Kori on tyhjä
Mixed exercises
{{exercise_number}}. Decide whether the following statements are true or false.
- If the remainder of a number is \latex{ 2 } when divided by \latex{ 9 }, then its remainder is also \latex{ 2 } when divided by \latex{ 3 }.
- If the remainder of a number is \latex{ 0 } when divided by \latex{ 3 }, then its remainder is also \latex{ 0 } when divided by \latex{ 9 }.
- If the remainder of a number is \latex{ 4 } when divided by \latex{ 5 }, then its remainder is also \latex{ 4 } when divided by \latex{ 10 }.
- If the remainder of a number is \latex{ 7 } when divided by \latex{ 10 }, then its remainder is also \latex{ 7 } when divided by \latex{ 5 }.
{{exercise_number}}. Choose two of the numbers \latex{ 108;\, 1,225;\, 729 } and \latex{ 5,255 } so that
- their sum is even;
- their sum is divisible by \latex{ 3 };
- their sum is a multiple of \latex{ 10 };
- their product is a multiple of \latex{ 6 };
- their product is not divisible by \latex{ 9 }.
{{exercise_number}}. Write \latex{ 576 } as
- the sum of two not even numbers;
- the sum of two numbers, one of which is divisible by \latex{ 9 };
- the product of two numbers greater than \latex{ 1 }, both multiples of \latex{ 3 }.
{{exercise_number}}. Complete the subtrahend with one digit, so the result of \latex{489-5\square} is
- divisible by \latex{ 5 };
- divisible by \latex{ 4 };
- divisible by \latex{ 3 }.
{{exercise_number}}. What is the remainder of \latex{ 41;\,\; 252;\,\; 1,812;\,\; 5,780 } and \latex{ 2,007 } when divided by
- \latex{ 2 };
- \latex{ 3 };
- \latex{ 4 };
- \latex{ 5 };
- \latex{ 9? }
{{exercise_number}}. Calculate the remainder of \latex{ 78;\,\; 95;\,\; 112;\,\; 101 } and \latex{ 129 } when divided by \latex{ 5 }. Write
- additions with three addends if the remainder of the sum is \latex{ 2 } when divided by \latex{ 5 };
- multiplications with three factors if the remainder of the product is \latex{ 0 } when divided by \latex{ 5 }.
{{exercise_number}}. Zoe bought several items at the store. The prices were \latex{ 156 }¢; \latex{ 339 }¢; \latex{ 150 }¢ and \latex{ 162 }¢. After calculating the total price, the cashier said: "How strange, you must pay exactly €\latex{ 10. }"
Zoe replied: "It is impossible." How did Zoe know that the cashier was wrong if she had not added together the prices of the items?
{{exercise_number}}. Without performing the divisions, choose which of the numbers \latex{ 13,548;\, 875;\, 76,524;\,\; 4,636;\,\; 774,375;\,\; 8,556;\,\; 49,512;\,\; 1,774,800 } and \latex{ 848,655 } are divisible by
- two;
- three;
- four;
- five;
- six;
- eight;
- nine;
- ten;
- \latex{ 25 };
- \latex{ 125 }.
{{exercise_number}}. Write a digit after \latex{ 3,758 } so that its remainder does not change when divided by
- three;
- four;
- five;
- nine.
{{exercise_number}}. Determine the highest common factor of the following numbers.
- \latex{ 144;\; 60 }
- \latex{ 60;\; 84;\; 90 }
- \latex{ 140;\; 210;\; 735 }
{{exercise_number}}. The lengths of every edge of a cuboid measured in \latex{ metres } are whole numbers. How long can the edges be if the volume of the cuboid is \latex{28\, m^{3}?} Find all the solutions. Calculate the surface area of the cuboids.
{{exercise_number}}. Perform the operations.
- \latex{\frac{5}{12} +\frac{7}{18}-\frac{2}{15}}
- \latex{\frac{3}{14} +\frac{8}{21}-\frac{2}{5}}
- \latex{\frac{14}{21} +\frac{19}{38}-\frac{45}{54}}
- \latex{\frac{28}{42} +\frac{45}{60}+\frac{55}{66} +\frac{57}{76}-\frac{74}{111}}
{{exercise_number}}. Write down three neighbouring two-digit whole numbers, then
- add them together;
- multiply them.
What number is certainly a factor of the product of the three numbers?
Using prime factor decomposition, find all the factors of the sum and the product.
{{exercise_number}}. Write down the first ten multiples of \latex{ 12 } and \latex{ 15 }, then represent them in a Venn diagram. List the common multiples. Circle the lowest common positive multiple. Find it using prime factor decomposition as well.
{{exercise_number}}. With the help of factor pairs, find every factor of \latex{ 84 } and \latex{ 56 }. Make a Venn diagram. List the common factors. Circle the highest common factor. Find it using prime factor decomposition as well.
{{exercise_number}}. Three friends, Andrew, Bob, and Frank, celebrate the birthday of one of them. Bob jokingly said that they should also celebrate the fact that the sum of their ages is \latex{ 100 }.
How old are they if Andrew's age is divisible by \latex{ 17 }, Bob's age by \latex{ 9 } and Frank's age by \latex{ 15 ?}
{{exercise_number}}. Once upon a time, there was a king who believed he was very clever and was never wrong. On one occasion, he told one of his prisoners the following: "Tell me a riddle, and I will solve it. Until I come up with a solution, you can walk freely around my court. However, you will be beheaded as soon as I solve the riddle." The prisoner came up with the following riddle: "Oh my King, find the smallest pair of four-digit amicable numbers." According to the story, the prisoner outlived the king. You know that the correct answer to the riddle is \latex{ 1,184 } and \latex{ 1,210 }. Prove that these numbers are amicable. (Amicable numbers are a pair of numbers in which each is the sum of the factors of the other number.)
Quiz
What is the area of the rectangle with the question mark?
?
\latex{12\,cm^{2}}
\latex{24\,cm^{2}}
\latex{36\,cm^{2}}
