Q1: Sarah wrote the expression \(5 + n\) to represent the total number of pencils she has. If she has 12 pencils in total, what is the value of \(n\)? (a) 5 (b) 7 (c) 12 (d) 17
Solution:
Ans: (b) Explanation: To find \(n\), we solve the equation \(5 + n = 12\). Subtracting 5 from both sides gives us \(n = 7\). Option (a) is the number Sarah started with, option (c) is the total, and option (d) adds instead of subtracts.
Q2: Which expression represents "8 less than a number \(x\)"? (a) \(8 - x\) (b) \(x - 8\) (c) \(x + 8\) (d) \(8x\)
Solution:
Ans: (b) Explanation: The phrase "less than" means we subtract from the number that comes after it. So "8 less than \(x\)" means \(x - 8\). Option (a) reverses the order, option (c) adds instead of subtracts, and option (d) represents multiplication.
Q3: What is the next number in the pattern: 3, 7, 11, 15, ___? (a) 17 (b) 18 (c) 19 (d) 20
Solution:
Ans: (c) Explanation: This is an arithmetic pattern where each number increases by 4. Following the rule: \(15 + 4 = 19\). Option (a) adds only 2, option (b) adds 3, and option (d) adds 5.
Q4: If \(m \times 6 = 48\), what is the value of \(m\)? (a) 6 (b) 7 (c) 8 (d) 9
Solution:
Ans: (c) Explanation: To solve for \(m\), we divide both sides by 6: \(m = 48 \div 6 = 8\). Option (b) gives 42 when multiplied by 6, option (d) gives 54, and option (a) gives 36.
Q5: Which equation matches this statement: "A number divided by 4 equals 9"? (a) \(4n = 9\) (b) \(n \div 4 = 9\) (c) \(n + 4 = 9\) (d) \(9 \div n = 4\)
Solution:
Ans: (b) Explanation:"A number divided by 4" translates to \(n \div 4\), and this equals 9, giving us \(n \div 4 = 9\). Option (a) represents multiplication, option (c) represents addition, and option (d) reverses the division.
Ans: (b) Explanation: Using the order of operations, we solve inside parentheses first: \(4 + 2 = 6\). Then multiply: \(3 \times 6 = 18\). Option (a) adds first without multiplying correctly, option (c) adds 3 to 4 then adds 2 incorrectly, and option (d) multiplies all three numbers.
Q7: If the rule for a pattern is "multiply by 2, then add 1," what number comes after 5? (a) 7 (b) 10 (c) 11 (d) 12
Solution:
Ans: (c) Explanation: Following the pattern rule: First multiply \(5 \times 2 = 10\), then add 1: \(10 + 1 = 11\). Option (a) only adds 2, option (b) only multiplies by 2, and option (d) multiplies by 2 then adds 2.
Q8: Which property is shown by the equation \(7 + 8 = 8 + 7\)? (a) Associative Property (b) Commutative Property (c) Distributive Property (d) Identity Property
Solution:
Ans: (b) Explanation: The Commutative Property states that the order of numbers in addition (or multiplication) can be changed without affecting the result. Option (a) deals with grouping, option (c) involves multiplication over addition, and option (d) involves adding zero.
Section B: Fill in the Blanks
Q9: A letter or symbol that represents an unknown number is called a(n) __________.
Solution:
Ans: variable Explanation: A variable is a symbol (usually a letter) used to represent a number that is not yet known or can change in value.
Q10: In the expression \(5x + 3\), the number 5 is called the __________.
Solution:
Ans: coefficient Explanation: A coefficient is the numerical factor that multiplies a variable in an algebraic expression.
Q11: To solve the equation \(x + 9 = 15\), you need to subtract __________ from both sides.
Solution:
Ans: 9 Explanation: To isolate the variable \(x\), we use the inverse operation of addition, which is subtraction. Subtracting 9 from both sides gives \(x = 6\).
Q12: The pattern 2, 4, 8, 16, 32 follows the rule: multiply by __________.
Solution:
Ans: 2 Explanation: Each term in this geometric pattern is obtained by multiplying the previous term by 2.
Q13: An equation is a mathematical sentence that uses an __________ sign to show two expressions are equal.
Solution:
Ans: equals (or equal) Explanation: An equation is a statement showing that two expressions have the same value, connected by an equals sign (=).
Q14: When you replace a variable with a number and calculate the result, you are __________ the expression.
Solution:
Ans: evaluating Explanation:Evaluating an expression means substituting a value for the variable and performing the calculation to find the result.
Section C: Word Problems
Q15: Maria has some stickers in her collection. She receives 12 more stickers from her friend, and now she has 35 stickers in total. Write an equation to represent this situation and solve it to find how many stickers Maria had originally.
Solution:
Ans: Equation: \(s + 12 = 35\) where \(s\) represents the original number of stickers Solving: \(s + 12 = 35\) \(s = 35 - 12\) \(s = 23\) Final Answer: Maria originally had 23 stickers.
Q16: A school bus route drops off students at several stops. At each stop, 6 students get off the bus. If 42 students got off the bus in total, how many stops did the bus make? Write and solve an equation.
Solution:
Ans: Equation: \(6n = 42\) where \(n\) represents the number of stops Solving: \(n = 42 \div 6\) \(n = 7\) Final Answer: The bus made 7 stops.
Q17: Jake is thinking of a number. When he multiplies his number by 4 and then adds 5, he gets 29. What number is Jake thinking of?
Solution:
Ans: Equation: \(4n + 5 = 29\) where \(n\) is the number Jake is thinking of Solving: \(4n + 5 = 29\) \(4n = 29 - 5\) \(4n = 24\) \(n = 24 \div 4\) \(n = 6\) Final Answer: Jake is thinking of the number 6.
Q18: A bakery packages cookies in boxes. Each box contains the same number of cookies. If 8 boxes contain 72 cookies in total, how many cookies are in each box?
Solution:
Ans: Equation: \(8c = 72\) where \(c\) represents cookies per box Solving: \(c = 72 \div 8\) \(c = 9\) Final Answer: Each box contains 9 cookies.
Q19: Emma creates a number pattern starting at 5. Her rule is: "Add 7 to get the next number." Write the first five numbers in Emma's pattern.
Solution:
Ans: Starting number: 5 First term: 5 Second term: \(5 + 7 = 12\) Third term: \(12 + 7 = 19\) Fourth term: \(19 + 7 = 26\) Fifth term: \(26 + 7 = 33\) Final Answer: The first five numbers are 5, 12, 19, 26, 33.
Q20: A rectangular garden has a width of 8 feet. The length is unknown, but the perimeter of the garden is 36 feet. Write an equation using the perimeter formula \(P = 2l + 2w\) and solve it to find the length of the garden.
Solution:
Ans: Given: \(P = 36\) feet, \(w = 8\) feet Equation: \(36 = 2l + 2(8)\) Solving: \(36 = 2l + 16\) \(36 - 16 = 2l\) \(20 = 2l\) \(l = 20 \div 2\) \(l = 10\) Final Answer: The length of the garden is 10 feet.
The document Worksheet (with Solutions): Algebraic Thinking is a part of the Grade 5 Course Math Grade 5.
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