Math 6 Chapter 1 Lesson 9: Order of performing calculations
1. Summary of theory Tóm
1.1. Again about the expression.
Numbers joined by signs of operations (addition, subtraction, multiplication, division, raising to power) make an expression.
Such as : \(5 + 3 – 2\) ; \(12 : 2 . 7 \) or \(4^2\) are expressions.
Attention :
a) Each number is also considered an expression.
b) The expression can have brackets to indicate the order in which calculations are performed.
1.2. Order of operations in expressions.
a) For expressions without brackets

If there is only addition, subtraction or only multiplication and division, we perform the calculation in order from left to right.
VD: \(48 – 32 + 8 = 16 + 8 = 24 \);
\(60 : 2 . 5 = 30 . 5 = 150.\)

If there are addition, subtraction, multiplication, division, and exponentiation operations, we perform the calculation to the power first, then multiply and divide, and finally add and subtract.
VD: \(4 . 3^2 – 5 . 6 = 4 . 9 – 5 . 6 = 36 – 30 = 6\)
b) For expressions with brackets
If the expression has brackets : round brackets ( ), square brackets [ ], curly braces { }, we do the calculation in the round brackets first, then the calculation in square brackets, and finally the calculation in the curly braces.
VD: \(100 : \{ 2 . [52 – (35 – 8) ]\} = 100 : \{ 2 . [ 52 – 27] \} = 100 : \{ 2 . 25 \} = 100 : 50 = 2\)
Conclude:

Order of operations for expressions without brackets: Power Multiplication and division Addition and subtraction

Order of operations for expressions with brackets: ( ) ⇒ [ ] { }
2. Illustrated exercise
Question 1: Do the math: \(6^2 : 4 . 3 + 2 . 5^2\)
Solution guide:
\(6^2 : 4 . 3 + 2 . 5^2 = 36 : 4 . 3 + 2 . 25 = 9 . 3 + 50 = 77\)
Verse 2: Do the math: \(150 : \{ 3 . [ 47 – ( 38 + 4 ) ] \}\)
Solution guide:
\(150 : \{ 3 . [ 47 – ( 38 + 4 ) ] \} = 150 : \{ 3 . [ 47 – 42 ] \} = 150 : \{ 3 . 5 \} = 150 : 15 = 10\)
Question 3: Find the natural number x, knowing : \(( 6x – 39 ) : 3 = 201\)
Solution guide:
\((6x – 39 ) : 3 = 201 \)
Derived from:
\((6x 39 ) = 201 . 3\)
\(6x – 39 = 303\)
\(6x = 303 – 39 = 264\)
\(x = 44\)
3. Practice
3.1. Essay exercises
Question 1: Do the math: \(8^2 : 4 . 3 + 2 . 4^2\)
Verse 2: Do the math: \(810 : \{ 3 . [ 59 ( 49 + 13 ) ] \}\)
Question 3: Find the natural number x, knowing: \(( 5x – 42 ) : 6 = 18\)
3.2. Multiple choice exercises Bài
Question 1: The order of operations for expressions without brackets is:
A. Multiply and divide ⇒ Powers ⇒ Add and subtract.
B. Powers ⇒ Multiply and divide ⇒ Add and subtract.
C. Add and subtract ⇒ Multiply and divide ⇒ Power.
D. Powers Add and subtract Multiply and divide
Verse 2: Find the natural number \(x\), know : \(25 + 5x = 5^6 : 5^3\)
A. 25
B. 20
C. 15
D. 10
Question 3: Choose the expression using the correct order of brackets:
A. \(100 : \{2 . [30 – (12 +7)]\}\)
B. \(100 : [2. (30 – \{12 + 7\})]\)
C. \(100 : (2. \{30 – [12 + 7]\})\)
D. \(100 : (2 . [30 – \{12 + 7\}])\)
Question 4: Do the calculation : \(4 . 5^2 – 6 . 3^2\)
A. \(4 . 5^2 – 6 . 3^2 = 2^2 . 5^2 – 6 . 3^2 = 7^2 – 6 . 3^2 = 4^2 . 6 = 96.\)
B. \(4 . 5^2 – 6 . 3^2 = 20^2 – 18^2 = 2^2 = 4.\)
C. \(4 . 5^2 – 6 . 3^2 = 4 . 25 – 6 . 9 = 100 – 54 = 46.\)
D. \(4 . 5^2 – 6 . 3^2 = 4 . 25 – 6 .9 = 4 . 19 .9 = 684.\)
Question 5: The result of the calculation \(60 – [120 – (42 – 33)^2]\) is :
A. 20
B. 21
C. 22
D. 23
Question 6: Which of the following is the correct order of operations for expressions without brackets?
A. Add and subtract => Multiply and divide => Power =>
B. Multiplication and division => Powers => Addition and subtraction
C. Powers => Multiplication and division => Addition and subtraction
D. All 3 answers above are correct
Verse 7: Which of the following is the correct order of operations for an expression with brackets?
A. [ ] => ( ) => { }
B. ( ) => [ ] => { }
C. { } => [ ] => ( )
D. [ ] => { } => ( )
Verse 8: The result of the calculation 24 – 50 : 25 + 13.7 is
A. 100
B. 95
C. 105
D. 80
Verse 9: The y value of the expression \(2\left[ {\left( {195 + 35:7} \right):8 + 195} \right] – 400\) is equal to
A. 140
B. 60
C. 80
D. 40
Question 10: The result of the calculation \({3^4}.6 – \left[ {131 – {{\left( {15 – 9} \right)}^2}} \right]\) is
A. 319
B. 931
C. 193
D. 391
Question 11: Tim x satisfied \[(65 – \left( {35:x + 3} \right).19 = 13\)
A. 7
B. 8
C. 9
D. 10
Câu 12: Số tự nhiên x cho bởi \(5\left( {x + 15} \right) = {5^3}\). giá trị của x là
A. 9
B. 10
C. 11
D. 12
Câu 13: Giá trị nào dưới đây của x thỏa mãn \({2^4}x – {3^2}.x = 145 – 225:51\)
A. 20
B. 30
C. 40
D. 80
Câu 14: Thực hiện phép tính \(\left( {{{10}^3} + {{10}^4} + {{125}^2}} \right):{5^3}\) một cách hợp lí ta được
A. 132
B. 312
C. 213
D. 215
Câu 15: Gía trị của x thỏa mãn \(65 – {4^{x + 2}} = {2020^0}\) là
A. 2
B. 4
C. 3
D. 1
4. Kết luận
Qua bài giảng Thứ tự thực hiện các phép tính này, các em cần hoàn thành 1 số mục tiêu mà bài đưa ra như:
 Nắm vững thứ tự thực hiện các phép tính.
 Làm được các bài toán liên quan.
.
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