**Priorities of operations**with corrected 5th grade math exercises on the priorities of operations between addition, subtraction, multiplication and division.

In fifth grade, we learned to work with numbers and to perform mathematical operations such as addition, subtraction, multiplication and division. We also studied operative priorities, which are rules that tell us in what order to perform these operations to get the correct result.Operative priorities are rules that tell us the order in which we should perform the mathematical operations in an expression.More complex calculations on priorities with nested parentheses.

Develop math skills with these corrected exercises on operative priorities that are similar to those in your textbook. In the plane, the student must know how to place a point knowing its coordinates with its abscissa and ordinate.

Exercise 1

Calculate the following expressions by writing the intermediate steps:

a) 7 + 4 8 b) 3 11 – 7 4 c) 37 – 6 5 d) 9 – 4 : 4 e) 32 ÷ 4 – 2 + 7 3 f) 9 4 : 2 – 5 2

Exercise 2

Calculate the following expressions by writing the intermediate steps:

A = 6 (3 + 7) B = 23 – 4 5 C = (3 + 5) (9 – 7) D = (13 – 7) : 2 E = 5 – [4 − (2 + 1)] F = (3 + 5 7) : 2 +1

Exercise 3

Aurélie buys 5 jars of jams at 1,50 € each and 12 baguettes at 0,95 € each.

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

Exercise 4

Copy the following expressions onto your paper, adding parentheses to make the equality true:

8 + 2 5 = 50; 9 – 3 2 + 5 = 42; 8 + 4 3 : 2 = 18

Exercise 5

Calculate the following expressions:

A = 24 – 5 – 1

B =14 3 – 5 2

C = 10 : [ 6 – 2 (1 – 0.5) ] 5

D = 8 : 4 – 0.25 2

E= 3 (7 – 2) – 4

F = 72 : 9 8 : 2 – 9 3

Exercise 6

Using the numbers 3; 7; 10 as many times as you want and the + – signs : ( ) try to obtain the following results:

20 ; 14 ; 31 ; 67 ; 40 ; 1.

Exercise 7

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

5 4 – 1 + 2 2 = 34

Exercise 8

The coach of a soccer team must buy 16 pieces of equipment for his players.

Each equipment is composed of a jersey for 24€, shorts for 11€ and a pair of socks for 4,50€.

Write the expression to calculate the amount of his purchases.

Exercise 9

A boxer weighs 86.2 kg one week before a fight.

He goes on a diet that allows him to lose 0.6 kg for 7 days.

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

Exercise 10

Calculate the following expressions:

A = 125 – 7 4 + 11

B = (125 – 7) 4 + 11

C = 125 – 7 (4 + 11)

D = 125 – (7 4) + 11

E = [(125 – 7) 4] + 11

F = 125 – [7 (4 + 11)]

Exercise 11:

Calculate with respect to priorities:

1) 12.7 + 3.1 2

2) 12.7 – 3.1 2

3) 12.7 3 + 3.1 7

4) 12.7 3 – 3.1 8

5) (5 – 3) (9.1 – 7.8)

6) (5 + 3) (9.1 + 7.8)

Exercise 12.

Writing the intermediate steps, calculate the following expressions:

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

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

C = 4 – (7 – 3 ) – [ 11 – ( 8 – 5)]

Exercise 13.

For each equality, indicate whether it is correct or not by placing the necessary brackets.

a) 6 + 5 5 – 3 = 28 b) 6 + 5 5 – 3 = 52

c) 6 + 5 5 – 3 = 16 d) 6 + 5 5 – 3 = 22

Exercise 14.

Calculate by indicating the intermediate steps:

A = 25 – 7 (8 – 5) B = (7 – 4) 3 + 4 – (7 2 – 8)

C = 8 3 – (12 : 3 + 2) 3 D = [10 + 5 (6 – 4)] : 4

Exercise 15

Link each calculation to its result with an arrow:

(5 + 5) (5 + 5) – – 6

5 (5 + 5 + 5) ) – – 10

5 + ((5 + 5) 5) – – 55

(5 + 5) (5 : 5) – – 75

(5 + (5 5)) : 5 – – 100

Exercise 16.

In the milk section of a supermarket, there are 52 packs of 6 bottles of milk each at the beginning of the day.

During the day, 18 full packs and 63 single bottles were sold.

1) Write an expression *with parentheses* to calculate the number of bottles remaining in the shelf at the end of the day.

2) Write also an expression *without parenthesis*.

3) Do the calculation.

Exercise 17.

We give the literal expression E =*2x* + *y *(*3y* – *x* ) – 5

1) Calculate E when *x* = 2 and *y* = 3

2) Calculate E when *x* = 3.5 and *y* = 1

3) Calculate E when *x* = 3 and *y* = 2

Exercise #18:

Perform the following calculations, highlighting the current calculation.

A=24+3×7 B=720 : 9+4

C=60-14+5×3+2 D=8×3-5×4×0.2

E=15 :5-2

Exercise #19:

Perform the following calculations, highlighting the current calculation.

A=25-(8-3)+1 B=25-(8-3+1)

C=18-[4×(5-3)+2] D=[2+0,1×(5+3)]:4 E=24 :[8-(3+1))]

Exercise #20:

Place the brackets so that the following equalities are true and check each of your answers.

a) 4×2+9=44 b) 1+13-14-7=7 c) 15-3×2=24

d) 2×5-2×4+1=30 e) 32 – 4+7×2=10 f) 7+7+6×7=98

Exercise #21:

Associate each expression with a sentence:

7×(4+3) – – The difference of the product of 4 by 3 and 7

7×4+3 – – The product of 7 and the sum of 4 and 3

4×3-7 – – The product of the difference of 7 and 4 by 3

(7-4) ×3 – – The sum of the product of 7 by 4 and 3

Exercise #22:

Translate each sentence into a mathematical expression.

a) A is the sum of the product of 5 by 2 and 3 then A=……

b) B is the product of 4 and the sum of 9 and 7 then B=…..

c) C is the difference of 17 and the product of 4 by 3 then C=…..

d) D is the quotient of the sum of 19 and 3 by 11 then D=….

Exercise 23: nested parentheses.

Calculate the following expressions in your notebook.

A=35-[4× (5+2)-7]

B=12×[32-(4+7) ×2]

C=(1+7) ×[11-(2+3)]

D=12+[(120-20)-2×4×5]

E=150-10-[(12+2) ×4+2]

F=(60-59,9) ×[30-(25-15)]

Exercise 24:

I) Calculate:

O = 17 – [3 × (5 – 2) + 8] + 12,3 × 4 – 4

Q = 2,5 × [3 + 2 × (13 – 3 × 3) – 6 – 3]

R = 38 – 8 × (7 – 2 × 3 + 1) – 4 + 2

S = 6 + 2 × 8 – 5 × 3 + 10 : 2

T = [(6 + 2) × (8 – 5) × 3 + 10] : 2

U = 6 + [2 × (8 – 5) × 3 + 10 : 2]

V = (19 – 7) × 4 – (28 – 14)

W = 25 – [18,7 – (9,2 + 4,5)]

X = [35 – (17 – 6)]: 8

Y = 2 × [(25 – 17,1) × 3 + 11,3]

Z = [35 – 56 : (28 – 20)] × 10

II) Clever calculation:

Exercise 25:

a. For each of the calculation programs below, write an expression that allows you to

calculate the number obtained when 0.7 is chosen as the starting number.

b. Calculate these expressions.

Exercise 26:

a. Which of the following phrases fits Sofiane’s description?

b. Calculate this expression.

Exercise 27:

Associate one of the expressions A, B, C or D with each of the three problems, then give the

answers to the problems.

Exercise 28:

Calculate each expression by hand.

Exercise 29:

Write the expression that corresponds to the sequence of operations, then calculate it.

Exercise 30:

Here are the purchases Clara wants to make with a 50€ bill.

1. Explain with orders of magnitude why the 50 € bill will be sufficient.

2. a. Write the expression R that calculates the amount to be returned to Clara.

b. Calculate R.

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