mozaMedical by Mozaik Education

Mixed exercises

{{exercise_number}}. Which number is greater?

a) \latex{20.49} or \latex{ 20.5}

b) \latex{20.5} or \latex{ 20.54}

c) \latex{20.48} or \latex{20.0489}

d) \latex{0.5} or \latex{ 0.\overset{.}{5}}

e) \latex{\frac{1}{3}} or \latex{ 0.3}

f) \latex{20.01724} or \latex{ 20.017342}

{{exercise_number}}. Convert the following fractions to decimals.

a) \latex{\frac{3}{4}}

b) \latex{\frac{9}{4}}

c) \latex{\frac{9}{40}}

d) \latex{\frac{5}{3}}

e) \latex{\frac{7}{9}}

f) \latex{\frac{10}{11}}

g) \latex{\frac{27}{10}}

h) \latex{\frac{10}{27}}

i) \latex{\frac{5}{7}}

j) \latex{\frac{7}{13}}

k) \latex{\frac{31}{7}}

l) \latex{\frac{91}{130}}

m) \latex{\frac{117}{26}}

n) \latex{\frac{1001}{100}}

{{exercise_number}}. What was the time difference between first and second place in the men's \latex{ 200 } \latex{ m } breaststroke at the Athens Olympics? The athletes' results are given in the table. Put them in the correct order based on their performance. (→)

Jim Piper

KAZ

USA

JPN

HUN

USA

ITA

CAN

AUS

Vladislav Polyakov

Scott Usher

Kosuke Kitajima

Dániel Gyurta

Brendan Hansen

Paolo Bossini

Mike Brown

\latex{ 2:11.76 }

\latex{ 2:11.95 }

\latex{ 2:09.44 }

\latex{ 2:10.80 }

\latex{ 2:10.87 }

\latex{ 2:11.20 }

\latex{ 2:11.94 }

excluded

{{exercise_number}}. Put the following numbers in ascending order.

a) \latex{19.48;\; 1;\; 0.197;\; 19.475;\; 19.5;\; 1.999}
b) \latex{0.0124;\; 0.0241;\; 0.124;\; 0.1024;\; 0.1204}
c) \latex{11.4;\; 1.14;\; 11.04;\; 11.14;\; \frac{114}{100} ;\; \frac{5}{4}}

{{exercise_number}}. Convert the following amounts into decimal form.

a) one quarter of \latex{ 375 }

b) ten quarters of \latex{ 375 }

c) one seventh of \latex{ 4.97 }

d) one seventh of \latex{ 49.7 }

e) one quarter of five times \latex{ 0.4 }

f) one fifth of four times \latex{ 0.4 }

{{exercise_number}}.

a) What number should be added to \latex{ 0.7 } to get \latex{ 1.35 ?}
b) What number should be subtracted from \latex{ 1.2 } to get \latex{ 0.88 ?}
c) \latex{ 35 } times what number is \latex{ 481.25 ?}
d) Which number, when divided by \latex{ 42 }, equals \latex{ 1.234 ?}

{{exercise_number}}. Count backwards.

"I thought of a number. I added \latex{ 1 } to it, subtracted \latex{ 1 } from half of the sum, and then multiplied it by \latex{ 5 } and divided the result by \latex{ 11 }. The quotient is \latex{ 0.5 }. What number did I think of originally?"

{{exercise_number}}. We get the next member in each sequence by multiplying the previous member by \latex{ 100 }. Write down the next three members in each sequences.

a) \latex{0.0001;\; 0.01; ... }

b) \latex{ 0.0023;\;0.23; ... }

c) \latex{ 1.0005;\; 100.05; ... }

d) \latex{ 0.76543;\; 76.543; ... }

{{exercise_number}}. Write down the next two members in each sequence. You get them by dividing the previous member by \latex{ 1,000 }.

a) \latex{ 2,300; ... }

b) \latex{ 7,654.3; ... }

c) \latex{ 701; ... }

d) \latex{ 10.5; ... }

{{exercise_number}}. Complete the calculations. Pay attention to the order of operations.

a) \latex{0.4 \times 2 + 2.75 \times 4}

b) \latex{0.4 \times (2 + 2.75 \times 4)}

c) \latex{3.14 \times 4 - 4.253 \times 2}

d) \latex{(3.14 \times 4 - 4.253) \times 2}

e) \latex{6.42 + 3.36 - 2.88 \div 6}

f) \latex{(6.42 + 3.36 - 2.88) \div 6}

{{exercise_number}}. Complete the calculations and then round the results to tenths.

a) \latex{49.702 + (5.02 - 1.8) \div 4}

b) \latex{49.702 + 5.02 - 1.8 \div 4}

c) \latex{6.4 \div 16 + 4.3 \times 4 - 19 \div 20}

d) \latex{(6.4 \div 16 + 4.3) \times 4 - 19 \div 20}

{{exercise_number}}. Complete the calculations and then round the results to integers.

a) \latex{(1.2 \div 6) \times 4}

b) \latex{1.2 \div (6 \times 4)}

c) \latex{1.2 \div 6 \times 4}

d) \latex{72.84 \times (12 \div 4) \times 3}

e) \latex{72.84 \times 12 \div (4 \times 3)}

f) \latex{72.84 \times 12 \div 4 \times 3}

g) \latex{27.48 \times (60 \div 4) \times 5}

h) \latex{(27.48 \times 60) \div 4 \times 5}

i) \latex{27.48 \times (60 \div 4 \times 5)}

{{exercise_number}}. Write down the results in ascending order.

\latex{A=\left(122.4+\frac{3}{4}-\frac{3}{5}\right)\times60}

\latex{B=122.4+\frac{3}{4}-\left(\frac{3}{5}\times60\right)}

\latex{C=122.4+\left(\frac{3}{4}-\frac{3}{5}\right)\times60}

\latex{D=122.4+\frac{3}{4}-\frac{3}{5}\times60}

{{exercise_number}}. What number can be written in the box ⬜ to make the inequality true?

a) \latex{3.7⬜ \lt 3.8\lt3.⬜1}

b) \latex{8.⬜7 \lt 8.2\lt8.2⬜}

c) \latex{0.058⬜ \lt 0.059\lt0.05⬜1}

{{exercise_number}}. The total width of a framed picture is \latex{ 41 } \latex{ cm } and its length is \latex{ 60 } \latex{ cm }. The frame takes up \latex{ 1.5 } \latex{ cm } of this. How many \latex{ square } \latex{ centimetres } is the frame?

{{exercise_number}}. A Hungarian bank's exchange rates for various currencies in the summer of \latex{ 2024 } were the following.

British Pound: \latex{ 1 } GBP → \latex{ 455.04 } HUF;
Swiss Frank: \latex{ 1 } CHF → \latex{ 387.30 } HUF;
USA-dollar: \latex{ 1 } USD → \latex{ 364.35 } HUF;
Euro: \latex{ 1 } EUR → \latex{ 405.49 } HUF.

How many Hungarian forints did you get after exchanging the following sums?

a) \latex{ 150 } CHF;
b) \latex{ 240 } USD;
c) \latex{ 1,125 } EUR;
d) \latex{ 170 } GBP?

{{exercise_number}}. A company has made a diagram of its mobile phone sales. The first diagram shows the number of mobile phones sold in the second quarter of the \latex{ year }, and the second diagram shows the revenue from these sales.

June

piece

April

May

\latex{ 500 }

\latex{ 450 }

\latex{ 400 }

\latex{ 350 }

\latex{ 300 }

\latex{ 250 }

\latex{ 200 }

\latex{ 150 }

\latex{ 100 }

\latex{ 50 }

\latex{ 357 }

\latex{ 265 }

\latex{ 402 }

revanues (€\latex{ 1,000 })

April

May

June

\latex{ 1,000 }

\latex{ 900 }

\latex{ 800 }

\latex{ 700 }

\latex{ 600 }

\latex{ 500 }

\latex{ 400 }

\latex{ 300 }

\latex{ 200 }

\latex{ 100 }

\latex{ 932.8 }

\latex{ 748.3 }

\latex{ 780.5 }

1. How much did the revenue from the sale of mobile phones change from \latex{ month } to \latex{ month? }

2. What was the average revenue in the second quarter?

3. In which \latex{ month } did they offer a discount? What was the average price of a mobile phone during that period?

Think of other questions you could ask about the diagram.

{{exercise_number}}. The table shows the results of a test on decimal numbers in two different classes.

Which class had the higher average grade?

Class \latex{ 7 }/b

Class \latex{ 7 }/a

\latex{ 9 }

A

B

C

D

F

\latex{ 1 }

\latex{ 2 }

\latex{ 3 }

\latex{ 5 }

\latex{ 8 }

\latex{ 7 }

\latex{ 6 }

{{exercise_number}}. A car uses \latex{ 7 } \latex{ litres } of petrol every \latex{ 100 } \latex{ kilometres }. Its fuel tank holds \latex{ 52.5 } \latex{ litres }.

a) How many \latex{ kilometres } can it go with a full tank?
b) How much will it cost to buy \latex{ 33.7 } \latex{ litres } of petrol, if \latex{ 1 } \latex{ litre } costs €\latex{ 1.4 }?

{{exercise_number}}.

a) Write \latex{ 0.056 } \latex{ km } in smaller units of length.
b) Write \latex{ 73,000 } \latex{ mm } using larger units of length.
c) Write \latex{ 0.000 56 } \latex{ km^{2} } using smaller units of area.
d) Write \latex{ 73,000,000 } \latex{ mm^{2} } in larger units of area.
e) Write \latex{ 0.0000056 } \latex{ m^{3} } using smaller units of volume.
f) Write \latex{ 0.056 } \latex{ cm^{3} } in larger units of volume.

{{exercise_number}}. How long is a commuter train if it consists of three \latex{ 14.20 } \latex{ m } long railway carriages?

{{exercise_number}}. How long is the commuter train, which consists of two first-class carriages (\latex{ 24.5 } \latex{ m }), six second-class carriages (\latex{ 26.4 } \latex{ m }), one dining car (\latex{ 24.5 } \latex{ m }), and one \latex{ 16.64 } \latex{ m } long locomotive?

{{exercise_number}}. A freight train consists of \latex{ 25 } wagons, each \latex{ 14.04 } \latex{ m } long, while another consists of \latex{ 35 } wagons, each \latex{ 16.52 } \latex{ m } long. Which train is longer if both are pulled by a \latex{ 16.64 } \latex{ m } long locomotive?

{{exercise_number}}. You can get the next member in each sequence by adding \latex{ 2.9 } to the preceding member. What numbers can be used to replace the letters?

a) \latex{ A }; \latex{ B }; \latex{ C }; \latex{ 13.4 }; \latex{ 16.3 }; \latex{ D }

b) \latex{ A }; \latex{ 3.01 }; \latex{ B }; \latex{ C }; \latex{ D }; \latex{ E }

c) \latex{ A }; \latex{ B }; \latex{ C }; \latex{ D }; \latex{ 17.7 }; \latex{ E }

{{exercise_number}}. You can get the next member in each sequence by adding the same number to the preceding member. What numbers can be used to replace the letters?

a) \latex{ A }; \latex{ B }; \latex{ 7.5; 9.1; } \latex{ C }; \latex{ D }

b) \latex{ A }; \latex{ 12.3 }; \latex{ B }; \latex{ 15.9 }; \latex{ C }; \latex{ D }

c) \latex{ A }; \latex{ B }; \latex{ 27.4 }; \latex{ C }; \latex{ D }; \latex{ 31.9 }

{{exercise_number}}. Replace the letters in the magic squares with numbers so that each row, column and diagonal adds up to \latex{ 42 }.

\latex{A}

\latex{B}

\latex{C}

\latex{D}

\latex{E}

\latex{F}

\latex{G}

\latex{H}

\latex{I}

\latex{J}

\latex{L}

\latex{K}

\latex{R}

\latex{Q}

\latex{P}

\latex{O}

\latex{N}

\latex{M}

\latex{ 14 }

\latex{ 13.9 }

\latex{ 14.4 }

\latex{ 18.2 }

\latex{ 15.4 }

\latex{ 9.8 }

\latex{ 13.75 }

\latex{ 13.875 }

\latex{ 14.5 }

{{exercise_number}}.

a) Replace the letters with numbers in a way that the difference between the adjacent numbers in the sequence is always the same:

\latex{ A }; \latex{ B }; \latex{ C }; \latex{ 8.35 }; \latex{ 8.7 }; \latex{ 9.05 }; \latex{ D }; \latex{ E }; \latex{ F }.

b) Put the nine numbers from exercise a) into a \latex{ 3\times3 } magic square so that the sum of the numbers is the same in each row, column and diagonal.

{{exercise_number}}. Rectangular room is \latex{ 3 } \latex{ m } wide, \latex{ 4 } \latex{ m } long and \latex{ 3.4 } \latex{ m } high. The door to the room is \latex{ 210 } \latex{ cm } high and \latex{ 1 } \latex{ m } wide, while the window is \latex{ 2 } \latex{ m } high and \latex{ 120 } \latex{ cm } wide. If \latex{ 1 } \latex{ kg } of paint covers \latex{ 9 } \latex{ m^{2} } and you also paint the ceiling, how many \latex{ kg } of paint do you need to buy to paint the room in a single coat?

{{exercise_number}}. Victoria has gone on holiday to Venezuela. She sent the following text messages to her parents back home.

trip:
\latex{ 2.1 } hours

game:
\latex{ 0.3 } hours

lunch:
\latex{ 1.2 } hours

trip:
\latex{ 2.8 } hours

football:
\latex{ 1.7 } hours

Mike, Victoria's brother, was the one who received the messages on his phone. He told their parents about everything Victoria had been up to but gave the times in \latex{ minutes } rather than \latex{ hours. } How did Mike tell the story about Victoria's day?

Quiz

Put the following decimals in ascending order. \latex{0.\overset{.}{1} 23\overset{.}{4};\;0.12\overset{.}{3}\overset{.}{4};\; 0.123\overset{.}{4};\;0.1\overset{.}{2}3\overset{.}{4} }

Mathematics 5.

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