5th Grade Math Quiz: Evaluate Expressions With Grouping Symbols
Practice Evaluate Expressions With Grouping Symbols in 5th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
What this quiz covers
This quiz focuses on Evaluate Expressions With Grouping Symbols, giving you a quick way to practice the rules, question types, and explanations that matter most for 5th Grade Math.
How to use this quiz
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
Question 1
Which expression has the same value as 8+4×(6−2)?
(8+4)×6−2
8+
Explanation: The original expression equals 8+4×4=8+16=24. Using the distributive property, , so choice B gives . Choice A gives . Choice C gives . Choice D gives .
Question 2
A class is packing pencils. The total is found using 3×[20−(4×2)]. What is the value of the expression? Grouping symbols show which operations to do first (inside the parentheses or brackets first).
36
52
Question 3
The expression 2×[15−(3+4)]+6 represents the number of stickers Anna has after following a multi-step process. What is the value of this expression?
20 stickers
Question 4
A calculator displays the result of [20−(4×3)]+[2×(5+3)]. If the calculator follows the correct order of operations, what number appears on the screen?
Question 5
Maya is calculating 12+3×(8−5)+2. She rewrites the expression by adding one pair of parentheses to change the value of the result. Which of these could be her new expression?
Question 6
The expression {[(12÷3)+2]×2}−4 uses three types of grouping symbols. What is its value?
8
Question 7
A student is finding the value of {25−[3×(4+1)]}. Grouping symbols show which operations to do first (inside parentheses first, then brackets, then braces). What is the value of the expression?
10
60
Question 8
A student is choosing between two expressions: (16−8)×3 and 16−(8×3). Grouping symbols indicate which operations to do first, so the parentheses change the order. Which value matches the expression ?
Question 9
A class is counting markers. The total is represented by [15+5]×4. Grouping symbols show which operations to do first, so work inside the brackets first. What is the value of [15+5]×4?
Question 10
A teacher writes the expression 8×(6+4) on the board and reminds the class that grouping symbols show which operations to do first (inside the parentheses first). What is the value of the expression 8×(6+4)?
Question 11
A teacher compares 30−(12−4) and (30−12)−4. Grouping symbols show which operations to do first (inside the parentheses first). What is the value of ?
Question 12
A student is comparing two ways to write a score calculation: 8×(9+3) and 8×9+3. Which statement best explains how the parentheses change the value? Grouping symbols show which operations to do first (inside the parentheses first).
Question 13
A student is evaluating 40−{6×(3+2)}. Grouping symbols indicate which operations to do first, so you add inside the parentheses first. Which value is the correct value of the expression 40−?
Question 14
A student is evaluating 50÷[5×(2+3)]. Grouping symbols show which operations to do first (inside parentheses first, then inside brackets). What is the value of the expression?
50
5
Question 15
A student writes two expressions: 8×(5+1) and 8×5+1. Grouping symbols show which operations to do first (inside the parentheses first). Which statement best explains how the parentheses change the value?
Question 16
A teacher writes two expressions on the board: 24÷(8−2) and 24÷8−2. Grouping symbols indicate which operations to do first, so the parentheses change the value. Which statement best explains how the grouping changes the value?
Question 17
A student is organizing books. The number of books is found using 60−{24÷(8−4)}. Grouping symbols indicate which operations to do first (inside parentheses first, then inside braces). What is the value of 60?
Question 18
Two students wrote different expressions for the same numbers: 9×(10−2) and (9×10)−2. Which statement is true about how the parentheses change the value? Grouping symbols show which operations to do first (inside the parentheses first).
Question 19
A student evaluates 72÷8+(9−3). Grouping symbols show which operations to do first (inside the parentheses first). What is the value of the expression?
60
15
3
Question 20
A student compares [40−(6×5)] and (40−6)×5. Grouping symbols show which operations to do first. What is the value of ?
(
4
×
6)−
(4×
2)
(8+4)×(6−2)
8×4+6−2
4×
(6−
2)=
4×
6−
4×
2
8+24−8=24
12×6−2=70
12×4=48
32+6−2=36
24
108
Explanation: Grouping symbols affect the order of operations, handling nested ones from inside out. Evaluate the innermost parentheses first, then the brackets. This changes the result by ensuring subtraction after multiplication inside. For pencils, 3×[20−(4×2)]=3×[20−8]=3×12=36. People might mistakenly ignore nesting and do 20-4 first, but order matters. Grouping symbols are key for complex expressions in packing or building. They provide structure and avoid errors in multi-step problems.
16 stickers
28 stickers
22 stickers
Explanation: When you see an expression with multiple operations and grouping symbols like brackets and parentheses, you need to follow the order of operations (PEMDAS). This means working from the inside out: parentheses first, then brackets, then multiplication and division from left to right, and finally addition and subtraction from left to right.Let's solve 2×[15−(3+4)]+6 step by step. Start with the innermost parentheses: (3+4)=7. Now the expression becomes 2×[15−7]+6. Next, solve what's inside the brackets: 15−7=8. This gives us 2×8+6. Now multiply: 2×8=16. Finally, add: 16+6=22.Looking at the wrong answers: Choice A (20) likely comes from incorrectly calculating 2×[15−(3+4)]=2×[15−7], then mistakenly adding only 4 instead of 6. Choice B (16) represents stopping after the multiplication step and forgetting to add the final 6. Choice C (28) probably results from adding before multiplying, calculating , then multiplying by 2.The correct answer is D (22 stickers).Remember this strategy: when you see nested grouping symbols, always work from the inside out and follow PEMDAS strictly. Write down each step to avoid losing track of where you are in a complex expression.
18
24
16
22
Explanation: Working inside out: First bracket: 4×3=12, then 20−12=8. Second bracket: 5+3=8, then 2×8=16. Finally: 8+16=24. Choice A incorrectly calculates the second bracket as 10. Choice C stops at the first bracket calculation. Choice D makes an error in the final addition.
(12+3)×(8−5)+2
12+(3×8)−5+2
12+3×(8−5+2)
(12+3)×8−5+2
Explanation: The original expression 12+3×(8−5)+2 equals 12+3×3+2=12+9+2=23. Choice C gives 12+3×(8−5+2)=12+3×5=, which is different. Choice A changes the structure too much by affecting multiplication. Choice B doesn't add parentheses, it moves them. Choice D also changes the structure too dramatically.
12
16
20
Explanation: Working from the innermost grouping outward: 12÷3=4. Then [(4)+2]=6. Next {6×2}=12. Finally 12−4=8. Choice B forgets the final subtraction. Choice C incorrectly calculates one of the intermediate steps as 8 instead of 6. Choice D makes an error in the multiplication step.
15
22
Explanation: Grouping symbols like braces, brackets, and parentheses affect the order in which we perform operations in an expression. We always evaluate the operations inside the innermost grouping symbols first, then brackets, then braces. This changes the result by nesting operations, making {25 - 15} = 10 after 3 × 5. For example, in {25 - [3 × (4 + 1)]}, we add inside parentheses, multiply inside brackets, subtract inside braces. A common misconception is to ignore the order of symbols and evaluate outward first, but we start innermost. Grouping symbols are important because they structure complex expressions clearly. They ensure precise calculations in layered math problems.
(16−8)×3
0
24
8
-8
Explanation: Grouping symbols affect the order of operations by isolating subtraction before multiplication. Evaluate inside the parentheses first to simplify the grouped part. This changes the result, as subtracting first leads to a positive product unlike multiplying first. For (16 - 8) × 3, subtract to get 8, then multiply by 3 for 24. A misconception is that parentheses don't change multiplication priority, but they do by grouping subtraction. Grouping symbols are important for conveying specific meanings. They are fundamental in creating distinct outcomes in expressions.
35
80
100
20
Explanation: Grouping symbols like brackets affect the order of operations by requiring evaluation inside them before external operations. You solve the addition or other operations within the brackets first, then multiply or proceed. This modifies the final value by combining numbers in a specific way. For example, in [15 + 5] × 4, add to 20 inside, then multiply by 4 to get 80. A common misconception is that you can multiply first and add later, ignoring the brackets. Grouping symbols are important because they provide structure to expressions. They allow for clear and unambiguous mathematical statements.
80
52
320
112
Explanation: Grouping symbols like parentheses affect the order of operations in an expression by specifying which calculations to perform first. To evaluate, you always start by solving the operations inside the grouping symbols before moving to the outside operations. This changes the result because it overrides the standard order of operations, such as multiplying before adding. For example, in 8 × (6 + 4), you add 6 + 4 inside the parentheses to get 10, then multiply by 8 to get 80. A common misconception is that you can ignore parentheses and just follow PEMDAS strictly, but parentheses must be addressed first. Grouping symbols are important because they ensure everyone interprets the expression the same way. They allow for precise control over the calculation sequence, preventing confusion in math problems.
30−(12−4)
14
22
10
18
Explanation: Grouping symbols like parentheses affect the order in which we perform operations in an expression. We always evaluate the operations inside the grouping symbols first before doing anything outside them. This changes the result by altering which subtraction happens first, making 30 - (12 - 4) equal to 22, while (30 - 12) - 4 equals 14. For example, in 30 - (12 - 4), we subtract inside to get 8, then 30 - 8 = 22. A common misconception is that all subtractions are done left to right regardless of parentheses, but parentheses must be resolved first. Grouping symbols are important because they prevent misinterpretation of expressions. They ensure accuracy in comparisons, like in teaching scenarios.
The parentheses make you add 9 and 3 first, so 8 is multiplied by the total.
The parentheses mean you multiply 8 and 9 first, then add 3 at the end.
The parentheses mean you add 8 and 9 first, then multiply by 3.
The parentheses do not change anything because you always go left to right.
Explanation: Grouping symbols affect the order of operations by indicating which parts to compute first. You evaluate inside the parentheses first, performing the addition before the multiplication. This changes the result from 75 without parentheses to 96 with them, as the addition is grouped. For instance, 8×(9+3) becomes 8×12=96, while 8×9+3=72+3=75. One misconception is thinking parentheses always mean multiply first, but they prioritize the operation inside. Grouping symbols are crucial for specifying exact calculations in scores or other applications. They prevent ambiguity and ensure accurate results in math.
{6×
(3+
2)}
10
34
4
70
Explanation: Grouping symbols like parentheses and braces affect the order of operations by indicating nested priorities. Evaluate inside the innermost parentheses first, then proceed to multiplication within braces. This alters the result by changing the sequence, such as doing addition before multiplication. For example, in 40 - {6 × (3 + 2)}, add 3 + 2 to 5, multiply by 6 to 30, then subtract from 40 to get 10. A misconception is ignoring braces and doing multiplication first everywhere, which would give 40 - 6 × 3 + 2 = 40 - 18 + 2 = 24. Grouping symbols are essential for directing calculations correctly. They ensure consistency in interpreting expressions across education and professions.
2
10
Explanation: Grouping symbols like parentheses and brackets affect the order in which we perform operations in an expression. We always evaluate the operations inside the innermost grouping symbols first, then work outward. This changes the result by nesting operations, making 50 ÷ [5 × 5] = 50 ÷ 25 = 2 after resolving 2 + 3 = 5 inside. For example, in 50 ÷ [5 × (2 + 3)], we add inside parentheses, multiply inside brackets, then divide. A common misconception is to multiply or divide outside before finishing inside all symbols, but we must complete inner ones first. Grouping symbols are important because they allow for complex expressions without ambiguity. They help in accurate calculations, like in student evaluations.
The parentheses make you add 5 and 1 first, so the product is larger than 8×5+1.
The parentheses mean you multiply 8 and 5 first, so both expressions have the same value.
The parentheses mean you add 8 and 5 first, then multiply by 1.
The parentheses mean you always divide before you add, so the value gets smaller.
Explanation: Grouping symbols like parentheses affect the order in which we perform operations in an expression. We always evaluate the operations inside the grouping symbols first before doing anything outside them. This changes the result by making us add before multiplying in 8 × (5 + 1), leading to 48, whereas without parentheses in 8 × 5 + 1, we multiply first to get 41. For example, the parentheses in 8 × (5 + 1) make the product larger by grouping the addition first. A common misconception is that parentheses always mean to multiply first, but they actually prioritize whatever is inside them. Grouping symbols are important because they control the sequence of operations to avoid confusion. They allow us to express complex ideas precisely in math.
The parentheses make you subtract first, so you divide by 6 instead of dividing by 8 first.
The parentheses make you divide first, so you divide 24 by 8 before subtracting 2.
The parentheses mean you should work strictly left to right no matter what.
The parentheses mean you should add 8 and 2 before dividing 24.
Explanation: Grouping symbols affect the order of operations by forcing certain parts of an expression to be calculated before others. You evaluate inside the grouping symbols first, performing subtraction or other operations there before division or the rest. This changes the result by altering what numbers are operated on, leading to different outcomes with and without symbols. For instance, in 24 ÷ (8 - 2), subtracting first gives 24 ÷ 6 = 4, unlike 24 ÷ 8 - 2 = 1. A misconception is that parentheses only group numbers without changing priority, but they do enforce inner operations first. Grouping symbols are important for specifying intent in math problems. They prevent misunderstandings and are essential in programming and engineering.
−
{24÷
(8−
4)}
51
45
54
12
Explanation: Grouping symbols such as braces and parentheses affect the order by nesting operations that must be resolved inward to outward. You evaluate the innermost parentheses first, then the division inside the braces, before subtracting. This sequence changes the result by prioritizing certain calculations. In 60 - {24 ÷ (8 - 4)}, subtract to 4, divide 24 by 4 to 6, then 60 - 6 = 54. One misconception is overlooking nested symbols and doing operations out of order. Grouping symbols are crucial for handling complexity in math. They ensure everyone arrives at the same answer consistently.
Both expressions have the same value because parentheses never change the value.
The first expression subtracts first, but the second expression multiplies first, so the values are different.
The first expression multiplies first, but the second expression subtracts first, so the values are different.
Both expressions have the same value because you always do multiplication before subtraction no matter what.
Explanation: Grouping symbols affect the order of operations by prioritizing inside them. Evaluate subtraction or multiplication inside first as grouped. This changes results, like 72 for the first and 88 for the second. For example, 9×(10-2)=9×8=72, while (9×10)-2=90-2=88. A misconception is thinking order is always multiplication first regardless of parentheses. Grouping symbols are vital for different interpretations in student work. They allow precise control over calculation sequences.
9
Explanation: Grouping symbols like parentheses affect the order in which we perform operations in an expression. We always evaluate the operations inside the grouping symbols first before doing anything outside them. This changes the result by adding the resolved parentheses after division, leading to 9 + 6 = 15. For example, in 72 ÷ 8 + (9 - 3), we subtract to 6 inside, divide 72 by 8, then add. A common misconception is that addition comes before division, but we do division and multiplication before addition after parentheses. Grouping symbols are important because they clarify priorities in mixed operations. They help students evaluate expressions correctly.
[40−(6×5)]
50
10
170
34
Explanation: Grouping symbols like brackets and parentheses affect the order in which we perform operations in an expression. We always evaluate the operations inside the innermost grouping symbols first, then work outward. This changes the result by nesting multiplication inside subtraction, making [40 - 30] = 10, different from 34 × 5 = 170. For example, in [40 - (6 × 5)], we multiply inside parentheses, subtract inside brackets. A common misconception is to subtract outside before inner multiplication, but inner symbols take priority. Grouping symbols are important because they allow precise control over operation order. They are essential for comparing expressions accurately.