Twój koszyk jest pusty
Mixed exercises
{{exercise_number}}. Decide whether the following statements are true or false.
- If the price of a product increases by \latex{ 20 }%, you have to pay €\latex{ 20 } more for it.
- If a number is decreased by \latex{ 4 }%, it becomes \latex{ 96 }% of the original number.
- \latex{ 96 }% of a number can be calculated by multiplying it by \latex{ 0.96}.
- The rate is the number of hundredths of the whole.
- \latex{\frac{4}{5}} of a number is \latex{ 80 }% of the number.
{{exercise_number}}. What percentage of
- \latex{ 1 \,m } is \latex{ 10 \,cm };
- \latex{ 1 \,t } is \latex{ 1 \,kg };
- \latex{ 1 \,hl } is \latex{ 1 \,l };
- \latex{ 1 \,m^2 } is \latex{ 100 \,cm^2 };
- \latex{ 1,000 \,cm^3 } is \latex{ 1 \,litre };
- \latex{ 1 \,cm } is \latex{ 1 \,m ?}
{{exercise_number}}. For which of the following pastries do you get at least a \latex{ 10 }% discount?
€\latex{\cancel{2}} €\latex{ 1.6}
€\latex{\cancel{3}} €\latex{ 2.55}
€\latex{\cancel{1.5}} €\latex{ 1.35}
€\latex{\cancel{4}} €\latex{ 3.2}
€\latex{\cancel{1.2}} €\latex{ 1.14}
{{exercise_number}}. \latex{ 10 }% vinegar (\latex{ 10 }% acetic acid, the rest is water) is a \latex{ 1 : 9 }; \latex{ 1 : 10 } or \latex{ 1 : 11 } mixture?
{{exercise_number}}. What % is the discount on a pair of headphones if they cost €\latex{ 13.5 } instead of €\latex{ 15? }
{{exercise_number}}. What percentage is the discount on a laminated flooring that costs €\latex{ 5.6 } instead of
€\latex{ 7\,per\,square\,metre?}
{{exercise_number}}. A box of paper tissues is discounted to €\latex{ 1.47 } from €\latex{ 2.1 }. What percentage is the discount when buying \latex{ 5 } boxes?
{{exercise_number}}. At a store, a €\latex{ 240 } fridge is discounted to €\latex{ 210 }, while another store offers a \latex{ 12 }% discount. Where should you buy the fridge?
{{exercise_number}}. What % of the minuend is the difference, if the subtrahend is \latex{\frac{1}{5}th} of the minuend?
{{exercise_number}}. \latex{ 30 }% of a number is subtracted from it, then \latex{ 25 }% of the difference is subtracted from the result to get \latex{ 42 }. What is the original number?
{{exercise_number}}. At a national park, \latex{ 518 } birds that were banded the previous \latex{ year } have been recaptured. How many birds were banded in the previous \latex{ year } if \latex{ 26 }% of them have not been recaptured this \latex{ year? }
{{exercise_number}}. \latex{\frac{2}{5}} of the students in a class walk to school, \latex{\frac{3}{10}} ride a bicycle, while the rest take the bus. How many students are in the class if \latex{ 9 } students take the bus to school? Make a diagram.
{{exercise_number}}. How many \latex{ degrees } is the angle that is
- \latex{ 40 }% of a straight angle;
- \latex{ 25 }% of a right angle larger than \latex{ 20 }% of a full angle?
*{{exercise_number}}. \latex{ 20 }% of the sum of two positive numbers is equal to the difference of the numbers. What percentage of the smaller number is the larger number?
{{exercise_number}}. A straight angle is divided into three angles. The first angle is \latex{150}% larger than the second angle, while the second angle is \latex{\frac{2}{3}} of the third angle. How many \latex{ degrees } are the angles?
{{exercise_number}}. The diagrams show the results of a test in two \latex{ 6th } grade classes. There are \latex{ 25 } students in Class \latex{ 6}/a.
Class \latex{ 6 }/a
Class \latex{ 6 }/b
\latex{ 4 }%
\latex{ 12 }%
\latex{ 44 }%
\latex{ 40 }%
A
B
C
D
number
of students
of students
\latex{ 8 }
\latex{ 6 }
\latex{ 4 }
\latex{ 2 }
\latex{ 0 }
A
B
C
D
- How many students are in class \latex{ 6 }/b?
- In which class did more students get an A on their test?
- What % of class \latex{ 6 }/b got a B on their test?
- How many more C’s are in class \latex{ 6 }/a than in class \latex{ 6 }/b?
{{exercise_number}}. A streaming platform has two types of subscriptions. There are \latex{ 5,400 } subscribers in total. The diagram shows the distribution of subscribers according to packages. \latex{ 10 }% of the subscribers of package \latex{ 1 } cancelled their subscription, while the number of subscribers of package \latex{ 2 } increased by \latex{ 15 }%. How did the total number of subscribers change?
package \latex{ 1 }
\latex{ 60 }%
\latex{ 60 }%
package \latex{ 2 }
\latex{ 40 }%
\latex{ 40 }%
{{exercise_number}}. How many \latex{ seconds } more is \latex{ 2 }% of one \latex{ hour } than \latex{ 30 }% of \latex{ 1 } \latex{ minute? }
{{exercise_number}}. You have read \latex{ 25 }% of a book. If you read \latex{ 50 } more pages, you will have \latex{ 16 } pages until the middle of the book. How many pages does the book have?
*{{exercise_number}}. What time is it now if the time passed from a \latex{ 24 }-\latex{ hour } day is \latex{ 60 }% of the remaining time?
{{exercise_number}}. The sum of two positive numbers is \latex{ 500 }, and the first number is \latex{ 25 }% of the second. What are the two numbers?
{{exercise_number}}. What is \latex{\frac{2}{3}} of the number, whose \latex{\frac{3}{5}} is \latex{ 36? }
{{exercise_number}}. The length of the sides of a square is increased by \latex{ 25 }%. By what percentage has its perimeter and area increased?
{{exercise_number}}. The length of the edges of a cube is increased by \latex{ 50 }%. By what percentage has its surface area and volume increased?
*{{exercise_number}}. Two positive numbers are reciprocals of each other. One number is decreased by \latex{ 20 }%. By what percentage should the other number be increased so that they remain the reciprocals of each other?
{{exercise_number}}. At birth, the length of a whale is \latex{\frac{2}{3}} of its length plus \latex{ 20 }% of its length plus \latex{ 92\;cm }. How long is the whale?
{{exercise_number}}. The length of the sides of a square is reduced to half. By what percentage has its perimeter and area decreased?
{{exercise_number}}. \latex{ 25 }% of one-fourth of a number is \latex{ 25 }. What is this number?
{{exercise_number}}. Two positive integers different from each other are increased by \latex{ 20 }%. By what percentage does
- their sum;
- their difference;
- their product;
- their quotient increase?
{{exercise_number}}. What percentage of the two-digit positive numbers are divisible by
- \latex{ 2 };
- \latex{ 3 };
- \latex{ 4 };
- \latex{ 5 };
- \latex{ 9 ?}
{{exercise_number}}. How many natural numbers meet the requirements below?
- \latex{ 25 }% are greater than \latex{ 10 }, while \latex{ 90 }% are smaller than \latex{ 45 }.
- \latex{ 25 }% are greater than \latex{ 10 }, while \latex{ 80 }% are smaller than \latex{ 32 }.
{{exercise_number}}. After asking for a loan of €\latex{ 198,000 }, you must pay €\latex{ 13,200 } as interest for one \latex{ year. } How much interest would you pay if you needed a loan of €\latex{ 105,600 } with the same conditions?
{{exercise_number}}. How much money would you have after \latex{ 1 } \latex{ year } if you had €\latex{ 500 } in your bank account at an interest rate of \latex{ 4 }%?
*{{exercise_number}}. \latex{\frac{2}{3}} of a number equals \latex{ 75 }% of another number. The smaller number is \latex{ 24 }. What is the absolute value of the two numbers' difference?
{{exercise_number}}. What percentage of \latex{ 75 }% of a number is half of the same number?
*{{exercise_number}}. At a school event, the \latex{ 6 }th graders are selling juice made from syrup. The syrup is mixed with water at a ratio of \latex{ 1:5 }. \latex{ 1\; litre } of the syrup costs €\latex{ 4 }, and \latex{ 1 \;l } of water costs €\latex{ 0.5 }. A \latex{ 200 \;ml } plastic cup costs €\latex{ 0.08 }. What should the price of a cup of juice be if the students want to obtain a profit of \latex{ 20 }% per cup?
{{exercise_number}}. \latex{ 6 }th-grade students asked a travel agency for a quote for the class trip. According to the offer, accommodation and food for \latex{4} days cost €\latex{ 280 } per person, and the bus rental for the whole trip is €\latex{700.} There are \latex{ 28 } people participating in the trip (including the teachers).
- How much does the trip cost for one person?
- How does the price change if the trip becomes shorter and the cost of the bus rental is reduced by \latex{ 12 }%?
*{{exercise_number}}. At a pet shop, two types of dog food (Charlie and Bloky) are mixed at a ratio of \latex{ 2:3 }. \latex{ 1 \;kilogram } of the mixture is sold for €\latex{ 3 }. One \latex{ kilogram } of Bloky dog food costs €\latex{ 2.8 }. How much does one \latex{ kilogram } of Charlie dog food cost? How much should the price of the mixture be increased if the price of the Charlie dog food increases by \latex{ 20 }%?