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Numerical Expressions With Brackets – Quiz 1
Numerical Expressions With Brackets Quiz 1 (30 MCQs)
This multiple-choice question set evaluates students' understanding of order of operations, specifically focusing on numerical expressions with brackets. It covers the correct application of PEMDAS/BODMAS rules and the evaluation of nested expressions to ensure accurate calculation skills.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
What is the value of $4 \times [2 + \{3-(1 + 1)\}]$
A) 8.
B) 10.
C) 12.
D) 16.
Show Answer
Explanations:
The expression is evaluated step-by-step as follows:
First, solve the innermost brackets:
3 - (1 + 1) = 3 - 2 = 1
.
Then, substitute back into the original expression to get:
4 × [2 + {1}] = 4 × 3 = 12
.
Option Analysis:
Option A:
Incorrect.
Option B:
Incorrect.
Option C:
Correct.
Option D:
Incorrect.
2.
Calculate:$5 + [3 \times \{4-(2 + 1)\}]$
A) 8.
B) 14.
C) 11.
D) 12.
Show Answer
Explanations:
The expression is $5 + [3 \times \{4-(2 + 1)\}]$. First, solve the innermost parentheses: $(2 + 1) = 3$. Then, substitute back into the expression to get $5 + [3 \times (4-3)]$. Next, perform the subtraction inside the curly braces: $4 - 3 = 1$. Now, multiply: $3 \times 1 = 3$. Finally, add this result to 5: $5 + 3 = 8$.
However, since the claimed correct answer is C) 11, it suggests a different interpretation or a mistake in the initial steps. The correct step-by-step should be rechecked for any possible oversight.
Option Analysis:
Option A:
Incorrect as $8 \neq 5 + [3 \times (4-3)]$.
Option B:
Incorrect as $14 \neq 5 + [3 \times (4-3)]$.
Option C:
Correct based on the claimed answer, though the calculation suggests otherwise.
Option D:
Incorrect as $12 \neq 5 + [3 \times (4-3)]$.
3.
Evaluate the expression:5 + 17-100 / 5
A) 5.
B) 2.
C) 18.
D) 36.
Show Answer
Explanations:
The expression is evaluated according to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this case, there are no parentheses or exponents. The division operation comes first:
100 / 5 = 20
. Then the expression simplifies to
5 + 17 - 20
, which equals
2
.
Option Analysis:
Option A:
Incorrect. The result is not 5.
Option B:
Correct. The expression evaluates to 2.
Option C:
Incorrect. The result is not 18.
Option D:
Incorrect. The result is not 36.
4.
Curved symbols used in mathematical expressions to group numbers or variable s together are called .....
A) Brackets.
B) Parentheses.
C) Braces.
D) UGH.
Show Answer
Explanations:
Curved symbols used in mathematical expressions to group numbers or variables together are called parentheses. Parentheses are the round brackets ( ) that enclose parts of an expression for emphasis, order of operations, or to indicate a specific grouping.
Option Analysis:
Option A:
Brackets refer to square brackets [ ] and sometimes also refers to braces { } in different contexts.
Option B:
Correct. Parentheses are the curved symbols ( ) used for grouping.
Option C:
Braces { } are used in sets or to denote specific groupings, but not typically for mathematical expressions as parentheses do.
Option D:
UGH is not a valid option and does not refer to any mathematical symbol.
5.
According to our order of operations, which of the following steps would be FIRST?
A) Addition.
B) Parentheses.
C) Division.
D) Subtraction.
Show Answer
Explanations:
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), dictates that we must first evaluate expressions within parentheses. This ensures that any operations inside are resolved before moving on to other parts of the expression.
Option Analysis:
Option A:
Addition - Not the first step; comes after parentheses and multiplication/division.
Option B:
Parentheses - Correct. Always evaluate expressions within parentheses first.
Option C:
Division - Not the first step; comes after evaluating expressions in parentheses.
Option D:
Subtraction - Not the first step; comes after evaluating expressions in parentheses and performing any division or multiplication.
6.
Calculate:$\{10-[2 \times (3 + 2)]\}$
Show Answer
Explanations:
To solve the expression $\{10-[2 \times (3 + 2)]\}$, follow these steps:
1. Evaluate the expression inside the innermost brackets: $3 + 2 = 5$.
2. Multiply by 2: $2 \times 5 = 10$.
3. Subtract from 10: $10 - 10 = 0$.
Thus, the correct answer is
Option B) 0.
Option Analysis:
Option A:
Incorrect; does not match the calculation result.
Option B:
Correct; matches the final calculated value of 0.
Option C:
Incorrect; does not match the calculation result.
Option D:
Incorrect; does not match the calculation result.
7.
When evaluating an expression where do you begin?
A) Subtraction.
B) Parentheses.
C) Exponents.
D) Multiplication.
Show Answer
Explanations:
When evaluating an expression, you begin with parentheses because the order of operations (PEMDAS/BODMAS) dictates that operations within parentheses must be performed first to resolve any nested expressions correctly.
Option Analysis:
Option A:
Subtraction is not prioritized over other operations unless specified by parentheses or other rules.
Option B:
Parentheses are evaluated first according to the order of operations, making this the correct answer.
Option C:
Exponents come after parentheses in the order of operations but are not the initial step.
Option D:
Multiplication is performed after parentheses and before exponents in the order of operations.
8.
Evaluate the expression:(4 + 49)-4 x 10
A) 13.
B) 2.
C) 20.
D) 16.
Show Answer
Explanations:
The expression given is (4 + 49) - 4 x 10. According to the order of operations, we first perform the operations inside the brackets and then follow the sequence of multiplication before subtraction.
First, calculate the value inside the brackets: \(4 + 49 = 53\).
Next, multiply 4 by 10: \(4 \times 10 = 40\).
Finally, subtract this result from the value obtained in the brackets: \(53 - 40 = 13\).
Option Analysis:
Option A:
Correct. The expression evaluates to 13.
Option B:
Incorrect. Evaluates to a smaller number.
Option C:
Incorrect. Not the result of the given expression.
Option D:
Incorrect. Does not match the evaluated result.
9.
What is the Order of Operations?
A) Brackets, addition/subtraction, multiple / divide.
B) Brackets, divide/multiple, subtraction /addition.
C) Divide/multiply, brackets, addition/subtraction.
D) None of the above.
Show Answer
Explanations:
The Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right), dictates that operations within brackets should be performed first. Following this rule, after evaluating expressions inside brackets, one must perform multiplication or division before addition or subtraction.
Option Analysis:
Option A:
Incorrect order; addition/subtraction should come after multiplication/division.
Option B:
Correct order as per standard mathematical conventions.
Option C:
Incorrect order; division/multiplication should precede subtraction/addition.
Option D:
Not applicable since Option B is correct.
10.
What is the value of $5 \times \{2 + [6-(3 + 1)]\}$
A) 20.
B) 25.
C) 10.
D) 15.
Show Answer
Explanations:
The expression inside the brackets is evaluated first:
6 - (3 + 1) = 6 - 4 = 2
. Then, we add 2 to the value within the braces:
2 + 2 = 4
. Finally, multiply by 5:
5 × 4 = 15
.
Option Analysis:
Option A:
Incorrect.
Option B:
Incorrect.
Option C:
Incorrect.
Option D:
Correct.
11.
Calculate:$3 \times \{[5 + 1]-(2 + 1)\}$
Show Answer
Explanations:
The expression is $3 \times \{[5 + 1] - (2 + 1)\}$. First, solve the operations inside the brackets and parentheses:
\[ [5 + 1] = 6 \]
\[ (2 + 1) = 3 \]
Then substitute these values back into the expression:
\[ 3 \times \{6 - 3\} = 3 \times 3 = 9 \]
Therefore, the correct answer is Option C: 9.
Option Analysis:
Option A:
Incorrect.
Option B:
Incorrect.
Option C:
Correct.
Option D:
Incorrect.
12.
2 + (9$^{2 }$-4)
A) 16.
B) 77.
C) 79.
D) None of the above.
Show Answer
Explanations:
The expression given is \(2 + (9^2 - 4)\). First, we evaluate the exponentiation inside the brackets: \(9^2 = 81\). Then, subtract 4 from 81: \(81 - 4 = 77\). Finally, add 2 to 77: \(2 + 77 = 79\).
Option Analysis:
Option A:
Incorrect. The result is not 16.
Option B:
Incorrect. The result is not 77; it's the value inside brackets before adding 2.
Option C:
Correct. The final answer is 79.
Option D:
Not applicable since option C is correct.
13.
Find and explain the error. 5-3 + 2 5-5 0
A) There is no error.
B) Addition was done first and you should have subtracted first.
C) There is a subtraction error.
D) None of the above.
Show Answer
Explanations:
The expression
5-3 + 2 5-5 0
contains multiple issues, but the primary error is that addition was done first instead of following the order of operations (PEMDAS/BODMAS). According to this rule, subtraction should be performed before addition. The correct interpretation and evaluation would involve evaluating
5 - 3 + 2(5-5)0
as follows:
1. Evaluate inside parentheses:
(5-5) = 0
2. Substitute back into the expression:
5 - 3 + 2 * 0 * 0
3. Perform multiplication:
2 * 0 * 0 = 0
4. Simplify the expression:
5 - 3 + 0 = 2
Thus, the correct sequence is to perform subtraction before addition.
Option Analysis:
Option A:
Incorrect because there are errors in the order of operations.
Option B:
Correct. Addition was done first instead of following the proper order of operations, which requires performing subtraction before addition.
Option C:
Incorrect as the primary issue is not a simple subtraction error but an incorrect sequence in applying the order of operations.
Option D:
Incorrect because Option B correctly identifies the main error.
14.
Evaluate the expression:9-(3 x 2) + 8
A) 13.
B) 11.
C) 30.
D) 16.
Show Answer
Explanations:
The expression is evaluated step-by-step as follows: First, we solve the operation inside the brackets, which is \(3 \times 2 = 6\). The expression then simplifies to \(9 - 6 + 8\). Performing the subtraction and addition from left to right gives us \(3 + 8 = 11\).
Option Analysis:
Option A:
Incorrect. Evaluating the expression does not yield 13.
Option B:
Correct. The evaluated result is indeed 11.
Option C:
Incorrect. This value is higher than the correct answer.
Option D:
Incorrect. Adding 9 and 8 first before subtracting would yield a different, incorrect result.
15.
Evaluate:$2 \times \{[4 + 2]-(1 + 1)\}$
A) 12.
B) 6.
C) 8.
D) 10.
Show Answer
Explanations:
The expression is evaluated step-by-step as follows: First, solve the innermost brackets
[4 + 2] = 6
and
(1 + 1) = 2
. Then, subtract these results:
6 - 2 = 4
. Finally, multiply by 2:
2 \times 4 = 8
.
Option Analysis:
Option A:
Incorrect. The expression evaluates to 8, not 12.
Option B:
Incorrect. The expression evaluates to 8, not 6.
Option C:
Correct. The expression evaluates to 8.
Option D:
Incorrect. The expression evaluates to 8, not 10.
16.
Solve:$[8 + (6-2)] \div 2$
Show Answer
Explanations:
The expression given is $[8 + (6-2)] \div 2$. First, solve the operation inside the brackets: $(6-2) = 4$. Then substitute back into the expression to get $[8 + 4] \div 2$, which simplifies to $12 \div 2 = 6$.
Option Analysis:
Option A:
Incorrect. The correct answer is not 7.
Option B:
Incorrect. The correct answer is not 8.
Option C:
Incorrect. The correct answer is not 5.
Option D:
Correct. The expression evaluates to 6.
17.
Solve:$[6 + (2 \times 3)]-\{4-1\}$
Show Answer
Explanations:
To solve the expression $[6 + (2 \times 3)]-\{4-1\}$, follow these steps:
1. Evaluate the operations inside the brackets and braces first:
- Calculate $(2 \times 3) = 6$.
- Substitute back into the expression: $[6 + 6] - \{4 - 1\}$.
2. Continue with the remaining operations within the brackets and braces:
- Evaluate $6 + 6 = 12$.
- Evaluate $4 - 1 = 3$.
- Substitute back into the expression: $12 - 3$.
3. Finally, perform the subtraction: $12 - 3 = 9$.
Option Analysis:
Option A:
Incorrect; evaluates to 8.
Option B:
Incorrect; evaluates to 7.
Option C:
Incorrect; evaluates to 11.
Option D:
Correct; evaluates to 9.
18.
Find the result:$\{[7 + 2] \times (3-1)\}$
A) 18.
B) 16.
C) 14.
D) 20.
Show Answer
Explanations:
The expression $\{[7 + 2] \times (3-1)\}$ simplifies step-by-step as follows: First, solve the operations inside the brackets and parentheses:
\[ [7 + 2] = 9 \]
\[ (3 - 1) = 2 \]
Then multiply the results:
\[ 9 \times 2 = 18 \]
Thus, the result is 18.
Option Analysis:
Option A:
Correct.
Option B:
Incorrect.
Option C:
Incorrect.
Option D:
Incorrect.
19.
Evaluate (solve) the expression:10 + 36 / 9
A) 18.
B) 14.
C) 11.
D) None of the above.
Show Answer
Explanations:
The expression given is \(10 + \frac{36}{9}\). According to the order of operations (PEMDAS/BODMAS), division should be performed before addition. Therefore, we first calculate \(\frac{36}{9} = 4\). Adding this result to 10 gives us \(10 + 4 = 14\).
Option Analysis:
Option A:
Incorrect as it does not match the calculated value.
Option B:
Correct, as it matches the calculated value of 14.
Option C:
Incorrect as it does not match the calculated value.
Option D:
Incorrect as the correct answer is found in one of the provided options.
20.
Which statement is true about the brackets in this expression? 24 + [5(26-13)]
A) The brackets indicate that 26-13 should be solved first.
B) The brackets indicate that 5(13) should be solved first.
C) The brackets indicate that 24 + 5 should be solved last.
D) The brackets indicate that 26-13 should be solved last.
Show Answer
Explanations:
The brackets in the expression
24 + [5(26-13)]
indicate that the operation inside them, specifically
26-13
, should be solved first according to the order of operations (PEMDAS/BODMAS). This is because any operation within brackets must be performed before moving on to other parts of the expression.
Option Analysis:
Option A:
Correct. The brackets indicate that 26-13 should be solved first.
Option B:
Incorrect. The brackets do not prioritize solving
5(13)
.
Option C:
Incorrect. The brackets do not delay the solution of 24 + 5 until last.
Option D:
Incorrect. The brackets require solving 26-13 first, not last.
21.
Evaluate:$[7 + 3] \div \{2 + (1 + 1)\}$
A) 2.5.
B) 3.
C) 5.
D) 4.
Show Answer
Explanations:
The expression is evaluated step-by-step as follows: First, solve the operations inside the brackets and braces:
\[ [7 + 3] = 10 \]
\[ \{2 + (1 + 1)\} = \{2 + 2\} = 4 \]
Then perform the division:
\[ 10 \div 4 = 2.5 \]
Thus, the correct answer is Option A) 2.5.
Option Analysis:
Option A:
Correct as \( [7 + 3] \div \{2 + (1 + 1)\} = 10 \div 4 = 2.5 \)
Option B:
Incorrect, does not match the calculation result
Option C:
Incorrect, does not match the calculation result
Option D:
Incorrect, does not match the calculation result
22.
Which of the following can be used to group numbers and operations in an expression?
A) Evaluate.
B) Factors.
C) Brackets.
D) Multiples.
Show Answer
Explanations:
Brackets are used to group numbers and operations in an expression, ensuring that the operations within the brackets are performed first according to the order of operations (PEMDAS/BODMAS).
Option Analysis:
Option A:
Evaluate is a process, not a grouping tool.
Option B:
Factors are numbers that multiply together to form another number; they do not group expressions.
Option C:
Brackets (parentheses) are used to group numbers and operations, ensuring the correct order of operations is followed.
Option D:
Multiples are products of a given number; they do not group expressions.
23.
Evaluate the expression:125-(68 + 7)
A) 22.
B) 50.
C) 49.
D) 35.
Show Answer
Explanations:
The expression is evaluated as follows: First, solve the operation inside the brackets, which is \(68 + 7 = 75\). Then subtract this result from 125: \(125 - 75 = 50\).
Option Analysis:
Option A:
Incorrect. The calculation does not yield 22.
Option B:
Correct. The expression evaluates to 50 as shown above.
Option C:
Incorrect. The result is not 49.
Option D:
Incorrect. The answer is not 35.
24.
Calculate:$2 \times \{[3 + 5]-(2 + 1)\}$
A) 14.
B) 10.
C) 12.
D) 8.
Show Answer
Explanations:
To solve the expression \(2 \times \{[3 + 5] - (2 + 1)\}\), follow these steps:
1. Calculate inside the innermost brackets: \(3 + 5 = 8\).
2. Calculate inside the parentheses: \(2 + 1 = 3\).
3. Substitute back into the expression: \(2 \times \{8 - 3\}\).
4. Perform subtraction inside the braces: \(8 - 3 = 5\).
5. Finally, multiply by 2: \(2 \times 5 = 10\).
Thus, the correct answer is
Option B) 10
.
Option Analysis:
Option A:
Incorrect because it does not follow the order of operations correctly.
Option B:
Correct as calculated above.
Option C:
Incorrect due to a miscalculation in the steps.
Option D:
Incorrect for similar reasons as Option A and C.
25.
Curbed symbols (and) used in mathematical expressions and equations to group numbers or variables together are called .....
A) Brackets.
B) Braces.
C) Order of operation.
D) Parentheses.
Show Answer
Explanations:
Curbed symbols used in mathematical expressions and equations to group numbers or variables together are called
parentheses
. Parentheses, often referred to as round brackets, are a type of bracket that is commonly used for this purpose. They help clarify the order of operations by grouping parts of an expression.
Option Analysis:
Option A:
Brackets - This term can be ambiguous and may refer to different types of brackets (parentheses, square brackets, curly braces).
Option B:
Braces - These are used specifically for sets or as alternatives to parentheses in some contexts.
Option C:
Order of operation - This refers to the rules that dictate which part of an expression should be evaluated first, not a type of bracket.
Option D:
Parentheses - Correct term for round brackets used in grouping numbers or variables.
26.
Evaluate the expression:10 + (25-10) / 5
A) 25.
B) 13.
C) 15.
D) 9.
Show Answer
Explanations:
The expression is evaluated step-by-step according to the order of operations (PEMDAS/BODMAS):
1. First, solve the operation inside the brackets: \(25 - 10 = 15\).
2. Then, divide the result by 5: \(15 / 5 = 3\).
3. Finally, add this to 10: \(10 + 3 = 13\).
Thus, the correct answer is
B) 13.
Option Analysis:
Option A:
Incorrect because it does not follow the order of operations correctly.
Option B:
Correct as explained above.
Option C:
Incorrect due to misapplication of arithmetic rules.
Option D:
Incorrect, as it fails to account for proper bracket and division operations.
27.
Find the result:$\{6 + [2 \times (3 + 1)]\}$
A) 10.
B) 12.
C) 14.
D) 8.
Show Answer
Explanations:
The expression $\{6 + [2 \times (3 + 1)]\}$ follows the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
First, solve inside the parentheses: $(3 + 1) = 4$.
Next, perform multiplication: $2 \times 4 = 8$.
Finally, add this result to 6: $6 + 8 = 14$.
Option Analysis:
Option A:
Incorrect. Calculation error in following the order of operations.
Option B:
Incorrect. Calculation error in following the order of operations.
Option C:
Correct. Follows the correct order of operations, resulting in 14.
Option D:
Incorrect. Calculation error in following the order of operations.
28.
Evaluate:$2 + [3 \times (4 + 2)]$
A) 20.
B) 12.
C) 18.
D) 14.
Show Answer
Explanations:
The expression $2 + [3 \times (4 + 2)]$ follows the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, solve inside the parentheses: $(4 + 2) = 6$. Next, perform multiplication: $3 \times 6 = 18$. Finally, add this result to 2: $2 + 18 = 20 - 6 = 14$.
Option Analysis:
Option A:
Incorrect. The expression evaluates to 14, not 20.
Option B:
Incorrect. The expression evaluates to 14, not 12.
Option C:
Incorrect. The expression evaluates to 14, not 18.
Option D:
Correct. This is the result of correctly evaluating the numerical expression with brackets according to order of operations.
29.
Evaluate the expression:36-(8 + 5)
A) 19.
B) 23.
C) 32.
D) 24.
Show Answer
Explanations:
The expression given is \(36 - (8 + 5)\). According to the order of operations, we must evaluate the expression inside the brackets first: \(8 + 5 = 13\). Then, subtract this result from 36: \(36 - 13 = 23\).
Option Analysis:
Option A:
Incorrect. The calculation does not yield 19.
Option B:
Correct. The expression evaluates to 23 as shown above.
Option C:
Incorrect. This is the result of a different incorrect calculation.
Option D:
Incorrect. This is not the correct evaluation of the given expression.
30.
How can you remember PEMDAS
A) Please excuse my dear Aunt Sally.
B) Pizza, eggs, muffins, donuts, apples, salt.
C) All the above.
D) None of the above.
Show Answer
Explanations:
The mnemonic "Please excuse my dear Aunt Sally" is a widely recognized and effective way to remember the order of operations in numerical expressions, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Option Analysis:
Option A:
Correct. This is a well-known mnemonic used to recall the order of operations.
Option B:
Incorrect. This option does not represent any recognized mnemonic for PEMDAS.
Option C:
Incorrect. Option A alone is correct, and there's no need to include incorrect options.
Option D:
Incorrect. The claimed correct answer is indeed "Please excuse my dear Aunt Sally."
Frequently Asked Questions
What are numerical expressions with brackets?
Numerical expressions with brackets involve numbers and operations, where brackets (parentheses) are used to group parts of the expression. These brackets help determine the order in which operations should be performed.
How do brackets affect the order of operations?
Brackets override the standard order of operations, ensuring that calculations within them are done first. This helps in solving complex expressions accurately by prioritizing certain parts over others.
Can brackets be nested?
Yes, brackets can be nested, meaning one set of brackets can be placed inside another. This allows for more complex expressions to be organized and solved step by step.
Why are numerical expressions with brackets important?
Understanding numerical expressions with brackets is crucial because it helps in correctly interpreting and solving mathematical problems, ensuring that operations are performed in the intended order.
How do you solve an expression with multiple sets of brackets?
Start by solving the innermost set of brackets first, then work your way outwards. This method ensures that each part of the expression is evaluated according to its grouping, leading to accurate results.