Operative priorities and calculations: answers to the exercises in 5th grade.

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The answer key to the math exercises in 5th grade on operating priorities and operations. Know the priority rules for the four operations.

Exercise 1:

Calculate the following expressions by writing the intermediate steps:

a) 7 + 4 x8 =7+32=39

b) 3 x11 – 7×4 =33-28=5

c) 37 – 6 x5 =37-30=7

d) 9 – 4 : 4=9-1=8

e) 32 ÷ 4 – 2 + 7×3 =8-2+21=27

f) 9 x4 : 2 – 5 x2=36:2-10=18-10=8

Exercise 2:

Calculate the following expressions by writing the intermediate steps:

A =6 x(3 + 7) =6×10=60

B =23 – 4 x5 =23-20=3

C =(3 + 5) x(9 – 7)=8×2=16

D =(13 – 7) : 2 =6:2=3

E =5 – [4 − (2 + 1)] =5-[4-3]=5-1=4

F =(3 + 5×7) : 2 +1=(3+35):2+1=38:2+1=19+1=20

Exercise 3:

Write a calculation to find the total price she has to pay.

5×9+12×6,50=123 euros

Exercise 4:

(8 + 2 )x5 =50 ; (9 – 3 )x(2 + 5 )=42 ; (8 + 4 )x(3 : 2) =18

Exercise 5:

A=24– 5 – 1=18

B =14 x3 – 5 x2=32

C =10 : [ 6 – 2x(1 – 0.5) ] x5=10

D =8 : 4 – 0.25×2=1.5

E =3 x(7 – 2) – 4=11

F =72 : 9 x8 : 2 – 9 x3=5

Exercise 6:

Using the numbers 3; 7; 10 and

as many times as you want the signs + – x : ( ) try to obtain the following results :

3+7+10=20 ;10+7-3= 14 .

Exercise 7:

Put the brackets and square brackets so that the equality is true:

[ 5 x4 -( 1+ 2) ]x2 = 34

Exercise 8:

Write the expression to calculate the amount of his purchases.

16(24+11+4,5)=632 €

Exercise 9:

Write the expression that calculates the boxer’s weight on the day of the fight.

86.2-7×0.6=82 kilos

Exercise 10:

A = 125 – 7 x4 + 11=108

B = (125 – 7) x4 + 11= 483

C = 125 – 7 x(4 + 11) = 20

D = 125 – (7 x4) + 11= 108

E = [(125 – 7) x4] + 11=483

F= 125 – [7 x(4 + 11)]=20

Exercise 11:

1) 12,7 + 3,1×2 =18,9

2) 12,7 – 3,1×2 =6,5

3) 12.7 x3 + 3.1×7=59.8

4) 12.7 x3 – 3.1×8 = 13.3

5) (5 – 3) x(9,1 – 7,8)=2,6

6) (5 + 3) x(9,1 + 7,8)= 135,2

Exercise 12:

A = – 4 + 15 + ( 9 – 4) – 2 + (-4 + 1 ) = 11

B = – 35 + [12 + ( 75 – 55) – (15 – 8 ) ] + 7 = – 3

C = 4 – (7 – 3 ) – [ 11 – ( 8 – 5)] = – 8

Exercise 15:

A = 7 + 4 x8=7+32=39

B = 3 x11- 7×4=33-28=5

C = 37 – 6 x5=37-30=7

D = 9 – 4 : 4=9-1=8

E = 32 ÷ 4 – 2 + 7×3=8-2+21=27

F = 9 x 4:2 – 5 x2=36:2-10=18-10=8

Exercise 16:

x = 132 – 11×10 + 4 x2,5=132-110+10=32

y = 12,5 – 2 – 5,1 + 15 – 1,2=19,2

z = 120 – 4×5 – 7x’8 + 54 : 9 =50

t = 22 + 3×1.5 – 1.5=25

Exercise 17:

X = 2.9 + 0.8 x5 =6.9

T = 4 x0.5 + 3 x1.36 =6.08

C = 12.8 – 0.7 x 9=6.5

A = 10 – 9,9 : 3 =6,7

E = 0.23 x 5 + 99.18 :17.1=6.95

Exercise 18:

M = (6 + 2) x 7=8×7=56

N = 17 x (15 – 11)=17×4=68

O = (3.5 + 6.5)x(14 – 9.5)10×4.5=45

P = (18 – 11) x(5 + 9)=7×14=98

Exercise 19:

A =6 x (3 + 7) =6×10=60

B =23 – 4 x 5 =23-20=3

C =(3 + 5)x (9 – 7) =8×2=16

D =(13 – 7) : 2=6:2=3

E =5 – [4 – (2 + 1)] =5-(4-3)=5-1=4

F =(3 + 5x 7) : 2 +1=(3+35):2+1=38:2+1=19+1=20

Exercise 23:
Perform the following calculations, detailing the various steps:

$A=8\times ,(26-14)=8\times ,12=96$

$C=(0,5+15+35+8,5+1,75)\times ,(55+45))=60,75\times ,100=6,075$
$D=(1,2+3,8)\times ,(5,5-4)-(7,5-6)=5\times ,1,5-1,5=6$

Exercise 24:
Calculate the expressions by detailing the calculations:

$A=7\times ,%5B16-(2+9)%5D=7\times ,(16-11)=7\times ,5=35$
$B=%5B9-(9-8)%5D\times ,%5B(2+7):3%5D=8\times ,3=24$
$C=4\times ,%5B39,2-(2,4+4,8)+3%5D=4\times ,35=140$
$D=120:,%5B(66-(25+8-7)):2+3%5D=120:(40:2+3)=120:23=\frac{120}{23}$ .

Exercise 25:
a. The sum of 7.5 and the product of 3 by 1.5 ;

$A=7,5+3\times ,1,5$

b. The product of 7.5 and the sum of 3 and 1.5 ;

$B=7,5\times ,(3+1,5)$

c. The quotient of the sum of 12 and 8 by 100 ;

$C=\frac{12+8}{100}$

d. The sum of the product of 3 by 6 and the result of subtracting 7 from 15.

$D=3\times ,6+(7-15)$

Exercise 26:

$A\,=\,12\,+\,8\,\times \,5\,-\,4\,+\,16\,: \,2\,\\A=12+40-4+8\\A=52+4\\A=56\\\,\.\,\\B\,=\,17\,-(3\,+\,8\,-\,5)\\B\,=\,17\,-(11\,-\,5)\\B\,=\,17\,-6\\B=11\,\\C\,=\,18\,+\,4\,\times \,(7\,\times \,2\,-\,6)\\C\,=\,18\,+\,4\,\times \,(14\,-\,6)\\C\,=\,18\,+\,4\,\times \,12\\C\,=\,18\,+\,48\\C=66\,\\D\,=\,75\,-\,(6\,+\,3\,\times \,10)\,: \,9\\D\,=\,75\,-\,(6\,+\,30)\,: \,9\,\\D\,=\,75\,-\,36\,: \,9\\D\,=\,75\,-\,4\\D=71\,\\E\,=\,3\,200\,\times \,0,01\,\times \,100\,-\,100\,\\E\,=\,3\,200\,\times \,1-100\\E=3100$

$\\F\,=\,(5,6\,+\,1,4)\,\times \,(3,4\,-\,1,4)\\F\,=\,7\,\times \,2=14\\\,\\G\,=\,48\,+\,2\,\times \,(7\,+\,3\,\times \,5\,-\,2\,\times \,10)\,\\G\,=\,48\,+\,2\,\times \,(7\,+\,15\,-\,20)\,\\G\,=\,48\,+\,2\,\times \,2\\G\,=\,48\,+\,4\\G\,=\,52\\H\,=\,5\,+\,3\,\times \,6\,-\,8\,: \,2\,\\H\,=\,5\,+\,3\,\times \,6\,-\,8\,: \,2\\\\H\,=\,5\,+\,18\,-\,4\\H\,=\,23\,-\,4\\H\,=19$

Exercise 27:

A = 12 + (3 × [5 + (4 × 7) + 2]) + (8 × 3)

A = 141

B = 25 – [12 – (3 + 4)]

B = 20

C = 81 + [(7 + 21) – 13] – (17 – 9)

C = 88

D = [(7,8 – 4,5) + 11]×(4 + 3)

D = 100,1

E = 6 + [(7 × 2) – (1,1 × 2)]

E = 17,8

Exercise 28:

How many shelves will it fill?

$130: \,13=10$

He will store them in 10 shelves.

Exercise 29:

At a flea market, Marc bought 8 books, 4 DVDs and 2 comics.

Each book cost 1.5 euro and a comic book 4 euros.

He paid a total of 38 euros.

What is the price of a DVD?

$8\times \,1,5+2\times \,4=12+8=20$

Conclusion : The price of a dvd was 4,5 euros .

Exercise 30:

Calculate the following expressions by writing the intermediate steps:

a) 7 + 4x 8=7+32=39

b) 3×11 – 7x 4 =33-28=5

c) 37 – 6x 5 = 37-30 =7

d) 9 – 4 : 4 = 9-1=8

e) 32 ÷ 4 – 2 + 7 x 3 =8-2+21=6+21=27

f) 9 x4 : 2 – 5x 2=36:2-10=18-10=8

Exercise 31:
1) A farmer has 102 eggs and collects 18 more. He must ship his eggs in boxes of 12. How many boxes will it ship?

2) The college bursar’s office purchases 102 cartons of white paper and 12 of colored paper. A box costs 18 €.
What is the total price to pay?

$(102+12)\times \,18=114\times \,18=2052$

3) A department store receives its delivery of fruit juice, 18 boxes of 12 bottles. It remains in reserve 102
bottles. How many bottles of juice are there now in this department store?

$18\times \,12+102=318$

Exercise 32:

A bookseller received a first package containing 50 Harry Potter books,
then a second one containing 80.
He stores them on shelves that can hold 13 books.
How many shelves will it fill?

He received a total of 130 pounds (80+50 = 130 ).

130:13=10

It will fill 10 shelves.

Exercise 33:

$A\,=\,15\,+\,60\,: \,5\,\times \,6\,-\,3\,\\=\,15\,+12\times \,6\,-\,3\\=\,15\,+72\,-\,3\\=\,84;\,\\\,B\,=\,45\,\times \,8\,-\,20\,: \,4\,\times \,2\\=\,360\,-\,10\\=350\,;\,\\\,C\,=\,150\,-\,(45\,-\,8\,-\,3)-\,34\\=\,150\,-\,34-\,34\\=82\,;\\\,D\,=\,25\,: \,(12\,-4\,-3)\,: \,5\,=1;\\\,E\,=\,48\,+\,36\,: \,6\,: \,3=50\,;\\\,M\,=\,40\,: \,4\,\times \,5=50\,;\,\\\,N\,=\,24\,: \,6\,\times \,2=8\,;\\\,O\,=\,15\,-\,7\,-\,6\,+\,1=3.$

Exercise 34:
$9\,+(\,3\times \,15)\,=\,180\,;\\\,(2\,+\,3)\,\times (\,5\,+\,4\,)=\,45\,;\\\,(8\,+\,9)\times \,6\,+\,4\,=\,106\,;\,\\\,9\,\times \,(5\,+\,17)\,=\,198\,;\\(\,1\,+\,2\,)\times \,3\,=\,9\,;\,\\\,2\,\times \,3\,+\,5\,\times \,8\,+\,2\,=\,106\,;\\\,7\,\times \,(2\,+\,6)\,=\,56\,;\,\\\,3\times \,(5\,+\,1)\,-\,10\,=\,8$

Exercise 35:

$A\,=(5\,+\,7)\times \,2$

$A\,=12\times \,2\,=24$ ;

B= 5 + 7x 2=5+14=19 ;

C= (12 – 4)x 3=8×3=24 ;

D= 12 – 4 x 3=12-12=0 ;

E= (21 – 18)x (12 – 10) + 1

E=3×2+1=7.

F= 18 + [12 – 2x (13 – 9)]

F=18+(12-2×4)

F=18+12-8

F=22.

G= (4.8 – (2.5 + 0.3))x (3 + 3.5)

G=(4.8-2.8)x6.5

G=2×6.5

G=13

H =[18 + 2 x(120 – 45)] x1.5

H=(18+2×75)x1.5

H=168×1,5

H=252

I =700 – [300 – (300 – 80)].

I = 700- (300-500)

I = 700- ( -200)

I = 700+200=900

Exercise 36:

$A=\,6\,+\,27\,:\,3=6+9=15\,\\\,B\,=\,24\,:\,3\,+\,16\,:\,8\,-\,2\,=8+2-2=8\\\,C\,=\,8\times \,6\,-23=48-23=25\,\\\,D\,=\,5\times \,6\,+\,4\,\times \,3=30+12=42\\\,E\,=\,7\,+\,15\,:\,3\,\times \,5=7+5\times \,5=7+25=\,32\\\,F\,=\,3\,+\,4\,\times \,5\,-\,1\,=3+20-1=22\\\,G\,=\,15\times \,5\,-\,2=75-2=73\,\\\,H\,=\,55\,-\,7\,\times \,6\,+\,1=55-42+1=14\\\,I\,=\,12\,\times 4\,-\,15\,:3=48-5=43.$

Exercise 37:

Write the calculation for the change given in a single expression and then perform the calculation.

$20-4\times \,2,5-6=20-10-6=4$

We gave him back 4 euros.

Exercise 38:

I bought a can of oil at 12 € and four tires at 45 € each.

Write the calculation for the amount of the expense in one expression.

$12+4\times \,45$

Then perform this calculation.

$12+4\times \,45=12+180=192$

The amount of the expense is 192 euros.

Exercise 39:

– F is the product of 4 and the sum of 12 and 5.

– G is the sum of the product of 6 by 8 and 20.

$G=6\times \,8+20$

– H is the sum of 9 and the product of 11 by 3.

$H=9+11\times \,3$

– I is the quotient of the sum of 8 and 4 by 6.

$I=\frac{8+4}{6}$

– J is the difference of 7 and the quotient of 25 by 7.

$J=7-25: \,7$

– K is the quotient of 9 by the difference of 7 and 4.

$K=9: \,(7-4)$

– L is the product of the difference of 15 and 7 by 8.

– M is the sum of the product of 8 by 4 and the product of 7 by 3.

$M=8\times \,4+7\times \,3$

– N is the product of the sum of 15 and 7 and the difference of 17 and 5.

$N=\,(\,15+7\,\,)(17-5)$

The answers to the exercises on operating priorities in 5th grade.

After having consulted the answers to these exercises on operating priorities in 5th grade, you can return to the exercises in 5th grade.

Fifth grade exercises.

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