improper fractions . This division is based on a comparison of the numerator and denominator.

Let us define proper and improper ordinary fractions.

Definition.

Proper fraction is an ordinary fraction whose numerator is less than the denominator, that is, if m

Definition.

Improper fraction is an ordinary fraction in which the numerator is greater than or equal to the denominator, that is, if m≥n, then the ordinary fraction is improper.

Here are some examples of proper fractions: 1/4, , 32,765/909,003. Indeed, in each of the written ordinary fractions the numerator is less than the denominator (if necessary, see the article comparing natural numbers), so they are correct by definition.

Here are examples of improper fractions: 9/9, 23/4, . Indeed, the numerator of the first of the written ordinary fractions is equal to the denominator, and in the remaining fractions the numerator is greater than the denominator.

There are also definitions of proper and improper fractions, based on comparison of fractions with one.

Definition.

correct, if it is less than one.

Definition.

An ordinary fraction is called wrong, if it is either equal to one or greater than 1.

So the common fraction 7/11 is correct, since 7/11<1 , а обыкновенные дроби 14/3 и 27/27 – неправильные, так как 14/3>1, and 27/27=1.

Let's think about how ordinary fractions with a numerator greater than or equal to the denominator deserve such a name - “improper”.

For example, let's take the improper fraction 9/9. This fraction means that nine parts are taken of an object that consists of nine parts. That is, from the available nine parts we can make up a whole object. That is, the improper fraction 9/9 essentially gives the whole object, that is, 9/9 = 1. In general, improper fractions with a numerator equal to the denominator denote one whole object, and such a fraction can be replaced by the natural number 1.

Now consider the improper fractions 7/3 and 12/4. It is quite obvious that from these seven third parts we can compose two whole objects (one whole object consists of 3 parts, then to compose two whole objects we will need 3 + 3 = 6 parts) and there will still be one third part left. That is, the improper fraction 7/3 essentially means 2 objects and also 1/3 of such an object. And from twelve quarter parts we can make three whole objects (three objects with four parts each). That is, the fraction 12/4 essentially means 3 whole objects.

The considered examples lead us to the following conclusion: improper fractions can be replaced either by natural numbers, when the numerator is divided evenly by the denominator (for example, 9/9=1 and 12/4=3), or by the sum of a natural number and a proper fraction, when the numerator is not evenly divisible by the denominator (for example, 7/3=2+1/3). Perhaps this is precisely what earned improper fractions the name “irregular.”

Of particular interest is the representation of an improper fraction as the sum of a natural number and a proper fraction (7/3=2+1/3). This process is called separating the whole part from an improper fraction, and deserves separate and more careful consideration.

It's also worth noting that there is a very close relationship between improper fractions and mixed numbers.

Positive and negative fractions

Each common fraction corresponds to a positive fractional number (see the article on positive and negative numbers). That is, ordinary fractions are positive fractions. For example, ordinary fractions 1/5, 56/18, 35/144 are positive fractions. When you need to highlight the positivity of a fraction, a plus sign is placed in front of it, for example, +3/4, +72/34.

If you put a minus sign in front of a common fraction, then this entry will correspond to a negative fractional number. In this case we can talk about negative fractions. Here are some examples of negative fractions: −6/10, −65/13, −1/18.

Positive and negative fractions m/n and −m/n are opposite numbers. For example, the fractions 5/7 and −5/7 are opposite fractions.

Positive fractions, like positive numbers in general, denote an addition, income, an upward change in any value, etc. Negative fractions correspond to expense, debt, or a decrease in any quantity. For example, the negative fraction −3/4 can be interpreted as a debt whose value is equal to 3/4.

On a horizontal and rightward direction, negative fractions are located to the left of the origin. The points of the coordinate line, the coordinates of which are the positive fraction m/n and the negative fraction −m/n, are located at the same distance from the origin, but on opposite sides of the point O.

Here it is worth mentioning fractions of the form 0/n. These fractions are equal to the number zero, that is, 0/n=0.

Positive fractions, negative fractions, and 0/n fractions combine to form rational numbers.

Operations with fractions

We have already discussed one action with ordinary fractions - comparing fractions - above. Four more arithmetic functions are defined operations with fractions– adding, subtracting, multiplying and dividing fractions. Let's look at each of them.

The general essence of operations with fractions is similar to the essence of the corresponding operations with natural numbers. Let's make an analogy.

Multiplying fractions can be thought of as the action of finding a fraction from a fraction. To clarify, let's give an example. Let us have 1/6 of an apple and we need to take 2/3 of it. The part we need is the result of multiplying the fractions 1/6 and 2/3. The result of multiplying two ordinary fractions is an ordinary fraction (which in a special case is equal to a natural number). Next, we recommend that you study the information in the article Multiplying Fractions - Rules, Examples and Solutions.

Bibliography.

• Vilenkin N.Ya., Zhokhov V.I., Chesnokov A.S., Shvartsburd S.I. Mathematics: textbook for 5th grade. educational institutions.
• Vilenkin N.Ya. and others. Mathematics. 6th grade: textbook for general education institutions.
• Gusev V.A., Mordkovich A.G. Mathematics (a manual for those entering technical schools).

Mathematics 5 "B" class

Date: 12/14/15

Lesson No. 83

Lesson topic: Picture of common fractions and mixed numbers on the coordinate ray.

The purpose of the lesson:

1.Give students the concept of a coordinate ray.
2.Develop the ability and skills of depicting ordinary fractions on a coordinate beam.
3. Foster a sense of collectivism and the ability to listen to others.

Lesson type: generalization and systematization of the material covered.
Teaching methods: partially search, self-test method.

During the classes.

I. Organizing time.

“Here in Kazakhstan, life will be better than in other countries. I promise you this"
N.A.Nazarbayev

Dear students!

Our lesson takes place on the eve of Independence Day. - But speaking about the state, it is impossible to remain silent about the head of state - the President of the Republic of Kazakhstan - N.A. Nazarbayev. The word president, translated from Latin, means “sitting in front”! The President ensures that the laws of the Constitution are not violated, the President protects the sovereignty of the state! December 1, 1991 N.A. Nazarbayev became the first President of sovereign Kazakhstan. And for many years Nazarbayev has been the first President of our state, thanks to this the welfare of our country is growing, sports complexes, kindergartens, schools, entertainment centers, and health centers are being built.

And I propose to start our lesson with the following task.

Let's solve the problem:

1. Determine how old N. Nazarbayev is, if it is known that the President has ruled the country for 25 years, which is 1/3 of his age. How old is he?

25*3/1=75 years.

Checking homework. (tasks on cards)

Proper and improper fractions

1. Select the whole part.

2. Represent an improper fraction as a mixed number

Answers: A) 17; IN 1; C) 3;

3. Represent the mixed number 5 as an improper fraction

Answers: A) ; IN) ; WITH) ;

4. Select the whole part.

a) 12 c) 25 c) 16 d) 15

5. Convert to an improper fraction.

6. Represent an improper fraction as a mixed number as an improper fraction.

Answers: A) ; IN) ; WITH) ; d)

Key (written on the board):

Oral counting (on cards)

Math simulator ( Students must complete the tasks of their version in 5 minutes )

Explanation of a new topic
Let's move on to the main part of our lesson.

Write down the topic of the lesson.
Coordinate beam. Image of ordinary fractions and mixed numbers on a coordinate ray.
Burkina S.
All sorts of fractions are needed
All fractions are important
Teach fractions
Then luck will shine for you,
If you know fractions,
Exactly the meaning of understanding them
It will even become easy
Difficult task.

We will climb the stairs step by step.
As we rise, we will repeat what we have learned and learn new things.

Updating of reference knowledge

What are the elements of a fraction above and below the line called?

What action can be used to replace a fractional line?

What is the name for dividing the numerator and denominator by the same number?

Work on learning new material.
1. Flipchart ( repetition of the definition of the coordinate ray )

2. Working with the reference diagram
Definition. The number corresponding to a point on a coordinate ray is called the coordinate of this point.

To depict a proper fraction on a coordinate ray you need to:

1. Divide a single segment into an equal number of parts corresponding to the number in the denominator.

2. From the beginning of the count, set aside the number of equal parts corresponding to the number in the numerator of the fraction.

For example:

Physical education minute
Dear Guys! We have already overcome half the journey, but there are still many difficulties ahead, so it’s time to relax a little and do some physical education.

We did a great job

And we'll have a nice rest

We'll do some exercises

And let's hit the road again.

Repeat all movements after me.

Hands behind your back, heads back,

Let your eyes look at the ceiling.

Let's lower our eyes and look at the desk,

And again up - where is the fly flying?

Let's look for her with our eyes,

And we decide again, a little more.

Now everyone has rested and you can continue on your way.

Solving problems from the textbook.
Each of you has to solve a task № 888, 889 . (the solution is carried out in notebooks).

Multi-level tasks

Image of ordinary fractions on a coordinate ray.

Countalkins

Draw a coordinate ray, taking 9 cells of the notebook as a unit segment. Mark the points on the coordinate ray: yu

Reshalkins

Draw a coordinate ray, taking 10 cells of the notebook as a unit segment. Mark the numbers on the coordinate ray:

Savvy

Draw a coordinate ray, taking 12 cells of the notebook as a unit segment. Mark point N on the coordinate ray, lay off segments on both sides of points NA and NB with a length equal to a unit segment. Find the coordinates of points A and B.

Lesson summary
Do you think that a fraction is a fraction of a small part of something? which you shouldn't pay attention to.

What if we were building your house, the one in which you live?
The architect made a slight mistake in his calculations.
What happened, do you know?
The house would turn into a heap of ruins.
You step on the bridge, it is reliable and strong.
What if the engineer weren’t accurate in his drawings?
Three tenths - and the walls are erected askew,
Three tenths - and the cars will fall off the slope.
Make a mistake only by three tenths, pharmacist,
It will become poisonous medicine, it will kill a person.

Homework. Learn the theory from section 5.6, solve No. 890, 891, 892

REFLECTION: Now you must evaluate your work in class.

Draw a face and rate yourself.

"5" "4" "3"

Therefore they say that
On a coordinate beam, equal fractions correspond to the same point (Fig. 117).

Two equal fractions represent the same fractional number. Fractions can be compared, added, subtracted, multiplied and divided. For brevity, we usually talk about comparing, adding, subtracting, multiplying, and dividing fractions.

The pie was cut into 5 slices and 2 slices were placed on one plate, and 3 slices on another (Fig. 118). Two shares make a pie, and three shares make a pie. Since 2 shares are less than 3 identical shares, then
Of the two fractions with the same denominators, the one with the smaller numerator is smaller, and the one with the larger numerator is larger.

A point on a coordinate ray that has a smaller coordinate lies to the left of a point that has a larger coordinate.

Give an example of two equal fractions with different numerators.
How are equal fractions represented on a coordinate ray?
Which of two fractions with the same denominators is smaller and which is larger?
Which point lies on the coordinate ray to the left - with a smaller or larger coordinate?

940. Explain with the help of a picture why

941. Draw a segment 18 cells long in your notebook. With the help of this segment explain why:

942. A unit segment is equal to 12 cells. Mark points on the coordinate ray . Explain the result.

943. Mark on the coordinate ray the points whose coordinates are equal:

944. A unit segment is equal to the length of 6 cells in a notebook. Mark points with coordinates on the coordinate ray . Which of these points is located to the left of all on the ray, and which is to the right of all?

945. Arrange the fractions in ascending order:

Arrange these fractions in descending order.

946. Replace the asterisk with a sign< или >in the entries:

947. Which fraction is greater:

948. Which point lies to the left on coordinate ray:

949. Calculate orally:

950. Read the fractions:

State the numerator and denominator.

951. The following points are marked on the coordinate ray:

Are there any matches among them?

952. What part in Figure 120 is:

a) triangle ABO from quadrilateral ABCO
b) triangle ABO from quadrilateral ABCD
c) quadrilateral ABCD from quadrilateral ABCD
d) quadrilateral ABCD from hexagon ABCDEK?

953. Try to find the shortest path along the surface of the cube from point A to point B (Fig. 121). How many such paths can you specify?

a) 5 to 2; b) 100 to 30; c) 29 by 9; d) 100 by 11.

955. What share is:

a) day from year; c) decimeter from meter;
b) day from week; d) 1 cm 3 from a liter?

Think about why 1 cm3 is also called a milliliter (1 ml).

956. Jug volume 5 l. A liter of water was poured into it. What part of the volume of the jug is occupied by water? Give the answer for a - 1; 2; 3; 4.

967. What part of the week is:

a) five days;

b) six days?

968. The mass of a pumpkin is 2 kg 800 g. Find the mass:

969. The house occupies only garden plot. Find the area of ​​the plot if the area of ​​land under the house is 40 m2.
970. Two motorcyclists are traveling towards each other. The speed of one motorcyclist is 62 km/h, and the speed of the other is 54 km/h. In how many hours will the motorcyclists meet if there are now 348 km between them?

971. The mass of a pack of cookies is 125 g, and the mass of a pack of crackers is 380 g. Which is heavier:

a) 9 packs of cookies or 4 packs of crackers;
b) 22 packs of cookies or 7 packs of crackers?

972. A liter jar holds 910 g of millet or 780 g of peas. Which mass is smaller:

a) 3 cans of millet or 4 cans of peas;
b) 7 cans of millet or 8 cans of peas?

973. From a piece of wire length a m the first time b m was cut, and the second time - see. What is the meaning of the following expressions:

a) b + c; b) a - (b + c); c) a - b; d) a - b - c

Which of these expressions take same values for any values ​​of the letters a, b, c? Check your answer with a = 45, b = 7 and c = 12.

N.Ya. VILENKIN, V. I. ZHOKHOV, A. S. CHESNOKOV, S. I. SHVARTSBURD, Mathematics Grade 5, Textbook for general education institutions

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