5.OA.1
Name: _______________________________________
_________________
# ________ HR Teacher:
Math Study Guide: Order of Operations
Vocabulary:
Numerical Expression:
A mathematical phrase that includes numerals and operational
symbols. It does not have an equal sign.
Brackets:
[[[[A pair of symbols used to group things together.]]]]
Braces:
The outer most grouping symbol used in mathematics.
Parentheses:
The symbols “(“ and “)” that are generally used for grouping.
Operation:
A mathematical process applied to solve a problem. Addition,
subtraction, multiplication, and division are the four basic
operations.
Sample Problems:
1.
5(3)
hint: numbers outside of parentheses should be multiplied by the inside value.
2. 4 (7 – 2 )
3. 11 ( 2 + 2 x 5 )
hint: complete operations inside of parentheses first.
hint: inside the parentheses, follow the order of operations; multiply before you add.
4. 20 ÷ 5 – 1 x 3
hint: when you have multiplication and division, work left to
right.
5. 10 ( 2 + 4 ) ( 14 ÷ 7 )
hint: remember to complete parentheses first and
move left to right.
6. 97 – [ 20 x (15 ÷ 5 )]
7. 2 x { 7 x 4 – [ (6 + 2) x 3 ] }
hint: work inside -> outside: parentheses,
brackets…
hint: work inside -> outside: parentheses,
brackets, and braces, oh my!
5.OA.1
Name: _______________________________________
_________________
# ________ HR Teacher:
Math Test: Order of Operations
Vocabulary: Match each word to the picture that best represents its definition.
1. __________ operations
A. ( )
2. __________ expression
B. { }
3. __________ brackets
C. +, -, x, ÷
4. __________ braces
D. [ ]
5. __________ parentheses
E. 7 ( 3 + 2 )
6. An expression is a mathematical phrase that does not have a(an) __________.
a.
b.
c.
d.
Value
Equal sign
Grouping symbol
Fraction
Computation: Find the value of each expression. SHOW YOUR WORK.
7. 19 – 3 x 5
8. 35 ÷ ( 8 ÷ 1 – 3 ) x 9
Value: __________
9. 4 ( 8 – 3 )
Value: __________
10. ( 36 ÷ 6 ) ( 2 X 4 )
Value: __________
Value: __________
11. [3 x (7 – 2)] -9
12. 72 – [60 + 32 ÷ (2 x 4)]
Value: __________
13. {100 – [10 x (2 + 1)] ÷ 5} - 85
Value: __________
14. 100 – {20 x [15 – (2 x 5)] - 50}
Value: __________
15. Which of the following expressions has a
value of 24?
Value: __________
16. Which of the following expressions has the
greatest value?
a. (2 + 1)(3 x 2)
a. (2 + 5) x 3 – 1
b. 100 ÷ 4 - 1
b. 2 + 5 x (3 – 1)
c. [15 + (12 ÷ 2) x 2] – 18
c. 2 + (5 x 3 – 1)
d. (24 x 1 – 1) – 1
d. they are all equal
17. Which of the following statements about the
order of operations is NOT true?
18. Which expression has a value of 0?
a. 13 – (12 – 7) x 2
a. Complete grouping symbols first.
b. Do multiplication before subtraction.
c. When multiplication and division are in
a problem, work from right to left.
d. You should always use the order of
operations when evaluating
expressions.
19.
b. 7 x 10 - 4 ÷ 2
c. [19 + (2 x 3 + 4)] x 0
d. 44 ÷ 44 + 1
Jack and Jill are evaluating the expression…
4+5x3
Jack believes the value is 27.
Jill says the value is 19.
Who is correct? _______________
Explain what the other person is doing incorrectly.
____________________________________________________________________________
____________________________________________________________________________
__________________
20. On a scale of 1 – 10 (1 being TERRIBLE and 10 being AMAZING)
How would you rate your ability to solve numerical expression using the order of operations? Circle
your answer.
0
1
2
3
4
5
6
7
8
9
10
Answer Key
5.OA.1
Name: _______________________________________
_________________
# ________ HR Teacher:
Math Test: Order of Operations
Vocabulary: Match each word to the picture that best represents its definition.
1. C.
operations
A. ( )
2. E.
expression
B. { }
3. D.
brackets
C. +, -, x, ÷
4. B.
braces
5. A.
parentheses
D. [ ]
E. 7 ( 3 + 2 )
6. An expression is a mathematical phrase that does not have a(an) equal sign.
a.
b.
c.
d.
Value
Equal sign
Grouping symbol
Fraction
Computation: Find the value of each expression. SHOW YOUR WORK.
7. 19 – 3 x 5
8. 35 ÷ ( 8 ÷ 1 – 3 ) x 9
19 - 15
35 ÷ (8 – 3) x 9
4
35 ÷ 5 x 9
7x9
Value: 4
9. 4 ( 8 – 3 )
63
Value: 63
10. ( 36 ÷ 6 ) ( 2 X 4 )
4 (5)
(6) (2 x 4)
20
(6) (8)
48
Value: 20
Value: 48
11. [3 x (7 – 2)] -9
12. 72 – [60 + 32 ÷ (2 x 4)]
72 – [60 + 32 ÷ 8]
[3 x 5] - 9
15 - 9
72 – [60 + 4]
6
72 - 64
8
Value: 6
Value: 8
13. {100 – [10 x (2 + 1)] ÷ 5} - 85
14. 100 – {20 x [15 – (2 x 5)] - 50}
{100 – [10 x 3] ÷ 5} - 85
100 – {20 x [15 – 10] – 50}
{100 – 30 ÷ 5} - 85
100 – {20 x 5 – 50}
{100 – 6} - 85
100 – {100 – 50}
94 - 85
100 - 50
9
50
Value: 9
15. Which of the following expressions has a
value of 24?
Value: 50
16. Which of the following expressions has the
greatest value?
a. (2 + 1)(3 x 2)
a. (2 + 5) x 3 – 1
b. 100 ÷ 4 - 1
b. 2 + 5 x (3 – 1)
c. [15 + (12 ÷ 2) x 2] – 18
c. 2 + (5 x 3 – 1)
d. (24 x 1 – 1) – 1
d. they are all equal
17. Which of the following statements about the
order of operations is NOT true?
18. Which expression has a value of 0?
a. 13 – (12 – 7) x 2
a. Complete grouping symbols first.
b. Do multiplication before subtraction.
c. When multiplication and division are in
a problem, work from right to left.
d. You should always use the order of
operations when evaluating
expressions.
19.
b. 7 x 10 - 4 ÷ 2
c. [19 + (2 x 3 + 4)] x 0
d. 44 ÷ 44 + 1
Jack and Jill are evaluating the expression…
4+5x3
Jack believes the value is 27.
Jill says the value is 19.
Who is correct? Jill
Explain what the other person is doing incorrectly.
____________________________________________________________________________
____________________________________________________________________________
__________________
20. On a scale of 1 – 10 (1 being TERRIBLE and 10 being AMAZING)
How would you rate your ability to solve numerical expression using the order of operations? Circle
your answer.
0
1
2
3
4
5
6
7
8
9
10