Сепетиңиз бош
How to calculate percentages
Total
120 pcs
120 pcs
35 %
Example 1
A museum moved \latex{ 35 }% of its \latex{ 120 }-piece butterfly collection to a new storage facility. How many butterflies were moved?
Solution 1 (deduction)
\latex{ \div100 }
\latex{ 35 }\latex{\times}
\latex{ 100 }%
\latex{ 35 }%
\latex{ \div100 }
\latex{ 120 } butterflies
? butterflies
\latex{ 35 }\latex{\times}
\latex{ 1 }%
\latex{ 35 }%
\latex{ 120\div100=1.2 } butterflies
\latex{ 35 }\latex{\times}\latex{ 1.2 =1.2 } butterflies\latex{ = 42 } butterflies
Solution 2 (calculating the percentage, multiplication)
if \latex{ 100 }% \latex{\longrightarrow } \latex{ 120 } butterflies, then
\latex{ 35 }% \latex{\rightarrow} \latex{\frac{35}{100}} \latex{\longrightarrow} \latex{\frac{35}{{\underset{5}{\cancel{100}}}}\times{\overset{6}{\cancel{120}}}=} \latex{ 42 } butterflies.
\latex{ 42 } butterflies were moved to the new storage facility.
Example 2
In January, a car factory produced \latex{ 3,500 } cars. In February, they made \latex{ 15 }% more cars. How many cars did they make in the first two \latex{ months } combined?
Solution 1 (deduction)
If you take the January amount as \latex{ 100 }%, then that of February is \latex{ 115 }%.
\latex{ \div100 }
\latex{ 115 }\latex{\times}
\latex{ 100 }%
\latex{ 115 }%
\latex{ \div100 }
\latex{ 3,500 } cars
? cars
\latex{ 115 }\latex{\times}
\latex{ 1 }%
\latex{ 115 }%
\latex{ 3,500\div100 = 35 } cars
\latex{ 115 } \latex{\times}\latex{ 35 } cars \latex{ = 4,025 } cars
The factory produced \latex{ 3,500 + 4,025 = 7,525 } cars in the first two \latex{ months } of the \latex{ year. }
Solution 2 (calculating the percentage, multiplication)
Take the \latex{ 3,500 } cars produced in January as \latex{ 100 }%. The number of cars made in February is \latex{ 15 }% more, which is \latex{ 115 }% of the January number. The total number of cars produced in January and February combined is 1\latex{ 00 + 115 = 215 }% of the number of cars produced in January.
\latex{ 100 }% \latex{\longrightarrow } \latex{ 3,500 } cars;
\latex{ 215 }% \latex{\longrightarrow } ? cars
\latex{ 215 }% \latex{\rightarrow} \latex{\frac{215}{100}} \latex{ = 2.15 } \latex{\longrightarrow } \latex{ 2.15 } \latex{\times } \latex{ 3,500 } cars \latex{ = 7,525 } cars.
The factory produced \latex{ 7,525 } cars in the first two \latex{ months. }
Example 3
The same car manufacturer increased the price of its €\latex{15,000 } model by \latex{ 20 }%. As this turned out to be too expensive for its customers, the company decided to reduce the new price by \latex{ 30 }%. What is the new price of the model now?
Solution
First, calculate the price of the car after the \latex{ 20 }% increase.
Original price
Increased price
\latex{ 100 }%
\latex{ 120 }%
\latex{ 1 }%
€\latex{ 15,000 }
€ ?
€\latex{ 150 }
Increased price
\latex{ 120 }%
€\latex{ 120 } \latex{\times} €\latex{ 150 = }€\latex{18,000 }
What does not add up?
\latex{ - 30 }%
sale
With the second price change, they reduced the previously increased price, so we now have to calculate with a base of €\latex{ 18,000 } (\latex{ 100 }%):
Increased price
Reduced price
\latex{ 100 }%
\latex{ 70 }%
\latex{ 1 }%
€\latex{ 18,000 }
€ ?
€\latex{ 180 }\latex{ }
Reduced price
\latex{ 70 }%
€\latex{ 70 } \latex{\times}€\latex{ 180 =} €\latex{12,600 }
The price of the car after two price changes is €\latex{ 12,600 }.
Exercises
{{exercise_number}}. Calculate the following percentages of \latex{ 900 }:
- \latex{ 1 }%;
- \latex{ 10 }%;
- \latex{ 5 }%;
- \latex{ 20 }%;
- \latex{ 25 }%;
- \latex{ 40 }%;
- \latex{ 80 }%;
- \latex{ 120 }%;
- \latex{ 150 }%;
- \latex{ 200 }%.
{{exercise_number}}. Match the fractions (\latex{ a-f }) and their corresponding percentages (\latex{ A-F }).
- \latex{\frac{2}{5}}
- \latex{\frac{1}{4}}
- \latex{\frac{1}{5}}
- \latex{\frac{3}{10}}
- \latex{\frac{6}{5}}
- \latex{\frac{3}{1000}}
- \latex{ 30 }%
- \latex{ 20 }%
- \latex{ 0.3 }%
- \latex{ 25 }%
- \latex{ 120 }%
- \latex{ 40 }%
{{exercise_number}}. How many \latex{ degrees } are the following percentages of a right angle, a straight angle and a full angle?
- \latex{ 50 }%
- \latex{ 10 }%
- \latex{ 40 }%
- \latex{ 100 }%
- \latex{ 200 }%
{{exercise_number}}. How many \latex{ minutes } is \latex{ 10 }% of the length of one \latex{ day? } Answer the question with the following percentages as well.
- \latex{ 25 }%
- \latex{ 72 }%
- \latex{ 100 }%
- \latex{ 150 }%
{{exercise_number}}. If \latex{ 45 }% of the students at a school are boys, how many girls are there if the total number of students is \latex{ 880 ?}
{{exercise_number}}. Let's take a cube with \latex{ 5 } \latex{ cm } edges and paint \latex{ 40 }% of its surface area red. How many \latex{ square } \latex{ centimetres } of the surface ends up red?
{{exercise_number}}. One side of a rectangle is \latex{ 14 } \latex{ cm } long and the other is \latex{ 75 }% of that length. What is the area and perimeter of the rectangle?
{{exercise_number}}. By the end of \latex{ 2000 }, \latex{ 820 } people had reached the summit of Mount Everest (Chomolungma). If \latex{ 85 }% of them used oxygen tanks, how many made it to the summit without one?
{{exercise_number}}. In one store, the price of a €\latex{ 5 } pen was increased by \latex{ 10 }%, while in another, it was reduced by \latex{ 10 }%. What percentage of the original price does the pen cost now, and how do the prices differ in the two stores?
{{exercise_number}}. What is \latex{ 20 }% of ...
- \latex{ 150; }
- \latex{ 55; }
- \latex{ 1,700; }
- \latex{ 3; }
- \latex{ 1.5 ?}
{{exercise_number}}. The result of which of the following multiplications is the same as taking \latex{ 40 }% of \latex{ 150 ?}
- \latex{150\times\frac{2}{5}}
- \latex{150\times0.4}
- \latex{150\times4}
- \latex{1.5\times40}
- \latex{150\times\frac{5}{2}}
- \latex{15\times4}
- \latex{15\times\frac{2}{5}}
- \latex{150\times\frac{4}{10}}
{{exercise_number}}. At a store, customers are given a discount on the price of a pair of glasses based on their age. How much did Gale pay for his glasses if he is \latex{ 11 } \latex{ years } old and the original price was €\latex{ 185 ?}
{{exercise_number}}. A square has sides that are \latex{ 12 } \latex{ cm } long. If we enlarge each side by \latex{ 35 }%, what will the area and perimeter of the new square be?
{{exercise_number}}. Residential use makes up \latex{ 67 }% of a city's water consumption, with factories, public buildings and other facilities using the rest. If the city uses \latex{ 12,000 } \latex{ m^{3} } of water per \latex{ day }, how many \latex{ cubic } \latex{ metres } are used by residents?
{{exercise_number}}. The price of a €\latex{ 12,800 } car was first reduced by \latex{ 20 }%. A few weeks later, the new price was increased by \latex{ 20 }%. What is the current price of the car?
{{exercise_number}}. The Expensive Junk Shop is having a closing-down sale. The price tags show the original price and the discount that applies at the checkout. Which item is the cheapest? By purchasing which 'treasure' will you save the most money? Create an imaginary advertising agency and think of different ways to advertise the shop and its products. Prices are given in Woodchips (WC), the official currency of Timberlandia.
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
WC
\latex{ 1320 }
\latex{ 880 }
\latex{ 980 }
\latex{ 1580 }
\latex{ 620 }
\latex{ 1050 }
\latex{ 780 }
WC
\latex{ 1040 }
\latex{ 760 }
\latex{ 1480 }
\latex{ 560 }
\latex{ 1100 }
\latex{ 820 }
\latex{ 480 }
\latex{ 1080 }
\latex{ 420 }
\latex{ -45 }%
\latex{ -55 }%
\latex{ -65 }%
\latex{ -75 }%
\latex{ -70 }%
\latex{ -45 }%
\latex{ -45 }%
\latex{ -25 }%
\latex{ -15 }%
\latex{ -15 }%
\latex{ -60 }%
\latex{ -40 }%
\latex{ -5 }%
\latex{ -35 }%
\latex{ -65 }%
\latex{ -65 }%
{{exercise_number}}. When dehydrating fruit, its water content is evaporated. How much dried fruit can we get from \latex{ 4.5 } \latex{ kg } of apples if their weight decreases by \latex{ 80 }% during dehydration?
{{exercise_number}}. The total land area of Earth is approximately \latex{ 150,000,000 } \latex{ km^{2} } . The land is divided among the continents as follows: Europe makes up \latex{ 7 }%, Asia \latex{ 30 }%, Africa \latex{ 20 }%, the Americas \latex{ 28 }%, Australia \latex{ 6 }%, and Antarctica \latex{ 9 }%. What is the area of each continent in \latex{ square } \latex{ kilometres? }
{{exercise_number}}. The adjacent sides of a rectangular garden are \latex{ 25 } \latex{ m } and \latex{ 16 } \latex{ m } long. Of its total area, \latex{ 30 }% is grass, \latex{ 60 }% is a kitchen garden, and the rest is planted with flowers. How many \latex{ square } \latex{ metres } are covered in flowers?
Q u i z
Imagine constructing a single large cube out of \latex{ 64 } small cubes of \latex{ 1 } \latex{ cm^{3} }. \latex{ 25 }% of the cubes are yellow. What will be the total area of the yellow cubes on the surface of the large cube?
