Fractions - high school - examples
- A large
A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
- Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
Grandfather gathered fresh mushrooms. The fifth was wormwood, and it was thrown away, the other dried up. He obtained 720 grams of dried mushrooms. How many kilograms did the grandfather collect, and by drying the mushrooms they lost 75% of their weight?
- Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together?
After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
- Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?
On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together?
Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
- TV fail
The TV has after 10,000 hours average 25 failures. Determine the probability of TV failure after 200 hours of operation.
- Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
- Mystery of stereometrie
Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
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