mozaMedical by Mozaik Education

The order of operations

Example 1

There are red and blue flowers in the holder shown in the image. How many flowers are there?

Solution

There are \latex{ 4 } + \latex{ 5 } flowers in a row, and since there are \latex{ 6 } rows, \latex{(4 + 5)\times 6 = 9\times6 = 54} flowers.

Perform the operations between brackets first.

Example 2

How many flowers will there be if a customer buys half of the flowers, then two customers take \latex{ 3 } red flowers each?

Solution

One of the customers buys half of the flowers, so \latex{54\div2} flowers are left. The other two customers take \latex{2\times3} red flowers. So there are \latex{54\div2-2\times3 = 27-6 = 21} flowers left.

Perform division and multiplication first.

Example 3

How many flowers will be left if one-third of the flowers are left in each row?

Solution

There are \latex{9 \div 3} flowers in a row. So there are \latex{9 \div 3 \times 6 = 3 \times 6 = 18} flowers left.

Perform the operations in the order they are written (from left to right).

Example 4

How many flowers will there be if a customer buys \latex{ 15 } blue flowers, then they put \latex{ 7 } yellow flowers in the holder?

Solution

There were \latex{ 54 } flowers in the holder, \latex{ 15 } of which were sold, so \latex{54− 15} were left.

\latex{ 7 } flowers were added, so there are \latex{54− 15 + 7 = 39 + 7 = 46} flowers.

Similarly to Example 3, perform the operations from left to right.

By convention, the order of operations is:

Operations in brackets
Divisions and multiplications (from left to right)
Additions and subtractions (from left to right)

Exercises

{{exercise_number}}. Perform the operations.

a) \latex{5\times6+4\times7}

b) \latex{9+11\times13}

c) \latex{7+3\times8-11}

d) \latex{38-(13+11)-4}

e) \latex{45-6\div3+12}

f) \latex{12\times15-15}

g) \latex{56-22+4}

h) \latex{48\div6\times2}

i) \latex{127-36\div9}

{{exercise_number}}. Complete the operations.

a) \latex{9+(8\times6-15)\div3}

b) \latex{70\div7\times2+20-4}

c) \latex{40-20+72\div9}

d) \latex{65-20\div4+6\times5\div3}

e) \latex{65-(20\div4+6)\times6\div3}

f) \latex{120-20\times4+15}

g) \latex{72-13\times4+10-2\times3}

h) \latex{144\div(3\times15-9)}

i) \latex{83-13\times2+5\times14-13}

{{exercise_number}}. Use brackets to get as many different results as possible. Choose one and write an exercise corresponding to it.

a) \latex{12+4\times5+2}

b) \latex{36\div4\times3+6}

c) \latex{36+24\div4+2}

{{exercise_number}}. Use the correct relation symbols (>;=;<) to make each statement true.

a) \latex{8\times(8+3)}⬜ \latex{7\times8+3}

b) \latex{9\times(5-4)}⬜ \latex{9\times5-4}

c) \latex{9\times(10+11)}⬜ \latex{9\times10+9\times11}

d) \latex{71-(18+23)}⬜ \latex{71-18+23}

e) \latex{52-(14+21)}⬜ \latex{9\times10+9\times11}

f) \latex{63-(47-18)}⬜ \latex{63-47+18}

g) \latex{7+6\times8-2}⬜ \latex{(7+6)\times(8-2)}

h) \latex{77\div(7+4)}⬜ \latex{77\div7+4}

{{exercise_number}}. Perform the operations.

a) \latex{2,295 \div 17 - 17 + 1}

b) \latex{2295 \div (17 - 17 + 1)}

c) \latex{45,637-(645-278)\times2}

d) \latex{45,637-(645-278\times2)}

e) \latex{(3,714+5,104)\times[4,765-(4,700+65)]}

f) \latex{81,439\times(456-9\times50-18\div3)}

{{exercise_number}}. How can you calculate the sum of the numbers on the cards quickly?

a)

b)

French-suited cards come in four suits, and the cards are numbered from \latex{ 2 } to \latex{ 10 }.

How many numbered cards are there in a pack?

What is the sum of the numbers on the cards?

{{exercise_number}}. On the planet of the Murmocks, \latex{ 1 } year is \latex{ 5 } months, and \latex{ 1 } month is \latex{ 12 } days long.

a) How many days did an \latex{ 8 }-year, \latex{ 3 }-month, \latex{ 7 }-day-old Murmock live?

b) How old is a \latex{ 360 }-day Murmock?

{{exercise_number}}. Perform the operations.

a) \latex{(76+23)−(48−33)}

b) \latex{(98+54)-(97+37)}

c) \latex{(546+268)−(87+69)}

d) \latex{(759+268)-(1,501-653)}

e) \latex{(3,417-1,079)+(6,804-3,119)}

f) \latex{(8,866-2,244)-(5,533-3,355)}

g) \latex{83+[54-(38-17)]}

h) \latex{4,160-[2,019-(483-216)]}

i) \latex{(35-18)-[27-(28-9)]}

j) \latex{5,426-[(357-186)-(253-199)]}

{{exercise_number}}. Perform the operations.

a) \latex{78 - 27 - (34 - 28 - 3 + 15 - 11)}

b) \latex{87 - (36 + 14) - (52 - 48)}

c) \latex{825−[413−(51−17)]+201}

d) \latex{(25−8)+[(43+7)−(58−19)]}

e) \latex{[(4,117−326)−(411+17)]−361}

f) \latex{398−[218−(184−93+11)]+51}

{{exercise_number}}. Put brackets in the correct places to make the following equalities true.

a) \latex{48-36÷4-3=0}

b) \latex{23-2\times6+1=9}

c) \latex{75-32+28-10=5}

d) \latex{64÷2\times8-3=1}

e) \latex{64÷8-6÷2=16}

f) \latex{27\times18\times5-5\times12=0}

{{exercise_number}}. Use the four basic operations and brackets to express

a) \latex{ 12 } with \latex{ 6 } \latex{ 1 }s;

b) \latex{ 7 } with \latex{ 5 } \latex{ 2 }s;

c) \latex{ 100 } with \latex{ 5 } \latex{ 5 }s;

d) \latex{ 100 } with \latex{ 5 } \latex{ 3 }s.

{{exercise_number}}. What numbers should be written instead of the symbols to make the equalities correct?

a) \latex{(21,478+516)\times\square=0}

b) \latex{(1,000+5\times\triangle)-1=1,104}

c) \latex{\triangledown\times(852-851)=200}

d) \latex{(7,145\div(314-\bigcirc)=7,145}

Quiz

What is the result of the following series of operations?

\latex{10 – 9 \times (9 – 8 \times (8 – 7 \times (7 – 6 \times (6 – 5 \times (5 – 4 \times (4 – 3 \times (3 – 2 \times (2 – 1))))))))}

Mathematics 5.

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