Soups based on chicken broth are always light and very tasty. This ideal option for dietary and low-calorie nutrition, especially if it is not supplemented with any pasta. You can cook this soup with any seasonal vegetables, such as carrots, pumpkin, zucchini, celery, herbs or mushrooms. Tasty, fresh and light for summer. For a more satisfying option, you can cook it with chicken broth, which creates a lot of scope for culinary experiments.
What meat should I choose for the broth?
The key to a good and tasty broth is fresh meat. Nothing compares to the taste; it turns out simply amazing, but not everyone has the opportunity to purchase it, much less grow it. Therefore, most often we buy store-bought chickens raised on poultry farms. When choosing it at the market or in a store, it is best to give preference to fresh, chilled, preferably buying from a reliable seller. The meat of a healthy and fresh bird should be light pink or white, the skin is thin and undamaged, there should be no mucus on the surface. You can, of course, use a frozen carcass. In this case, it must first be defrosted at room temperature. Frozen meat most often loses its texture, ice crystals break the fibers, and the taste changes as a result, and not in better side, besides, some unscrupulous manufacturers purposefully pump the carcass with water, which, by the way, is visible to the naked eye by numerous punctures in the skin. This results in significant weight loss upon thawing.
Cook whole or in parts?
Cooking chicken broth is not at all difficult; even a novice housewife can handle it. But there are a few nuances that are worth knowing. It is best to make broth from a whole chicken, not from wings, breasts or backs. The carcass must first be washed in cold water, thoroughly, so that no blood clots remain, as this will hinder transparency in the future.
For a chicken weighing about a kilogram you will need 5 liters of water. The meat is placed in cold water and then brought to a boil. It is not necessary to remove the foam that forms on the surface, since it will settle later anyway, and the broth will need to be strained. Strong boiling should also not be allowed; the surface should only tremble slightly. Cooking on average will take about an hour or a little more. Around this time you can add vegetables and spices. The best supplement Add onions, carrots and celery to the chicken broth. It is best not to cut vegetables, but to boil them whole and then remove them.
If you want to get a broth of deep amber color, then carrots and onions (whole) must be lightly baked until golden brown in a frying pan without oil and only then used for soup.
As for spices, give preference to tastes that are not too intrusive, for example, you can use black peppercorns, dill, and parsley. In this case, bright and fluffy greens can be left for serving, and the stems can be boiled in the broth. It is best to avoid allspice or cloves, as they will overpower the delicate flavor of the chicken.
After the meat is ready, remove the broth from the heat. The chicken is removed, allowed to cool slightly and divided into portions. The broth is carefully strained - this is an excellent basis for cooking chicken soup with chicken dumplings (or quenelles).
Dumplings are a traditional European invention, very rich flour products, popular not only in soups, but also as a separate dish, for example as a side dish for meat. Czech dumplings or their direct relatives. Most popular in our country, they will be an excellent addition to a light vegetable soup with chicken broth. Let's consider several options for their preparation, as well as chicken quenelles. When it comes to the question of how to make dumplings for potato or chicken soup from dough, then there are many options, each housewife chooses to suit her taste. Some people prefer to use raw potatoes, while others prefer boiled ones. Both options have a right to exist. But in any case, soup with dumplings in chicken broth will turn out to be very satisfying.
Boiled potato dumplings
It is necessary to boil a dozen peeled large potatoes until full readiness. Drain the water and grind into puree, let cool. Then add three chicken yolks, one and a half cups of flour, salt and knead into a homogeneous dough. Roll it into a rope and cut into small pieces - these are the future dumplings, which must be boiled in salted water for 5-10 minutes, and then added to a plate in portions of 3-4 pieces. Soup with dumplings in chicken broth will perfectly diversify the lunch menu and will become perhaps the most favorite.
Raw potato dumplings
The second option involves using raw potatoes. To do this, you need to grate it on a fine grater and squeeze out excess liquid properly. Then add half a glass of hot milk, a glass of flour, one egg, salt, pepper to the mixture and knead the dough. Carefully place the dumplings formed with a spoon into boiling water and cook until tender, about 6-7 minutes.
You can diversify these dumplings with various fillings: mushrooms, cheese. You just need to first boil all the ingredients and mince them or chop them finely. Soup with potato dumplings in chicken broth will appeal to children and will delight adults; it is very filling and rich, perfect for a winter lunch.
Chicken dumplings (quenelles)
They are called quenelles, meatballs, dumplings, but the essence remains the same. To cook them, you will need chicken fillet (breast). You can separate it from the whole carcass, which is intended for broth. The meat must be turned into minced meat, then add onions, spices and one egg. Then there are two possible options. You can make meatballs from it, and then lower them into the broth and cook until tender. Or use a spoon to form quenelles and bake them in the oven, and only then serve them on plates with the finished soup. In any case, it turns out great in taste and original with dumplings. A step-by-step cooking recipe will help you do everything correctly and please your family with a delicious dinner. No one will refuse the supplement!
Chicken soup with dumplings: recipe
To begin with, you should use the simplest recipe, and only then start culinary experiments. In this case, it is best to remove the skin and not use it when serving. So, given that the chicken has already been cooked, the dumplings are cooked and the broth has been strained, let’s start “assembling” the soup. The finished chicken carcass must be divided into pieces and carefully remove the meat from the bones, putting everything in a separate dish. In the future, it will need to be divided into portions on plates. There are two simplest ways to prepare soup with dumplings in chicken broth.
Option one: carrots and celery have already been boiled in broth
Of the raw vegetables, only potatoes and onions are needed (green can be used), since the boiled one has already given away all its taste, it will not be needed anymore. The finished carrots and celery should be chopped and set aside for a while. Peel the potatoes, cut into cubes and place in the boiling broth, cook until half cooked, then add finely chopped onions and cook for about five more minutes. Remove soup from heat, add carrots and celery. Mix thoroughly, let stand for five minutes and only then pour into plates, not forgetting to put dumplings in each portion and sprinkle generously with herbs.
This soup is good because you can add any vegetables you like: bell peppers, zucchini, tomatoes, cauliflower or Brussels sprouts, pumpkin.
Option two: if you only have chicken broth
Considering that a whole chicken yields about four liters of broth, it is best to divide it into two servings, especially since it will be perfectly stored in the refrigerator and the next day you can cook fresh soup or prepare a sauce for dinner based on it.
So, in this case, all vegetables (based on two liters: one carrot, 2-3 potatoes, one onion, bell pepper, celery, you can add 200-300 g pumpkin) must be peeled and cut into cubes.
Next, bring the chicken broth to a light boil, add carrots and cook for about 3-4 minutes, then add potatoes (pumpkin), celery and cook until the vegetables are ready. About five minutes before the end of cooking, add the finely chopped onion. After removing from the heat, you need to let the soup sit for a while and only then serve it in the same way as in the first case.
It’s quite easy to prepare chicken soup with dumplings in a slow cooker or on the stove, it won’t take much time, and your household will definitely like it. Cost-effectiveness in a set of products, minimum calories and maximum pleasure - an excellent combination.
Dumplings or dumplings are considered to be small in size and different shapes pieces of dough made with eggs and flour. They can act as an independent dish or be used as an ingredient in soups, main courses, and desserts. In addition to flour and eggs, potatoes and cottage cheese, semolina or corn grits can also be used as the basis for dumplings.
In China, dumplings are often prepared with meat filling. In our country, dumplings are often used in soups. As for me, the most delicious among this type of soup is. Hearty and nutritious, but at the same time dietary and not fatty, the soup will be an excellent addition to lunch or dinner.
Ingredients for soup for a 2.5 liter saucepan:
- Chicken - (leg, wings, drumsticks or giblets) - about 250-300 gr.,
- Bay leaf – 1-2 pcs.,
- Onion – 1 head,
- Carrots – 1 pc.,
- Spices - to taste
- Salt to taste
- Potatoes – 4-5 pcs.,
- Parsley for sprinkling the finished soup
For the dumplings:
- Flour - 100-120 gr.,
- Water – 50-70 ml.,
- Egg – 1 pc.,
- Salt - a pinch
Chicken soup with dumplings - recipe
First you need to cook chicken broth. Rinse any parts of the chicken. Place in a saucepan. Fill in hot water. Add bay leaf, peeled onion, salt and spices to it. Cover the pan with a lid. Simmer for 15-25 minutes, depending on which parts of the chicken you used. As it cooks, remove the foam from the broth with a slotted spoon. While the broth is cooking, prepare the vegetables for the soup. Peel the carrots too. Potatoes for soup with dumplings are cut into standard pieces as for soup or borscht.
Carrots can be cut into half circles or grated.
Remove the chicken from the prepared chicken broth. Onion and bay leaf.
Add potatoes and carrots.
Chicken soup with dumplings. Photo
Examples with fractions are one of the basic elements of mathematics. There are many different types equations with fractions. Below is detailed instructions for solving examples of this type.
How to solve examples with fractions - general rules
To solve examples with fractions of any type, be it addition, subtraction, multiplication or division, you need to know the basic rules:
- In order to add fractional expressions with the same denominator (the denominator is the number located at the bottom of the fraction, the numerator is at the top), you need to add their numerators, and leave the denominator the same.
- In order to subtract a second fractional expression (with the same denominator) from one fraction, you need to subtract their numerators and leave the denominator the same.
- To add or subtract fractional expressions with different denominators, you need to find the smallest common denominator.
- In order to find a fractional product, you need to multiply the numerators and denominators, and, if possible, reduce.
- To divide a fraction by a fraction, you multiply the first fraction by the second fraction reversed.
How to solve examples with fractions - practice
Rule 1, example 1:
Calculate 3/4 +1/4.
According to Rule 1, if fractions have two (or more) same denominator, you just need to add their numerators. We get: 3/4 + 1/4 = 4/4. If a fraction has the same numerator and denominator, the fraction will equal 1.
Answer: 3/4 + 1/4 = 4/4 = 1.
Rule 2, example 1:
Calculate: 3/4 – 1/4
Using rule number 2, to solve this equation you need to subtract 1 from 3 and leave the denominator the same. We get 2/4. Since two 2 and 4 can be reduced, we reduce and get 1/2.
Answer: 3/4 – 1/4 = 2/4 = 1/2.
Rule 3, Example 1
Calculate: 3/4 + 1/6
Solution: Using the 3rd rule, we find the lowest common denominator. The lowest common denominator is a number that is divisible by the denominators of all fractional expressions example. Thus, we need to find the minimum number that will be divisible by both 4 and 6. This number is 12. We write 12 as the denominator. Divide 12 by the denominator of the first fraction, we get 3, multiply by 3, write 3 in the numerator *3 and + sign. Divide 12 by the denominator of the second fraction, we get 2, multiply 2 by 1, write 2*1 in the numerator. So, we get a new fraction with a denominator equal to 12 and a numerator equal to 3*3+2*1=11. 11/12.
Answer: 11/12
Rule 3, Example 2:
Calculate 3/4 – 1/6. This example is very similar to the previous one. We do all the same steps, but in the numerator instead of the + sign, we write a minus sign. We get: 3*3-2*1/12 = 9-2/12 = 7/12.
Answer: 7/12
Rule 4, Example 1:
Calculate: 3/4 * 1/4
Using the fourth rule, we multiply the denominator of the first fraction by the denominator of the second and the numerator of the first fraction by the numerator of the second. 3*1/4*4 = 3/16.
Answer: 3/16
Rule 4, Example 2:
Calculate 2/5 * 10/4.
This fraction can be reduced. In the case of a product, the numerator of the first fraction and the denominator of the second and the numerator of the second fraction and the denominator of the first are canceled.
2 cancels from 4. 10 cancels from 5. We get 1 * 2/2 = 1*1 = 1.
Answer: 2/5 * 10/4 = 1
Rule 5, Example 1:
Calculate: 3/4: 5/6
Using the 5th rule, we get: 3/4: 5/6 = 3/4 * 6/5. We reduce the fraction according to the principle of the previous example and get 9/10.
Answer: 9/10.
How to solve examples with fractions - fractional equations
Fractional equations are examples where the denominator contains an unknown. In order to solve such an equation, you need to use certain rules.
Let's look at an example:
Solve the equation 15/3x+5 = 3
Let us remember that you cannot divide by zero, i.e. the denominator value must not be zero. When solving such examples, this must be indicated. For this purpose, there is an OA (permissible value range).
So 3x+5 ≠ 0.
Hence: 3x ≠ 5.
x ≠ 5/3
At x = 5/3 the equation simply has no solution.
Having indicated the ODZ, in the best possible way decide given equation will get rid of fractions. To do this, let’s first imagine everything fractional values in the form of a fraction, in in this case number 3. We get: 15/(3x+5) = 3/1. To get rid of fractions you need to multiply each of them by the lowest common denominator. In this case it will be (3x+5)*1. Sequence of actions:
- Multiply 15/(3x+5) by (3x+5)*1 = 15*(3x+5).
- Open the brackets: 15*(3x+5) = 45x + 75.
- We do the same with the right side of the equation: 3*(3x+5) = 9x + 15.
- We equate left and right side: 45x + 75 = 9x +15
- Move the X's to the left, numbers to the right: 36x = – 50
- Find x: x = -50/36.
- We reduce: -50/36 = -25/18
Answer: ODZ x ≠ 5/3. x = -25/18.
How to solve examples with fractions - fractional inequalities
Fractional inequalities of the type (3x-5)/(2-x)≥0 are solved using the number axis. Let's look at this example.
Sequence of actions:
- We equate the numerator and denominator to zero: 1. 3x-5=0 => 3x=5 => x=5/3
2. 2-x=0 => x=2 - We're drawing number axis, writing the resulting values on it.
- Draw a circle under the value. There are two types of circles - filled and empty. A filled circle means that the given value is within the solution range. An empty circle indicates that this value is not included in the solution range.
- Since the denominator cannot be equal to zero, under the 2nd there will be an empty circle.
- To determine the signs, we substitute any number greater than two into the equation, for example 3. (3*3-5)/(2-3)= -4. the value is negative, which means we write a minus above the area after the two. Then substitute for X any value of the interval from 5/3 to 2, for example 1. The value is again negative. We write a minus. We repeat the same with the area located up to 5/3. We substitute any number less than 5/3, for example 1. Again, minus.
- Since we are interested in the values of x at which the expression will be greater than or equal to 0, and there are no such values (there are minuses everywhere), this inequality has no solution, that is, x = Ø (an empty set).
Answer: x = Ø
496. Find X, If:
497. 1) If you add 10 1/2 to 3/10 of an unknown number, you get 13 1/2. Find the unknown number.
2) If you subtract 10 1/2 from 7/10 of an unknown number, you get 15 2/5. Find the unknown number.
498 *. If you subtract 10 from 3/4 of an unknown number and multiply the resulting difference by 5, you get 100. Find the number.
499 *. If you increase an unknown number by 2/3 of it, you get 60. What number is this?
500 *. If to unknown number add the same amount, and also 20 1/3, then you get 105 2/5. Find the unknown number.
501. 1) The potato yield with square-cluster planting averages 150 centners per hectare, and with conventional planting it is 3/5 of this amount. How much more potatoes can be harvested from an area of 15 hectares if potatoes are planted using the square-cluster method?
2) An experienced worker produced 18 parts in 1 hour, and an inexperienced worker produced 2/3 of this amount. How long more details made by an experienced worker in a 7-hour working day?
502. 1) The pioneers collected within three days 56 kg of different seeds. On the first day, 3/14 of the total amount was collected, on the second, one and a half times more, and on the third day, the rest of the grain. How many kilograms of seeds did the pioneers collect on the third day?
2) When grinding the wheat, the result was: flour 4/5 of the total amount of wheat, semolina - 40 times less than flour, and the rest is bran. How much flour, semolina and bran separately were produced when grinding 3 tons of wheat?
503. 1) Three garages can accommodate 460 cars. The number of cars that fit in the first garage is 3/4 times the number of cars that fit in the second, and in the third garage it is 1 1/2 times more cars than in the first one. How many cars fit in each garage?
2) A factory with three workshops employs 6,000 workers. In the second workshop there are 1 1/2 times less workers than in the first, and the number of workers in the third workshop is 5/6 of the number of workers in the second workshop. How many workers are there in each workshop?
504. 1) First 2/5, then 1/3 of the total kerosene was poured from a tank with kerosene, and after that 8 tons of kerosene remained in the tank. How much kerosene was in the tank initially?
2) The cyclists raced for three days. On the first day they covered 4/15 of the entire journey, on the second - 2/5, and on the third day the remaining 100 km. How far did the cyclists travel in three days?
505. 1) The icebreaker fought its way through the ice field for three days. On the first day he walked 1/2 of the entire distance, on the second day 3/5 of the remaining distance and on the third day the remaining 24 km. Find the length of the path covered by the icebreaker in three days.
2) Three groups of schoolchildren planted trees to green the village. The first detachment planted 7/20 of all trees, the second 5/8 of the remaining trees, and the third the remaining 195 trees. How many trees did the three teams plant in total?
506. 1) A combine harvester harvested wheat from one plot in three days. On the first day, he harvested from 5/18 of the entire area of the plot, on the second day from 7/13 of the remaining area, and on the third day from the remaining area of 30 1/2 hectares. On average, 20 centners of wheat were harvested from each hectare. How much wheat was harvested in the entire area?
2) On the first day, the rally participants covered 3/11 of the entire route, on the second day 7/20 of the remaining route, on the third day 5/13 of the new remainder, and on the fourth day the remaining 320 km. How long is the route of the rally?
507. 1) On the first day the car covered 3/8 of the entire distance, on the second day 15/17 of what it covered on the first, and on the third day the remaining 200 km. How much gasoline was consumed if a car consumes 1 3/5 kg of gasoline for 10 km?
2) The city consists of four districts. And 4/13 of all residents of the city live in the first district, 5/6 of the residents of the first district live in the second, 4/11 of the residents of the first live in the third; two districts combined, and 18 thousand people live in the fourth district. How much bread does the entire population of the city need for 3 days, if on average one person consumes 500 g per day?
508. 1) The tourist walked on the first day 10/31 of the entire journey, on the second 9/10 of what he walked on the first day, and on the third the rest of the way, and on the third day he walked 12 km more than on the second day. How many kilometers did the tourist walk on each of the three days?
2) The car covered the entire route from city A to city B in three days. On the first day the car covered 7/20 of the entire distance, on the second 8/13 of the remaining distance, and on the third day the car covered 72 km less than on the first day. What is the distance between cities A and B?
509. 1) The executive committee allocated the land workers of three factories under garden plots. The first plant was allocated 9/25 of the total number of plots, the second plant 5/9 of the number of plots allocated for the first, and the third - the remaining plots. How many total plots were allocated to the workers of three factories, if the first factory was allocated 50 fewer plots than the third?
2) The plane delivered a shift of winter workers to the polar station from Moscow in three days. On the first day he flew 2/5 of the entire distance, on the second - 5/6 of the distance he covered on the first day, and on the third day he flew 500 km less than on the second day. How far did the plane fly in three days?
510. 1) The plant had three workshops. The number of workers in the first workshop is 2/5 of all workers in the plant; in the second workshop there are 1 1/2 times fewer workers than in the first, and in the third workshop there are 100 more workers than in the second. How many workers are there in the factory?
2) The collective farm includes residents of three neighboring villages. The number of families in the first village is 3/10 of all families on the collective farm; in the second village the number of families is 1 1/2 times greater than in the first, and in the third village the number of families is 420 less than in the second. How many families are there on the collective farm?
511. 1) The artel used up 1/3 of its stock of raw materials in the first week, and 1/3 of the rest in the second. How much raw material is left in the artel if in the first week the consumption of raw materials was 3/5 tons more than in the second week?
2) Of the imported coal, 1/6 of it was spent for heating the house in the first month, and 3/8 of the remainder in the second month. How much coal is left to heat the house if 1 3/4 more was used in the second month than in the first month?
512. 3/5 of the total land of the collective farm is allocated for sowing grain, 13/36 of the remainder is occupied by vegetable gardens and meadows, the rest of the land is forest, and the sown area of the collective farm is 217 hectares more area forests, 1/3 of the land allocated for grain crops is sown with rye, and the rest with wheat. How many hectares of land did the collective farm sow with wheat and how many with rye?
513. 1) The tram route is 14 3/8 km long. Along this route, the tram makes 18 stops, spending on average up to 1 1/6 minutes per stop. The average speed of the tram along the entire route is 12 1/2 km per hour. How long does it take for a tram to complete one trip?
2) Bus route 16 km. Along this route the bus makes 36 stops of 3/4 minutes each. on average each. The average bus speed is 30 km per hour. How long does a bus take for one route?
514*. 1) It’s 6 o’clock now. evenings. What part is the remaining part of the day from the past and what part of the day is left?
2) A steamer travels the distance between two cities with the current in 3 days. and back the same distance in 4 days. How many days will the rafts float downstream from one city to another?
515. 1) How many boards will be used to lay the floor in a room whose length is 6 2/3 m, width 5 1/4 m, if the length of each board is 6 2/3 m, and its width is 3/80 of the length?
2) A rectangular platform has a length of 45 1/2 m, and its width is 5/13 of its length. This area is bordered by a path 4/5 m wide. Find the area of the path.
516. Find the average arithmetic numbers:
517. 1) The arithmetic mean of two numbers is 6 1/6. One of the numbers is 3 3/4. Find another number.
2) The arithmetic mean of two numbers is 14 1/4. One of these numbers is 15 5/6. Find another number.
518. 1) The freight train was on the road for three hours. In the first hour he covered 36 1/2 km, in the second 40 km and in the third 39 3/4 km. Find the average speed of the train.
2) The car traveled 81 1/2 km in the first two hours, and 95 km in the next 2 1/2 hours. How many kilometers did he walk on average per hour?
519. 1) The tractor driver completed the task of plowing the land in three days. On the first day he plowed 12 1/2 hectares, on the second day 15 3/4 hectares and on the third day 14 1/2 hectares. On average, how many hectares of land did a tractor driver plow per day?
2) A group of schoolchildren, making a three-day tourist trip, were on the road for 6 1/3 hours on the first day, 7 hours on the second. and on the third day - 4 2/3 hours. How many hours on average did schoolchildren travel every day?
520. 1) Three families live in the house. The first family has 3 light bulbs to illuminate the apartment, the second has 4 and the third has 5 light bulbs. How much should each family pay for electricity if all the lamps were the same, and the total electricity bill (for the whole house) was 7 1/5 rubles?
2) A polisher was polishing the floors in an apartment where three families lived. The first family had a living area of 36 1/2 square meters. m, the second is 24 1/2 sq. m, and the third - 43 sq. m. For all the work, 2 rubles were paid. 08 kop. How much did each family pay?
521. 1) In the garden plot, potatoes were collected from 50 bushes at 1 1/10 kg per bush, from 70 bushes at 4/5 kg per bush, from 80 bushes at 9/10 kg per bush. How many kilograms of potatoes are harvested on average from each bush?
2) The field crew on an area of 300 hectares received a harvest of 20 1/2 quintals of winter wheat per 1 hectare, from 80 hectares to 24 quintals per 1 ha, and from 20 hectares - 28 1/2 quintals per 1 ha. What is the average yield in a brigade with 1 hectare?
522. 1) The sum of two numbers is 7 1/2. One number is 4 4/5 greater than the other. Find these numbers.
2) If you add up the numbers expressing the width of Tatarsky and the width Kerch Straits together, we get 11 7/10 km. Strait of Tartary 3 1/10 km wider than Kerch. What is the width of each strait?
523. 1) The sum of three numbers is 35 2 / 3. First number more than the second by 5 1/3 and more than the third by 3 5/6. Find these numbers.
2) Islands New Earth, Sakhalin and Severnaya Zemlya together occupy an area of 196 7/10 thousand square meters. km. The area of Novaya Zemlya is 44 1/10 thousand square meters. km more area Severnaya Zemlya and 5 1/5 thousand sq. km larger than the area of Sakhalin. What is the area of each of the listed islands?
524. 1) The apartment consists of three rooms. The area of the first room is 24 3/8 sq. m and is 13/36 of the entire area of the apartment. The area of the second room is 8 1/8 square meters. m more than the area of the third. What is the area of the second room?
2) A cyclist during a three-day competition on the first day was on the road for 3 1/4 hours, which was 13/43 of the total travel time. On the second day he rode 1 1/2 hours more than on the third day. How many hours did the cyclist travel on the second day of the competition?
525. Three pieces of iron weigh together 17 1/4 kg. If the weight of the first piece is reduced by 1 1/2 kg, the weight of the second by 2 1/4 kg, then all three pieces will have the same weight. How much did each piece of iron weigh?
526. 1) The sum of two numbers is 15 1/5. If the first number is reduced by 3 1/10, and the second is increased by 3 1/10, then these numbers will be equal. What is each number equal to?
2) There were 38 1/4 kg of cereal in two boxes. If you pour 4 3/4 kg of cereal from one box into another, then there will be equal amounts of cereal in both boxes. How much cereal is in each box?
527 . 1) The sum of two numbers is 17 17 / 30. If you subtract 5 1/2 from the first number and add it to the second, then the first will still be greater than the second by 2 17/30. Find both numbers.
2) There are 24 1/4 kg of apples in two boxes. If you transfer 3 1/2 kg from the first box to the second, then in the first there will still be 3/5 kg more apples than in the second. How many kilograms of apples are in each box?
528 *. 1) The sum of two numbers is 8 11/14, and their difference is 2 3/7. Find these numbers.
2) The boat moved along the river at a speed of 15 1/2 km per hour, and against the current at 8 1/4 km per hour. What is the speed of the river flow?
529. 1) There are 110 cars in two garages, and in one of them there are 1 1/5 times more than in the other. How many cars are in each garage?
2) The living area of an apartment consisting of two rooms is 47 1/2 sq. m. m. The area of one room is 8/11 of the area of the other. Find the area of each room.
530. 1) An alloy consisting of copper and silver weighs 330 g. The weight of copper in this alloy is 5/28 of the weight of silver. How much silver and how much copper is in the alloy?
2) The sum of two numbers is 6 3/4, and the quotient is 3 1/2. Find these numbers.
531. The sum of three numbers is 22 1/2. The second number is 3 1/2 times, and the third is 2 1/4 times the first. Find these numbers.
532. 1) The difference of two numbers is 7; quotient of division more for less 5 2/3. Find these numbers.
2) The difference between two numbers is 29 3/8, and their multiple ratio is 8 5/6. Find these numbers.
533. In a class, the number of absent students is 3/13 of the number of students present. How many students are in the class according to the list if there are 20 more people present than absent?
534. 1) The difference between two numbers is 3 1/5. One number is 5/7 of another. Find these numbers.
2) Father older than my son for 24 years. The number of the son's years is equal to 5/13 of the father's years. How old is the father and how old is the son?
535. The denominator of a fraction is 11 units greater than its numerator. What is the value of a fraction if its denominator is 3 3/4 times the numerator?
No. 536 - 537 orally.
536. 1) The first number is 1/2 of the second. How many times is the second number greater than the first?
2) The first number is 3/2 of the second. What part of the first number is the second number?
537. 1) 1/2 of the first number is equal to 1/3 of the second number. What part of the first number is the second number?
2) 2/3 of the first number is equal to 3/4 of the second number. What part of the first number is the second number? What part of the second number is the first?
538. 1) The sum of two numbers is 16. Find these numbers if 1/3 of the second number is equal to 1/5 of the first.
2) The sum of two numbers is 38. Find these numbers if 2/3 of the first number is equal to 3/5 of the second.
539 *. 1) Two boys collected 100 mushrooms together. 3/8 of the number of mushrooms, collected first boy, are numerically equal to 1/4 of the number of mushrooms collected by the second boy. How many mushrooms did each boy collect?
2) The institution employs 27 people. How many men work and how many women work if 2/5 of all men are equal to 3/5 of all women?
540 *. Three boys bought a volleyball. Determine the contribution of each boy, knowing that 1/2 of the contribution of the first boy is equal to 1/3 of the contribution of the second, or 1/4 of the contribution of the third, and that the contribution of the third boy is 64 kopecks more than the contribution of the first.
541 *. 1) One number is 6 more than the other. Find these numbers if 2/5 of one number are equal to 2/3 of the other.
2) The difference of two numbers is 35. Find these numbers if 1/3 of the first number is equal to 3/4 of the second number.
542. 1) The first team can complete some work in 36 days, and the second in 45 days. In how many days will both teams, working together, complete this job?
2) A passenger train covers the distance between two cities in 10 hours, and a freight train covers this distance in 15 hours. Both trains left these cities at the same time towards each other. In how many hours will they meet?
543. 1) A fast train covers the distance between two cities in 6 1/4 hours, and a passenger train in 7 1/2 hours. How many hours later will these trains meet if they leave both cities at the same time towards each other? (Round answer to the nearest 1 hour.)
2) Two motorcyclists left simultaneously from two cities towards each other. One motorcyclist can travel the entire distance between these cities in 6 hours, and another in 5 hours. How many hours after departure will the motorcyclists meet? (Round answer to the nearest 1 hour.)
544. 1) Three vehicles of different carrying capacity can transport some cargo, working separately: the first in 10 hours, the second in 12 hours. and the third in 15 hours. In how many hours can they transport the same cargo, working together?
2) Two trains leave two stations simultaneously towards each other: the first train covers the distance between these stations in 12 1/2 hours, and the second in 18 3/4 hours. How many hours after leaving will the trains meet?
545. 1) Two taps are connected to the bathtub. Through one of them the bath can be filled in 12 minutes, through the other 1 1/2 times faster. How many minutes will it take to fill 5/6 of the entire bathtub if you open both taps at once?
2) Two typists must retype the manuscript. The first driver can complete this work in 3 1/3 days, and the second 1 1/2 times faster. How many days will it take both typists to complete the job if they work simultaneously?
546. 1) The pool is filled with the first pipe in 5 hours, and through the second pipe it can be emptied in 6 hours. After how many hours will the entire pool be filled if both pipes are opened at the same time?
Note. In an hour, the pool is filled to (1/5 - 1/6 of its capacity.)
2) Two tractors plowed the field in 6 hours. The first tractor, working alone, could plow this field in 15 hours. In how many hours would the second tractor, working alone, plow this field?
547 *. Two trains leave two stations simultaneously towards each other and meet after 18 hours. after his release. How long does it take the second train to cover the distance between stations if the first train covers this distance in 1 day 21 hours?
548 *. The pool is filled with two pipes. First they opened the first pipe, and then after 3 3/4 hours, when half of the pool was filled, they opened the second pipe. After 2 1/2 hours collaboration the pool was full. Determine the capacity of the pool if 200 buckets of water per hour poured through the second pipe.
549. 1) A courier train left Leningrad for Moscow and travels 1 km in 3/4 minutes. 1/2 hour after this train left Moscow, a fast train left Moscow for Leningrad, the speed of which was equal to 3/4 the speed of the express train. At what distance will the trains be from each other 2 1/2 hours after the courier train leaves, if the distance between Moscow and Leningrad is 650 km?
2) From the collective farm to the city 24 km. A truck leaves the collective farm and travels 1 km in 2 1/2 minutes. After 15 min. After this car left the city, a cyclist drove out to the collective farm, at a speed half as fast as the speed of the truck. How long after leaving will the cyclist meet the truck?
550. 1) A pedestrian came out of one village. 4 1/2 hours after the pedestrian left, a cyclist rode in the same direction, whose speed was 2 1/2 times the speed of the pedestrian. How many hours after the pedestrian leaves will the cyclist overtake him?
2) A fast train travels 187 1/2 km in 3 hours, and a freight train travels 288 km in 6 hours. 7 1/4 hours after the freight train leaves, an ambulance departs in the same direction. How long will it take the fast train to catch up with the freight train?
551. 1) From two collective farms through which the road to district center, two collective farmers rode out to the area on horseback at the same time. The first of them traveled 8 3/4 km per hour, and the second was 1 1/7 times more than the first. The second collective farmer caught up with the first after 3 4/5 hours. Determine the distance between collective farms.
2) 26 1/3 hours after the departure of the Moscow-Vladivostok train, the average speed of which was 60 km per hour, a TU-104 plane took off in the same direction, at a speed 14 1/6 times the speed of the train. How many hours after departure will the plane catch up with the train?
552. 1) The distance between cities along the river is 264 km. The steamer covered this distance downstream in 18 hours, spending 1/12 of this time stopping. The speed of the river is 1 1/2 km per hour. How long would it take a steamship to travel 87 km without stopping in still water?
2) Powerboat walked 207 km along the river in 13 1/2 hours, spending 1/9 of this time on stops. The speed of the river is 1 3/4 km per hour. How many kilometers can this boat travel in still water in 2 1/2 hours?
553. The boat covered a distance of 52 km across the reservoir without stopping in 3 hours 15 minutes. Further, going along the river against the current, the speed of which is 1 3/4 km per hour, this boat covered 28 1/2 km in 2 1/4 hours, making 3 stops of equal duration. How many minutes did the boat wait at each stop?
554. From Leningrad to Kronstadt at 12 o'clock. The steamer left in the afternoon and covered the entire distance between these cities in 1 1/2 hours. On the way, he met another ship that left Kronstadt for Leningrad at 12:18 p.m. and walking at 1 1/4 times the speed of the first. At what time did the two ships meet?
555. The train had to cover a distance of 630 km in 14 hours. Having covered 2/3 of this distance, he was detained for 1 hour 10 minutes. At what speed should he continue his journey in order to reach his destination without delay?
556. At 4:20 a.m. morning a freight train left Kyiv for Odessa with average speed 31 1/5 km per hour. After some time, a mail train came out of Odessa to meet him, the speed of which was 1 17/39 times higher than the speed of a freight train, and met the freight train 6 1/2 hours after its departure. At what time did the postal train leave Odessa, if the distance between Kiev and Odessa is 663 km?
557*. The clock shows noon. After how long does the clock and minute hand will they coincide?
558. 1) The plant has three workshops. The number of workers in the first workshop is 9/20 of all workers of the plant, in the second workshop there are 1 1/2 times fewer workers than in the first, and in the third workshop there are 300 fewer workers than in the second. How many workers are there in the factory?
2) There are three secondary schools in the city. The number of students in the first school is 3/10 of all students in these three schools; in the second school there are 1 1/2 times more students than in the first, and in the third school there are 420 fewer students than in the second. How many students are there in total? three schools?
559. 1) Two combine operators worked in the same area. After one combiner harvested 9/16 of the entire plot, and the second 3/8 of the same plot, it turned out that the first combiner harvested 97 1/2 hectares more than the second. On average, 32 1/2 quintals of grain were threshed from each hectare. How many centners of grain did each combine operator thresh?
2) Two brothers bought a camera. One had 5/8, and the second 4/7 of the cost of the camera, and the first had 2 rubles. 25 kopecks more than the second one. Everyone paid half the cost of the device. How much money does everyone have left?
560. 1) A passenger car leaves city A for city B, the distance between them is 215 km, at a speed of 50 km per hour. At the same time, he left city B for city A. truck. How many kilometers did the passenger car travel before meeting the truck, if the truck's speed per hour was 18/25 the speed of the passenger car?
2) Between cities A and B 210 km. A passenger car left city A for city B. At the same time, a truck left city B for city A. How many kilometers did the truck travel before meeting the passenger car, if the passenger car was traveling at a speed of 48 km per hour, and the speed of the truck per hour was 3/4 of the speed of the passenger car?
561. The collective farm harvested wheat and rye. 20 hectares more were sown with wheat than with rye. The total rye harvest amounted to 5/6 of the total wheat harvest with a yield of 20 c per 1 ha for both wheat and rye. The collective farm sold 7/11 of the entire harvest of wheat and rye to the state, and left the rest of the grain to satisfy its needs. How many trips did the two-ton trucks need to make to remove the bread sold to the state?
562. Rye and wheat flour were brought to the bakery. The weight of wheat flour was 3/5 of the weight of rye flour, and 4 tons more rye flour was brought than wheat flour. How much wheat and how much rye bread will the bakery bake from this flour if the baked goods make up 2/5 of the total flour?
563. Within three days, a team of workers completed 3/4 of the entire work on repairing the highway between the two collective farms. On the first day, 2 2/5 km of this highway were repaired, on the second day 1 1/2 times more than on the first, and on the third day 5/8 of what was repaired in the first two days together. Find the length of the highway between collective farms.
564. Fill in free seats in the table, where S is the area of the rectangle, A- the base of the rectangle, a h-height (width) of the rectangle.
565. 1) The length of a rectangular plot of land is 120 m, and the width of the plot is 2/5 of its length. Find the perimeter and area of the site.
2) The width of the rectangular section is 250 m, and its length is 1 1/2 times the width. Find the perimeter and area of the site.
566. 1) The perimeter of the rectangle is 6 1/2 dm, its base is 1/4 dm more height. Find the area of this rectangle.
2) The perimeter of the rectangle is 18 cm, its height is 2 1/2 cm less than the base. Find the area of the rectangle.
567. Calculate the areas of the figures shown in Figure 30 by dividing them into rectangles and finding the dimensions of the rectangle by measurement.
568. 1) How many sheets of dry plaster will be required to cover the ceiling of a room whose length is 4 1/2 m and width 4 m, if the dimensions of the plaster sheet are 2 m x l 1/2 m?
2) How many boards, 4 1/2 m long and 1/4 m wide, are needed to lay a floor that is 4 1/2 m long and 3 1/2 m wide?
569. 1) A rectangular plot 560 m long and 3/4 of its length wide was sown with beans. How many seeds were required to sow the plot if 1 centner was sown per 1 hectare?
2) A wheat harvest of 25 quintals per hectare was collected from a rectangular field. How much wheat was harvested from the entire field if the length of the field is 800 m and the width is 3/8 of its length?
570 . 1) A rectangular plot of land, 78 3/4 m long and 56 4/5 m wide, is built up so that 4/5 of its area is occupied by buildings. Determine the area of land under the buildings.
2) On a rectangular plot of land, the length of which is 9/20 km and the width is 4/9 of its length, the collective farm plans to lay out a garden. How many trees will be planted in this garden if an average area of 36 sq.m. is required for each tree?
571. 1) For normal daylight illumination of the room, it is necessary that the area of all windows be at least 1/5 of the floor area. Determine whether there is enough light in a room whose length is 5 1/2 m and width 4 m. Does the room have one window measuring 1 1/2 m x 2 m?
2) Using condition previous task, find out if there is enough light in your classroom.
572. 1) The barn has dimensions of 5 1/2 m x 4 1/2 m x 2 1/2 m. How much hay (by weight) will fit in this barn if it is filled to 3/4 of its height and if 1 cu. m of hay weighs 82 kg?
2) The woodpile has the shape rectangular parallelepiped, the dimensions of which are 2 1/2 m x 3 1/2 m x 1 1/2 m. What is the weight of the woodpile if 1 cu. m of firewood weighs 600 kg?
573. 1) A rectangular aquarium is filled with water up to 3/5 of its height. The length of the aquarium is 1 1/2 m, width 4/5 m, height 3/4 m. How many liters of water are poured into the aquarium?
2) A pool in the shape of a rectangular parallelepiped is 6 1/2 m long, 4 m wide and 2 m high. The pool is filled with water up to 3/4 of its height. Calculate the amount of water poured into the pool.
574. A fence needs to be built around a rectangular piece of land, 75 m long and 45 m wide. How many cubic meters of boards should go into its construction if the thickness of the board is 2 1/2 cm and the height of the fence should be 2 1/4 m?
575. 1) What angle is the minute and hour hand at 13 o'clock? at 15 o'clock? at 17 o'clock? at 21 o'clock? at 23:30?
2) How many degrees will the hour hand rotate in 2 hours? 5 o'clock? 8 o'clock? 30 min.?
3) How many degrees does the arc contain? equal to half circles? 1/4 circle? 1/24 of a circle? 5/24 circles?
576. 1) Using a protractor, draw: a) a right angle; b) an angle of 30°; c) an angle of 60°; d) angle of 150°; e) an angle of 55°.
2) Using a protractor, measure the angles of the figure and find the sum of all the angles of each figure (Fig. 31).
577. Follow these steps:
578. 1) The semicircle is divided into two arcs, one of which is 100° larger than the other. Find the size of each arc.
2) The semicircle is divided into two arcs, one of which is 15° less than the other. Find the size of each arc.
3) The semicircle is divided into two arcs, one of which is twice as large as the other. Find the size of each arc.
4) The semicircle is divided into two arcs, one of which is 5 times smaller than the other. Find the size of each arc.
579. 1) The diagram “Population Literacy in the USSR” (Fig. 32) shows the number of literate people per hundred people of the population. Based on the data in the diagram and its scale, determine the number of literate men and women for each of the indicated years.
Write the results in the table:
2) Using the data from the diagram “Soviet envoys to Space” (Fig. 33), create tasks.
580. 1) According to the pie chart “Daily routine for a fifth grade student” (Fig. 34), fill out the table and answer the questions: what part of the day is allocated to sleep? for homework? to school?
2) Construct a pie chart about your daily routine.
