Сепетиңиз бош
Mixed exercises
{{exercise_number}}. Replace the symbols with rational numbers to make the inequalities true.
- \latex{-\frac{5}{2}\lt \square \leq -\frac{1}{2} }
- \latex{-\frac{4}{5}\leq \triangle \leq \frac{1}{2} }
- \latex{-1.5\leq \bigcirc\lt -0.25}
Show the numbers on a number line.
{{exercise_number}}. Write two numbers for each statement.
- greater than \latex{-\frac{4}{5}} and smaller than \latex{-\frac{3}{5}}
- smaller than \latex{\frac{8}{5}} and greater than \latex{\frac{7}{5}}
- not smaller than \latex{\frac{3}{4}} and not larger than \latex{\frac{4}{4}}
{{exercise_number}}. In music, note values are indicated by fractions. The following image shows the note and the rest values.
whole
note
note
dotted half
note
note
half
note
note
dotted
quarter note
quarter note
quarter
note
note
two eighth
notes
notes
eighth
note
note
two sixteenth
notes
notes
sixteenth
note
note
quarter
rest
rest
eighth
rest
rest
Check whether the notations of the following song are correct by adding the note values.
rall.
Moderato
\latex{ p }
Sol
Re
Sol
Sol
Sol\latex{ 7 }
Do
Sol
Re\latex{ 7 }
Re\latex{ 7 }
you!
hap-py
birth-day
to
Hap-py
birth-day
(name)
you,
hap-py
birth-day
to
to
Hap-py
birth-day
to
you,
\latex{ , }
\latex{ , }
\latex{ , }
{{exercise_number}}. Decide whether the following statements are true or false.
- There is a fraction whose reciprocal is a whole.
- There is a multiplication with two factors where both factors are smaller than the product.
- The quotient of two rational numbers can be zero.
- There is a fraction that is greater than \latex{\frac{5}{7}} but smaller than \latex{\frac{6}{7}}.
- The sum of two fractions can be zero.
{{exercise_number}}. Arrange the results of the following operations in ascending order.
- \latex{-1\frac{2}{3}\div \left(-\frac{5}{6} \right)}
- \latex{\frac{8}{17}\times \left(-5\frac{2}{3} \right)}
- \latex{\frac{25}{4}\div \left(-6\frac{1}{4} \right)}
- \latex{\frac{2}{3}\div \left(-\frac{3}{4} \right)\times \frac{3}{2}}
{{exercise_number}}. Write down the following operations using brackets.
- The sum of \latex{\frac{3}{4}} and \latex{\left(-\frac{5}{6} \right)} multiplied by \latex{\frac{4}{5}}.
- Add \latex{1} to the double of the difference of \latex{1}\latex{\frac{1}{2}} and \latex{\left(-\frac{1}{6} \right)}.
- Half of the product of \latex{3.5} and \latex{\frac{1}{2}}.
- The number \latex{\frac{2}{3}} smaller than \latex{\frac{9}{8}}, divided by \latex{\frac{7}{8}}.
{{exercise_number}}. Perform the operations in mind and write down the results.
- \latex{\frac{2}{3}\times \left(-\frac{1}{2} \right)\times \frac{3}{2}\times 6}
- \latex{-\frac{1}{4}\times 7.8\times (-4)}
- \latex{0.125\times 1.6\times (-8)}
{{exercise_number}}. Without calculating, determine which operations will have the same results.
- \latex{\left(\frac{1}{2}+\frac{4}{5} \right) \div \frac{4}{3}}
- \latex{\left(\frac{4}{5}+\frac{1}{2} \right) \times \frac{3}{4}}
- \latex{\left(-\frac{1}{2}-\frac{4}{5} \right) \times \left(-\frac{3}{4} \right)}
- \latex{\left(-\frac{1}{2}-\frac{4}{5} \right) \div \left(-\frac{4}{3} \right)}
- \latex{\left(-\frac{4}{5}+\frac{1}{2} \right) \div \left(-\frac{3}{4} \right)}
- \latex{\left(\frac{4}{5}-\frac{1}{2} \right) \div \left(-\frac{4}{3} \right)}
{{exercise_number}}. Perform the operations. Pay attention to the order of operations.
- \latex{\left(\frac{7}{8}+\frac{3}{4} \right)\times 4-\frac{1}{2}}
- \latex{\frac{7}{8}\times 4+\frac{4}{5}\times 4-\frac{1}{2}}
- \latex{\frac{7}{8}+\left(\frac{3}{4}\times 4-\frac{1}{2} \right)}
- \latex{\frac{7}{8}\times \left(\frac{3}{4}+4 \right)\div \frac{1}{2}}
- \latex{\frac{7}{8}\times \frac{3}{4} +4\div \frac{1}{2}}
- \latex{\frac{7}{8}\times \left(\frac{3}{4}+4\div \frac{1}{2} \right)}
{{exercise_number}}. A barrel contained \latex{ 80\;litres } of rainwater. A vessel was immersed into the barrel \latex{ 24 } times to remove \latex{2\frac{3}{5}} \latex{ litres } of water from the barrel. How many \latex{ 1.6\;l } watering cans can be filled with the water left in the barrel? Check your answer.
{{exercise_number}}. Replace the symbols with numbers that make the equalities true.
- \latex{\frac{2}{3}+\square =-2}
- \latex{-\frac{5}{9}-\triangle =\frac{7}{9}}
- \latex{\bigtriangledown+\left(-\frac{5}{4} \right)=-\frac{7}{12}}
- \latex{\bigcirc\div \left(-\frac{2}{3} \right)=-\frac{1}{2}}
- \latex{\frac{4}{9}\times \Diamond=\frac{5}{12}}
- \latex{\left(\heartsuit -\frac{1}{4} \right) \times \frac{2}{3}=1}
{{exercise_number}}. Arrange the results of the operations A, B, C, and D in descending order.
- \latex{\left(+\frac{2}{35} \right) \times \left(+\frac{7}{3} \right)\times \left(-\frac{15}{4} \right)}
- \latex{2.475\div (-3.12-(-1.47))}
- \latex{\left(\frac{71}{9}-8 \right)\div \left(\frac{5}{18}+\frac{1}{6} \right)}
- \latex{\left[-\frac{2}{3}+\frac{4}{5}+\left(-\frac{7}{15} \right) \right]\div 3}
{{exercise_number}}. A supermarket sells \latex{ 272.5\;kg } of dog food in \latex{7\frac{2}{5}} \latex{kg} and \latex{3\frac{1}{2}} \latex{kg} packages. The number of the two types of packages is equal.
How many packages are there in total? How much dog food is left? Check your answer.
{{exercise_number}}. I have thought of two numbers. Their difference is \latex{6\frac{3}{10}}, and their sum is \latex{13\frac{3}{10}}.
What are the two numbers?
{{exercise_number}}. Grandma is making jam in two pots. One pot holds \latex{ 6.5 } \latex{ litres }, and the other contains \latex{ 4.3 } \latex{ litres }. How many \latex{\frac{3}{4}} \latex{ litre } jars can be filled with this amount? Will there be jars that will not be full?
{{exercise_number}}. Write the correct relation symbol between the numbers.
- \latex{\frac{3}{5}} \latex{0.{6} }
- \latex{\frac{1}{3}} \latex{0.3}
- \latex{\frac{1}{3}} \latex{0.\dot{3} }
- \latex{0.9 } \latex{0.\dot{9} }
- \latex{2.202} \latex{2.0202}
- \latex{0.\dot{6} } \latex{0.666 }
{{exercise_number}}. Find two integers whose quotient is
- \latex{0.6};
- \latex{2\frac{1}{4}};
- \latex{3.8};
- \latex{0};
- \latex{0.\dot{6}};
- \latex{-4\frac{2}{5}}.
Cut a \latex{ 2 × 5 } rectangle out of cling film. Cover any part of the following image with it. Write several series of operations using the covered numbers and operations and calculate the result in each case. Circle the series of operations that results in the largest number. Before starting to calculate, estimate which series of operations will be the largest number.
\latex{2\frac{1}{5} }
\latex{\frac{3}{10} }
\latex{\frac{5}{6} }
\latex{\frac{9}{4} }
\latex{\frac{5}{2} }
\latex{\frac{13}{3} }
\latex{-3.7 }
\latex{-2.4 }
\latex{-2.6 }
\latex{0.25 }
\latex{0 }
\latex{0.01 }
\latex{7\frac{1}{2} }
\latex{-1.8 }
\latex{2\frac{1}{5} }
\latex{\frac{3}{4} }
\latex{-\frac{4}{5} }
\latex{\frac{2}{3} }
\latex{\frac{3}{2} }
\latex{-\frac{2}{5} }
\latex{\frac{5}{4} }
\latex{\times}
\latex{\times}
\latex{\times}
\latex{\div}
\latex{+}
\latex{+}
\latex{+}
\latex{-}
\latex{-}
\latex{-}
\latex{\div}
\latex{\div}
