Сагс хоосон байна
Mixed exercises
{{exercise_number}}. The cylindrical containers shown in the image contain a liquid. What fraction of each container is filled with the liquid? (→)
a)
b)
c)
{{exercise_number}}. What fraction of the chess boards is occupied by the pieces?
a)
\latex{ H }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ G }
\latex{ F }
\latex{ E }
\latex{ D }
\latex{ C }
\latex{ B }
\latex{ 1 }
\latex{ A }
\latex{ 8 }
\latex{ 7 }
\latex{ 6 }
\latex{ 5 }
\latex{ 4 }
\latex{ 3 }
\latex{ 2 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
\latex{ H }
b)
\latex{ H }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ H }
\latex{ G }
\latex{ F }
\latex{ E }
\latex{ D }
\latex{ C }
\latex{ B }
\latex{ 1 }
\latex{ A }
\latex{ 8 }
\latex{ 7 }
\latex{ 6 }
\latex{ 5 }
\latex{ 4 }
\latex{ 3 }
\latex{ 2 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
b)
\latex{ H }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{ F }
\latex{ G }
\latex{ H }
\latex{ G }
\latex{ F }
\latex{ E }
\latex{ D }
\latex{ C }
\latex{ B }
\latex{ 1 }
\latex{ A }
\latex{ 8 }
\latex{ 7 }
\latex{ 6 }
\latex{ 5 }
\latex{ 4 }
\latex{ 3 }
\latex{ 2 }
\latex{ 1 }
\latex{ 2 }
\latex{ 3 }
\latex{ 4 }
\latex{ 5 }
\latex{ 6 }
\latex{ 7 }
\latex{ 8 }
{{exercise_number}}. What fraction of a straight angle are the following angles?
a) \latex{ 90 }°
b) \latex{ 45 }°
c) \latex{ 60 }°
d) \latex{ 30 }°
e) \latex{ 20 }°
{{exercise_number}}.
a) How many \latex{ degrees } is one-fourth of \latex{ 60 }º?
b) How many \latex{ degrees } is one-third of a right angle?
c) How many \latex{ degrees } is one-ninth of a full angle?
b) How many \latex{ degrees } is one-third of a right angle?
c) How many \latex{ degrees } is one-ninth of a full angle?
\latex{\alpha}
\latex{\beta}
\latex{\gamma}
straight
angle
angle
right
angle
angle
full
angle
angle
Help:
{{exercise_number}}. What proportion of an \latex{ hour } is/are
a) \latex{ 1 } \latex{ minute; }
b) \latex{ 2 } \latex{ minutes; }
c) \latex{ 3 } \latex{ minutes; }
d) \latex{ 4 } \latex{ minutes; }
e) \latex{ 5 } \latex{ minutes; }
f) \latex{ 6 } \latex{ minutes; }
g) \latex{ 10 } \latex{ minutes; }
h) \latex{ 12 } \latex{ minutes; }
i) \latex{ 20 } \latex{ minutes; }
j) \latex{ 36 } \latex{ minutes? }
{{exercise_number}}. How many \latex{ minutes } is/are
a) \latex{\frac{1}{2}} \latex{ hour; }
b) \latex{\frac{1}{4}} \latex{ hour; }
c) \latex{\frac{3}{4}} \latex{ hour; }
d) \latex{\frac{1}{3}} \latex{ hour; }
e) \latex{\frac{5}{3}} \latex{ hour; }
f) \latex{\frac{7}{60}} \latex{ hour; }
g) \latex{\frac{4}{5}} \latex{ hour; }
h) \latex{\frac{5}{6}} \latex{ hour; }
i) \latex{\frac{7}{10}} \latex{ hour; }
j) \latex{\frac{11}{12}} \latex{ hour? }
{{exercise_number}}. Simplify the fractions.
a) \latex{\frac{24}{36}}
b) \latex{\frac{18}{27}}
c) \latex{\frac{48}{64}}
d) \latex{\frac{77}{154}}
e) \latex{\frac{120}{140}}
f) \latex{\frac{30}{45}}
{{exercise_number}}. You throw with a black and a white dice. If the number on the white dice is the numerator and the number on the black dice is the denominator, how many different fractions can you get? Are there fractions that can be simplified? Are there equal fractions?
{{exercise_number}}. What numbers do the letters represent on the number lines?
a)
b)
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ A }
\latex{ B }
\latex{ C }
\latex{ D }
\latex{ E }
\latex{\frac{2}{3}}
\latex{\frac{3}{2}}
\latex{\frac{2}{5}}
\latex{\frac{5}{2}}
{{exercise_number}}.
a) Find numbers greater than \latex{\frac{3}{4}} and less than \latex{\frac{4}{5}}.
b) Find numbers greater than \latex{\frac{4}{5}} and less than \latex{\frac{5}{6}}.
{{exercise_number}}. Which fraction is greater? Justify your answer.
a) \latex{\frac{15}{5}} or \latex{\frac{17}{6}}
b) \latex{\frac{9}{4}} or \latex{\frac{13}{6}}
c) \latex{\frac{57}{15}} or \latex{\frac{30}{7}}
d) \latex{\frac{28}{9}} or \latex{\frac{34}{11}}
e) \latex{\frac{5}{8}} or \latex{\frac{7}{10}}
f) \latex{\frac{7}{12}} or \latex{\frac{3}{5}}
{{exercise_number}}. Which fraction is greater?
a) Four times \latex{\frac{7}{12}} or two times \latex{\frac{21}{18}}
b) Five times \latex{4\frac{1}{2}} or six times \latex{3\frac{1}{3}}
c) Four times \latex{\frac{16}{11}} or three times \latex{\frac{64}{33}}
d) Seven times \latex{\frac{10}{8}} or seven times \latex{\frac{30}{24}}
{{exercise_number}}. Perform the operations by grouping the fractions cleverly.
a) \latex{\frac{1}{2}+\frac{3}{4}-\frac{3}{6}+\frac{3}{5}-\frac{3}{4}}
b) \latex{\frac{3}{5}+\frac{1}{3}+\frac{2}{5}-\frac{1}{4}+\frac{2}{3}}
c) \latex{1\frac{3}{4}+\frac{3}{5}-\frac{7}{4}+2\frac{2}{3}+\frac{2}{5}-\frac{2}{3}}
{{exercise_number}}.
a) Show the fractions \latex{\frac{3}{4}; \frac{1}{5};\frac{1}{2}; \frac{1}{4}; \frac{2}{5}} and \latex{\frac{9}{20}} on a number line.
b) How many different additions with two addends can you write using these fractions?
c) Jan and Pan chose two fractions each and added them. The sums calculated by the girls were equal. Write down the two additions.
{{exercise_number}}. Matt wakes up \latex{ 1 } \latex{ hour } before arriving at school. He spends \latex{\frac{1}{6}} of the \latex{ hour } taking a shower, \latex{\frac{2}{15}} dressing, \latex{\frac{1}{4}} eating breakfast and \latex{\frac{3}{10}} tidying. Then he leaves for school. What fraction of the \latex{ hour } does it take him to get there? How many \latex{ minutes } is this?
{{exercise_number}}. Perform the following conversions.
a) \latex{\frac{1}{20}} \latex{ dkg } = ....... \latex{ g }
b) \latex{\frac{4}{5}} \latex{ m } = ....... \latex{ dm }
c) \latex{\frac{3}{4}} \latex{ km } = ....... \latex{ m }
d) \latex{\frac{25}{2}} \latex{ km } = ....... \latex{ m }
e) \latex{\frac{500}{25}} \latex{ cm } = ....... \latex{ dm }
f) \latex{\frac{2}{3}} \latex{ hours } = ....... \latex{ minutes }
{{exercise_number}}. Perform the operations.
a) \latex{\left(\frac{5}{6}-\frac{7}{10}\right)\times5}
b) \latex{\frac{3}{4}\times5-\frac{2}{3}\times4}
c) \latex{2\frac{8}{9}-\frac{2}{5}\times6}
{{exercise_number}}. Perform the operations.
a) \latex{\left(\frac{4}{7}+\frac{2}{7}\right)\div3}
b) \latex{\left(\frac{2}{5}+\frac{4}{5}\right)\div11}
c) \latex{\left(\frac{20}{9}-\frac{2}{3}\right)\div7}
d) \latex{\frac{4}{9}\div\left(\frac{5}{8}+\frac{3}{8}\right)}
e) \latex{\frac{8}{9}\div\left(\frac{10}{3}-\frac{4}{3}\right)}
f) \latex{\frac{15}{7}\div\left(\frac{2}{3}+\frac{26}{6}\right)}
g) \latex{\left(\frac{4}{10}-\frac{2}{5}\right)\div5}
h) \latex{12\div\left(\frac{4}{6}-\frac{6}{9}\right)}
{{exercise_number}}. Perform the operations and compare the results. In which case, could you calculate faster?
a) \latex{\left(\frac{2}{5}+\frac{3}{5}\right)\times4}
\latex{\frac{2}{5}\times4+\frac{3}{5}\times4}
b) \latex{\left(5\frac{1}{2}+\frac{3}{6}\right)\div2}
\latex{5\frac{1}{2}\div2+\frac{3}{6}\div2}
{{exercise_number}}. Perform the operations. Pay attention to the order of the operations.
a) \latex{\frac{2}{7}+\frac{1}{7}\div3}
b) \latex{\left(\frac{2}{7}+\frac{1}{7}\right)\div3}
c) \latex{5\frac{2}{3}-1\frac{1}{3}\div2}
d) \latex{\left(5\frac{2}{3}-1\frac{1}{3}\right)\div2}
e) \latex{\frac{14}{3}\div7-\frac{18}{5}\div6}
f) \latex{\frac{2}{5}\times3+\frac{4}{7}\div2}
g) \latex{\frac{16}{21}\div4+\frac{5}{7}\div3}
h) \latex{3\frac{5}{8}+\frac{3}{4}\times7}
i) \latex{2\frac{7}{10}-3\frac{3}{5}\div9}
j) \latex{\left(\frac{3}{4}+\frac{5}{6}\right)\times4-3\frac{1}{3}}
k) \latex{\frac{7}{10}-\left(\frac{1}{2}-\frac{2}{5}\right)\times6}
l) \latex{\left(3\frac{1}{2}-\frac{5}{9}\right)\times6-10\frac{2}{3}\div16}
{{exercise_number}}. Perform the calculation.
\latex{2\times \left(1-\frac{1}{2}\right)+3\times\left(1-\frac{1}{3}\right)+4\times\left(1-\frac{1}{4}\right)+...+10\times\left(1-\frac{1}{10}\right)=?}
{{exercise_number}}. You are copying your digital images onto a memory card. When four-fifths of the files are copied to the memory card, you see on your screen that there are \latex{ 12 } \latex{ seconds } left to complete the process.
a) What fraction of the images is copied to the memory card in \latex{ 1 } \latex{ second? }
b) How many \latex{ minutes } does the whole process take?
{{exercise_number}}. The letters \latex{ W }, \latex{ X }, \latex{ Y }, and \latex{ Z } symbolise different whole numbers from the set {\latex{ 1; 2; 3; 4 }} but not necessarily in this order.
Which letter represents which number if \latex{\frac{W}{X}-\frac{Y}{Z}=1 ?}
