Arithmetic, Fractions
Fractions represent parts of a whole or ratios between numbers. This topic covers understanding, comparing, simplifying, and performing arithmetic operations (addition, subtraction, multiplication, division) with fractions and mixed numbers. Questions often involve practical applications.
-
Question
One-seventh of mathematicians are philosophers, and one-ninth of philosophers are mathematicians. Which are there more of – philosophers or mathematicians?
Sources: -
Question
The journey from home to school takes Yossi `20` minutes. One day, when Yossi was already on his way to school, he remembered that he had forgotten his pen at home. If he continues to school now, he will arrive `3` minutes before the bell. And if he goes back home to get the pen, he will be `7 ` minutes late for class. What fraction of the way to school had Yossi traveled when he remembered that he didn't have a pen?
Note: Yossi walks at a constant speed the entire time.
Sources: -
Question
How can you divide `7` apples equally among `12` children, if you are not allowed to cut any apple into more than `5` pieces?
Sources: -
Question
The sum of several numbers is equal to `1`. Is it possible that the sum of their squares is less than one-tenth?
Sources: -
Shlomi's Schedule
Shlomi dedicates `1/3` of his time to playing games on the tablet, `1/5` of his time to studying at school, `1/6` to watching movies, `1/70` to solving mathematical problems, and `1/3` to sleeping.
Is it possible to live like that?
Sources: -
The Cookies
Avi, Benny, and Danny's mother left a plate of cookies on the table in the morning. Avi woke up, ate one-third of the total number of cookies, and went to school. After that, Benny woke up, unaware that Avi had already eaten some, so he ate one-third of the remaining cookies and also went to school. After that, Danny woke up and ate one-third of the cookies that were left. When their mother returned home, she saw that there were `8` cookies left. How many cookies were there at the beginning?
Sources: -
Question
Calculate the sum:
`1/(1*2)+1/(2*3)+1/(3*4)+...+1/(99*100)`
Topics:Algebra -> Sequences Arithmetic -> Fractions Algebra -> Algebraic Techniques -> Telescoping Sums -
Question
Calculate the product:
`(1-1/2)(1-1/3)(1-1/4)*...*(1-1/100)`
Topics:Algebra -> Sequences Arithmetic -> Fractions Algebra -> Algebraic Techniques -> Telescoping Sums -
Question
Calculate the product:
`(1-1/4)(1-1/9)(1-1/16)*...*(1-1/225)`
-
An Ancient Russian Riddle
Two woodcutters, Ivan and Prokhor, were working together in the forest. They settled down to eat lunch. Ivan had `4` pitas, and Prokhor had `8`. At that moment, a hunter passed by them and asked to join the meal, so they divided the `12` pitas equally among the three of them. After the meal, the hunter really wanted to thank the woodcutters and gave them `15` kopecks. After he left, Ivan and Prokhor began to discuss how to divide the money.
Prokhor suggested simply dividing it equally. But Ivan argued that this would not be fair, because he had twice as few pitas, therefore, in his opinion, Prokhor should receive `10` kopecks and Ivan himself - `5`. How do you think the money should be divided fairly?