Jūsu grozs ir tukšs
Calculating the rate
(\latex{ 26.3}%)
SZEGED
VESZPRÉM
-
-
:
\latex{ 28 }
\latex{ 25 }
\latex{ 25 /54}
\latex{ 28 /47}
\latex{ 3 /4}
\latex{ 2 /3}
\latex{ 10 /38}
\latex{ 13 /38}
(\latex{ 34.2}%)
(\latex{ 75}%)
BLOCKS / SHOTS
(\latex{ 46.3}%)
(\latex{ 66.7}%)
(\latex{ 59.6}%)
MEN´S HANDBALL CHANPIONSHIP
GOALS / SHOT
\latex{ 7 }M / SHOTS
Example 1
In minute \latex{ 25 }, Szeged was leading against Veszprém \latex{ 15:12 }. Szeged needed \latex{ 20 } shots to score \latex{ 15 } goals. What is their efficiency %\latex{?}
Solution 1
\latex{ 20 } shots
\latex{ 15 } goals
\latex{ 100 }%
?
\latex{20}
\latex{100}
shots
\latex{ 1 }%
\latex{\qquad 15 \quad} goals \latex{ \qquad\qquad\qquad15\div\frac{20}{100}}% \latex{=15\times\frac{\overset{5}{\cancel{100}}}{\underset{1}{\cancel{20}}}}% \latex{=75}%
Solution 2
\latex{\qquad 20 \qquad} shots\latex{ \qquad\qquad\qquad\qquad100 }%
\latex{\qquad1\qquad} shot \latex{ \qquad\qquad\qquad\qquad\frac{100}{20}}% \latex{ =5 }%
\latex{\qquad 15 \qquad} goals\latex{ \qquad\qquad\qquad\qquad15\times5 }% \latex{ =75 }%
\latex{\qquad1\qquad} shot \latex{ \qquad\qquad\qquad\qquad\frac{100}{20}}% \latex{ =5 }%
\latex{\qquad 15 \qquad} goals\latex{ \qquad\qquad\qquad\qquad15\times5 }% \latex{ =75 }%
Solution 3
\latex{ 1 } shot is \latex{\frac{1}{20}} of \latex{ 20 } shots,
\latex{ 15 } goals are \latex{\qquad\frac{15}{20}} of \latex{ 20 }.
\latex{\frac{15}{20}=\frac{75}{100}\rightarrow75} %.
Until minute \latex{25}, the efficiency of Szeged was \latex{75}%.
Example 2
Last \latex{ year, } there were \latex{ 30 } athletes at a school. This \latex{ year }, there are \latex{ 42 }. What percentage of last \latex{ year's } number of athletes is the current number of athletes?
Solution 1
Last \latex{ year's } number of athletes should be \latex{ 100 }%.
\latex{ 30 } athletes
\latex{ 42 } athletes
\latex{ 100 }%
?
\latex{1} athlete
\latex{ 100 }
\latex{ 30 }
%
\latex{\qquad 42 \quad} athletes \latex{ \qquad\qquad\qquad\overset{7}{\cancel{42}}\times\frac{{100}}{\underset{5}{\cancel{30}}}}% \latex{=\frac{700}{5}}% \latex{=140}%
Solution 2
\latex{ 42 } athletes are \latex{\frac{42}{30}} times \latex{ 30 } athletes.
\latex{\frac{42}{30}=\frac{7}{5}=1.4.} \latex{ 1.4 } \latex{\rightarrow140}%.
This \latex{ year's } number of athletes is \latex{ 140 }% of last \latex{ year's } number of athletes.
Example 3
At a store, there is a \latex{ 25 }% discount on a juice; at another, there is a 'buy two, get one free' offer for the same juice. In which store should you buy the juice?
Solution 1
At the first store, the discount is \latex{ 25 }%.
At the other store, you can get three boxes of juice for the price of two.
\latex{ 3 } boxes of juice \latex{ 100 }%
\latex{ 1 } box of juice \latex{\frac{100}{3} }%
\latex{ 2 } boxes of juice \latex{2\times\frac{100}{3}}% \latex{=66.\dot{6}}% \latex{ \approx 66.7}%
\latex{ 1 } box of juice \latex{\frac{100}{3} }%
\latex{ 2 } boxes of juice \latex{2\times\frac{100}{3}}% \latex{=66.\dot{6}}% \latex{ \approx 66.7}%
Thus, the discount is \latex{ 100 }%\latex{ - 66.7 }% \latex{ = 33.3 }%.
Solution 2
If you can get \latex{ 3 } boxes of juice for the price of \latex{ 2 }, then one box costs \latex{\frac{2}{3}} of the price of \latex{ 2 } boxes.
\latex{\frac{2}{3}=0.66\dot6 \approx 0.667.\quad 0.667} \latex{\rightarrow 66.7 }%. The discount is \latex{ 33.3 }%.
It is worth buying the juice at the second store.
Exercises
{{exercise_number}}. Conduct a survey in your class and make a table.
What % of the students in your class
- wear glasses;
- have been abroad;
- went to the zoo last year;
- take the bus to school?
{{exercise_number}}. Conduct a survey in your class and make a table.
- What % of the students got an \latex{ A }, a \latex{ B }, a \latex{ C }, a \latex{ D }, and an \latex{ F } on the last maths test?
- What percentage of the students in your class have \latex{0}; \latex{1}; \latex{2}; \latex{3} or more than \latex{ 3 } siblings?
{{exercise_number}}. Think of similar questions as in exercises \latex{ 1 } and \latex{ 2 }, and conduct a survey.
{{exercise_number}}. What % of \latex{ 50 } are the following numbers?
- \latex{1}
- \latex{2}
- \latex{5}
- \latex{22}
- \latex{65}
- \latex{150}
{{exercise_number}}. What percentage of \latex{ 1 \;hour } is
- \latex{60\,minutes};
- \latex{15 \,minutes};
- \latex{75 \,minutes};
- \latex{6 \,minutes};
- \latex{3 \,minutes};
- \latex{90 \,minutes?}
{{exercise_number}}. What percentage of \latex{ 2 \,km } is
- \latex{800 \,m};
- \latex{240\,m};
- \latex{1,625 \,m};
- \latex{2.3\,km};
- \latex{20 \,m};
- \latex{80 \,m?}
{{exercise_number}}. The price of a €\latex{ 25 } dress was increased by €\latex{ 5 }. What percentage of the original price is the new price?
{{exercise_number}}. The price of a €\latex{ 30 } item was reduced by €\latex{ 18 }. What percentage of the original price is the new price?
{{exercise_number}}. \latex{ 2,430 } of the \latex{ 45,000 } books in a library are in a foreign language. What percentage of the books in the library are in a foreign language?
{{exercise_number}}. At a shooting gallery, \latex{ 15 } of \latex{ 36 } shots hit the target. What percentage of the shots hit the target?
{{exercise_number}}. The diagram shows the results of a survey conducted among sixth-graders on how many smart devices they have. What percentage of the students have \latex{ 1 }, \latex{ 2 }, and \latex{ 3 } smart devices?
\latex{ 42 } students
\latex{ 12 }
students
students
\latex{ 6 }
\latex{ 1 } device
\latex{ 3 } devices
\latex{ 2 } devices
students
{{exercise_number}}. A car travelled \latex{ 168 \;km } of a \latex{ 250 \;km } long journey. What percentage of the journey is completed?
{{exercise_number}}. A pen costs \latex{ 50 \;cents, } while a pencil costs \latex{ 40 \;cents }. What percentage of
- the pen's price is the price of a pencil;
- the pencil's price is the price of a pen;
- the sum of a pencil's and a pen's price is the price of a pen;
- the sum of a pencil's and a pen's price is the price of a pencil?
{{exercise_number}}. A family's monthly income is €\latex{ 2,600 }. They spend €\latex{ 350 } on bills (gas, electricity, water, telephone, Internet, newspapers), €\latex{ 450 } on food and household items, and €\latex{ 110 } on transport and other expenses. What percentage of the monthly income is spent on each type of expense?
{{exercise_number}}. Ask your parents what percentage of your income is spent on bills and food. What percentage of your income do you spend on leisure?
{{exercise_number}}. The table shows the number of students from each grade participating in a maths competition.
grade
number of students
\latex{ 3rd }
\latex{ 4th }
\latex{ 5th }
\latex{ 6th }
\latex{ 7th }
\latex{ 8th }
\latex{ 9 }
\latex{ 15 }
\latex{ 33 }
\latex{ 27 }
\latex{ 24 }
\latex{ 12 }
What percentage of the students were third, fourth, fifth, ..., eighth-graders?
{{exercise_number}}. By what percentage did the store reduce the price of each winter sportswear item?
\latex{ \text{\textemdash} }
€\latex{ 60 }
€\latex{ 6 }
€\latex{ 80 }
€\latex{ 12 }
€\latex{51 }
\latex{ \text{\textemdash} }
\latex{ \text{\textemdash} }
\latex{ \text{\textemdash} }
\latex{ \text{\textemdash} }
€8
€\latex{ 6 }
€\latex{ 9 }
€\latex{ 72 }
€\latex{3 }
Quiz
Crisis in the New Village sports club.
The local newspaper tried to find out what caused the poor performance of the local NVS football team.
– I think the criticism we got is just unfair. Our performance in the second half of the season improved by
The local newspaper tried to find out what caused the poor performance of the local NVS football team.
– I think the criticism we got is just unfair. Our performance in the second half of the season improved by
\latex{ 100 }% – said the coach.
– The NVS has never performed so poorly. We only won \latex{ 3 } of our \latex{ 30 } games –complained a fan.
They both told the truth. How is this possible?
– The NVS has never performed so poorly. We only won \latex{ 3 } of our \latex{ 30 } games –complained a fan.
They both told the truth. How is this possible?