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NY Grade 5 Math study materials
NY Grade 5 Math study resources

NY Grade 5 Math practice questions

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Question 1Operations and Algebraic Thinking

A theater has 14 rows of seats with 25 seats in each row. What is the total number of seats?

  1. 39
  2. 325
  3. 375
  4. 350 Correct answer.

Explanation

Multiply the number of rows by the number of seats per row: 14 × 25. Breaking 25 into 100 ÷ 4 makes this easy: 14 × 100 = 1400, and 1400 ÷ 4 = 350. The total is 350 seats.

Question 2Operations and Algebraic Thinking

Evaluate 6 + 4 × 3.

  1. 18 Correct answer.
  2. 24
  3. 30
  4. 10

Explanation

Order of operations says multiplication is performed before addition. So first compute 4 × 3 = 12, then add 6 to get 18.

Question 3Operations and Algebraic Thinking

Which expression has a value of 7?

  1. 20 − 4 × 3
  2. (2 + 5) × 2
  3. 3 + 12 ÷ 3 Correct answer.
  4. 36 ÷ 6 + 2

Explanation

In 3 + 12 ÷ 3, divide first: 12 ÷ 3 = 4, then add 3 to get 7. Checking the others confirms none equals 7.

Question 4Operations and Algebraic Thinking

A number machine follows the rule 'multiply by 4, then subtract 3.' What comes out when 6 goes in?

  1. 27
  2. 11
  3. 24
  4. 21 Correct answer.

Explanation

Apply the rule in order: 6 × 4 = 24, then 24 − 3 = 21. The output is 21.

Question 5Operations and Algebraic Thinking

What is the value of 5²?

  1. 7
  2. 10
  3. 32
  4. 25 Correct answer.

Explanation

The exponent 2 means multiply the base 5 by itself: 5 × 5 = 25. It does not mean 5 × 2.

Question 6Operations and Algebraic Thinking

Which list shows the first four multiples of 9?

  1. 9, 18, 27, 36 Correct answer.
  2. 1, 3, 9, 27
  3. 18, 27, 36, 45
  4. 9, 10, 11, 12

Explanation

Multiples of 9 are the products 9 × 1, 9 × 2, 9 × 3, 9 × 4. Those products are 9, 18, 27, and 36.

Question 7Operations and Algebraic Thinking

Solve for n: n + 17 = 42.

  1. 24
  2. 35
  3. 59
  4. 25 Correct answer.

Explanation

Subtract 17 from both sides to undo the addition: 42 − 17 = 25. Check: 25 + 17 = 42, so n = 25.

Question 8Operations and Algebraic Thinking

A pattern starts at 3 and adds 6 each time: 3, 9, 15, 21, ... What is the next term?

  1. 30
  2. 24
  3. 27 Correct answer.
  4. 26

Explanation

Each term is 6 more than the one before it. Adding 6 to 21 gives 27, so the next term is 27.

Question 9Operations and Algebraic Thinking

Which expression correctly represents '8 more than 5 times a number x'?

  1. 8x + 5
  2. 5(x + 8)
  3. 8 − 5x
  4. 5x + 8 Correct answer.

Explanation

'5 times a number x' is 5x, and '8 more than' that means add 8. So the expression is 5x + 8.

Question 10Operations and Algebraic Thinking

Evaluate (18 − 6) ÷ 3 + 4.

  1. 10
  2. 2
  3. 8 Correct answer.
  4. 6

Explanation

Parentheses first: 18 − 6 = 12. Then divide: 12 ÷ 3 = 4. Finally add 4 to get 8.

Question 11Operations and Algebraic Thinking

A baker packs 96 muffins equally into boxes of 8. How many boxes are filled?

  1. 10
  2. 14
  3. 88
  4. 12 Correct answer.

Explanation

Divide the total number of muffins by the number per box: 96 ÷ 8 = 12. So 12 boxes are filled.

Question 12Operations and Algebraic Thinking

Solve for m: 7m = 63.

  1. 56
  2. 70
  3. 7
  4. 9 Correct answer.

Explanation

Divide both sides by 7 to undo the multiplication: 63 ÷ 7 = 9. Check: 7 × 9 = 63, so m = 9.

Question 13Operations and Algebraic Thinking

Which number is a multiple of both 4 and 6?

  1. 24 Correct answer.
  2. 18
  3. 16
  4. 8

Explanation

A common multiple must be divisible by both 4 and 6. 24 ÷ 4 = 6 and 24 ÷ 6 = 4, so 24 works. The others fail at least one division.

Question 14Operations and Algebraic Thinking

A rule says 'add 5, then multiply by 2.' If the output is 26, what was the input?

  1. 8 Correct answer.
  2. 13
  3. 16
  4. 10

Explanation

Work backward: undo multiply by 2 by dividing 26 ÷ 2 = 13, then undo add 5 by subtracting 13 − 5 = 8. Check: (8 + 5) × 2 = 26.

Question 15Operations and Algebraic Thinking

Which expression is equivalent to 3 × (10 + 4)?

  1. 30 + 12 Correct answer.
  2. 30 + 4
  3. 3 + 10 + 4
  4. 13 + 7

Explanation

The distributive property says 3 × (10 + 4) = 3 × 10 + 3 × 4. That equals 30 + 12, which is 42 (and 3 × 14 = 42).

Question 16Operations and Algebraic Thinking

What is the value of 2³ + 4²?

  1. 32
  2. 12
  3. 24 Correct answer.
  4. 20

Explanation

Compute each power: 2³ = 8 and 4² = 16. Adding them gives 8 + 16 = 24.

Question 17Operations and Algebraic Thinking

A movie ticket costs $9 and a snack costs $4. A family buys 3 tickets and 2 snacks. Which expression gives the total cost?

  1. (3 + 2) × (9 + 4)
  2. 3 × 9 + 2 × 4 Correct answer.
  3. 3 × 4 + 2 × 9
  4. 3 + 9 + 2 + 4

Explanation

Cost equals quantity times price for each item, then add. Three tickets cost 3 × 9 and two snacks cost 2 × 4, so the total is 3 × 9 + 2 × 4 = 27 + 8 = 35.

Question 18Operations and Algebraic Thinking

A pattern is 2, 6, 18, 54, ... What rule produces this pattern?

  1. Add 12 each time
  2. Multiply by 2 each time
  3. Multiply by 3 each time Correct answer.
  4. Add 4 each time

Explanation

Check the ratio between terms: 6 ÷ 2 = 3, 18 ÷ 6 = 3, and 54 ÷ 18 = 3. Each term is 3 times the one before, so the rule is multiply by 3.

Question 19Operations and Algebraic Thinking

Which statement about the expression 4 + 12 ÷ 2 × 3 is true?

  1. The addition is done first, and the value is 24.
  2. The multiplication is done first, and the value is 6.
  3. The division is done first, and the value is 22. Correct answer.
  4. The expression is done left to right, and the value is 24.

Explanation

Multiplication and division are done before addition, and they are done left to right. So 12 ÷ 2 = 6, then 6 × 3 = 18, then 4 + 18 = 22.

Question 20Operations and Algebraic Thinking

A number n satisfies 3n − 5 = 16. What is n?

  1. 5
  2. 7 Correct answer.
  3. 21
  4. 11

Explanation

Add 5 to both sides: 3n = 21. Then divide by 3: n = 7. Check: 3 × 7 − 5 = 21 − 5 = 16.

Question 21Operations and Algebraic Thinking

Which pair of expressions is equivalent for all values of x?

  1. 6(x + 2) and 6x + 8
  2. 6(x + 2) and x + 12
  3. 6(x + 2) and 6x + 2
  4. 6(x + 2) and 6x + 12 Correct answer.

Explanation

Distribute the 6 to both terms inside the parentheses: 6 × x = 6x and 6 × 2 = 12. So 6(x + 2) equals 6x + 12 for every x.

Question 22Operations and Algebraic Thinking

A number machine follows 'multiply by 3, then add 4.' A second machine reverses it. What does the reverse machine do?

  1. Add 4, then multiply by 3
  2. Divide by 3, then subtract 4
  3. Subtract 4, then divide by 3 Correct answer.
  4. Subtract 3, then divide by 4

Explanation

To undo a sequence, reverse the order and use inverse operations. The last step was add 4, so first subtract 4; the first step was multiply by 3, so then divide by 3.

Question 23Operations and Algebraic Thinking

The expression 2 + 3 × 4² has what value?

  1. 146
  2. 98
  3. 50 Correct answer.
  4. 26

Explanation

Exponents come first: 4² = 16. Then multiply: 3 × 16 = 48. Finally add: 2 + 48 = 50.

Question 24Operations and Algebraic Thinking

A pattern begins 1, 4, 9, 16, 25, ... Which expression gives the nth term?

  1. n + 3
  2. n² Correct answer.
  3. 2n
  4. 2n + 1

Explanation

The terms are the squares of the counting numbers: 1² = 1, 2² = 4, 3² = 9, 4² = 16. So the nth term is n².

Question 25Operations and Algebraic Thinking

Two expressions are 5(2x + 3) and 10x + 15. A student claims they are equal only when x = 2. Which statement is correct?

  1. They are equal for every value of x because distributing 5 gives 10x + 15. Correct answer.
  2. They are never equal because one has parentheses.
  3. They are equal only when x = 2, as the student claims.
  4. They are equal only when x = 0.

Explanation

Distributing the 5 gives 5 × 2x = 10x and 5 × 3 = 15, so 5(2x + 3) is identical to 10x + 15. Equivalent expressions are equal for every value of x, not just one.

Question 26Operations and Algebraic Thinking

A rule is written as 4 × (6 + 3). Using the order of operations, what value does this expression have?

  1. 36 Correct answer.
  2. 24
  3. 18
  4. 27

Explanation

Operations inside grouping symbols are done first, so 6 + 3 = 9. Then multiply 4 × 9 = 36. Multiplying before adding the 6 and 3 would ignore the parentheses.

Question 27Operations and Algebraic Thinking

Which symbol belongs in the box to make the number sentence true? 48 ÷ 6 □ 2 × 4

  1. +
  2. = Correct answer.
  3. <
  4. >

Explanation

Evaluate each side: 48 ÷ 6 = 8 and 2 × 4 = 8. Since both sides equal 8, the equals sign makes the sentence true.

Question 28Operations and Algebraic Thinking

Which of these is a factor of 36 but not a factor of 24?

  1. 9 Correct answer.
  2. 6
  3. 4
  4. 3

Explanation

A factor divides a number with no remainder. 36 ÷ 9 = 4 exactly, but 24 ÷ 9 leaves a remainder of 6, so 9 is a factor of 36 only. The other choices divide both 24 and 36 evenly.

Question 29Operations and Algebraic Thinking

Which list shows all the positive factor pairs of 28 exactly once, counting reversed pairs as the same pair?

  1. 1 × 28, 2 × 14, 3 × 9, 4 × 7
  2. 2 × 14, 4 × 7, 7 × 4
  3. 1 × 28, 2 × 14, 4 × 7 Correct answer.
  4. 1 × 28, 2 × 14, 7 × 4, 14 × 2

Explanation

Factor pairs multiply to 28, and each distinct pair should be listed once. The pairs are 1 × 28, 2 × 14, and 4 × 7. Reversing the factors does not create a new pair.

Question 30Operations and Algebraic Thinking

Which number is prime?

  1. 29 Correct answer.
  2. 21
  3. 27
  4. 33

Explanation

A prime number has exactly two factors, 1 and itself. 29 is not divisible by 2, 3, or 5, so its only factors are 1 and 29. Each other choice has a factor other than 1 and itself.

Question 31Operations and Algebraic Thinking

A number machine uses the rule 'multiply by 4, then subtract 3.' What is the output when the input is 7?

  1. 28
  2. 31
  3. 16
  4. 25 Correct answer.

Explanation

Apply the rule in order: 7 × 4 = 28, then 28 − 3 = 25. The subtraction happens after the multiplication, so the output is 25.

Question 32Operations and Algebraic Thinking

Which expression means 'subtract 6 from 20, then divide the result by 2'?

  1. 20 ÷ 2 − 6
  2. (20 ÷ 2) − 6
  3. (20 − 6) ÷ 2 Correct answer.
  4. 20 − 6 ÷ 2

Explanation

The subtraction must happen first, so it goes inside parentheses: (20 − 6) ÷ 2. Without parentheses, division would be done before subtraction, which changes the result.

Question 33Operations and Algebraic Thinking

A rule says 'multiply by 5.' What is the input when the output is 45?

  1. 50
  2. 225
  3. 9 Correct answer.
  4. 40

Explanation

To undo multiplying by 5, divide by 5. Since 45 ÷ 5 = 9, the input is 9, and 9 × 5 = 45 checks the answer.

Question 34Operations and Algebraic Thinking

A pattern follows the rule 'multiply by 2, then add 1.' The first term is 3. What are the next two terms?

  1. 9 and 19
  2. 6 and 12
  3. 7 and 13
  4. 7 and 15 Correct answer.

Explanation

Apply the rule to each term: 3 × 2 + 1 = 7, then 7 × 2 + 1 = 15. Both steps must be done in order for each new term.

Question 35Operations and Algebraic Thinking

A pattern is 80, 40, 20, 10, ... Which rule describes it?

  1. subtract 30
  2. subtract 40
  3. divide by 4
  4. divide by 2 Correct answer.

Explanation

Each term is half the term before it: 80 ÷ 2 = 40, 40 ÷ 2 = 20, and 20 ÷ 2 = 10. A rule must work for every step, not just the first one.

Question 36Operations and Algebraic Thinking

A pattern starts with 5 and follows the rule 'add 4.' Which expression gives the 10th term?

  1. 5 + 10 × 4
  2. 5 × 4 + 10
  3. 5 + 4 × 4
  4. 5 + 9 × 4 Correct answer.

Explanation

The first term is 5, and the rule 'add 4' is applied 9 times to reach the 10th term. So the 10th term is 5 + 9 × 4 = 41.

Question 37Operations and Algebraic Thinking

Evaluate: 5 + 3 × (8 − 2)

  1. 48
  2. 13
  3. 21
  4. 23 Correct answer.

Explanation

First do the parentheses: 8 − 2 = 6. Then multiply 3 × 6 = 18, and finally add 5 + 18 = 23.

Question 38Operations and Algebraic Thinking

Which expression has the same value as 6 × 7 + 6 × 3?

  1. (6 + 7) × (6 + 3)
  2. 6 × 10 + 3
  3. 6 × (7 + 3) Correct answer.
  4. 6 × 7 + 3

Explanation

Both products share the factor 6, so the distributive property lets you write 6 × 7 + 6 × 3 = 6 × (7 + 3). Both sides equal 60.

Question 39Operations and Algebraic Thinking

Which expression is equivalent to 8 × 47?

  1. 8 × 50 − 8
  2. 8 × 40 + 8 × 7 Correct answer.
  3. 8 × 40 + 7
  4. 8 + 40 × 7

Explanation

Break 47 into 40 + 7, then use the distributive property: 8 × 47 = 8 × (40 + 7) = 8 × 40 + 8 × 7. Both sides equal 376.

Question 40Operations and Algebraic Thinking

A class has 15 boxes with 12 pencils in each box. Which expression shows the total number of pencils found by breaking 12 into 10 + 2?

  1. 15 × 12 + 10 + 2
  2. 15 + 10 × 2
  3. 15 × 10 + 15 × 2 Correct answer.
  4. 15 × 10 + 2

Explanation

The distributive property splits 12 into 10 + 2: 15 × 12 = 15 × (10 + 2) = 15 × 10 + 15 × 2 = 180. The 15 must be multiplied by each part.

Question 41Operations and Algebraic Thinking

Which word phrase matches the expression 3 × (n + 6)?

  1. the sum of three and six times a number
  2. three more than a number times six
  3. three times the sum of a number and six Correct answer.
  4. three times a number, plus six

Explanation

The parentheses show that n + 6 is found first, and then the whole sum is multiplied by 3. So the phrase is 'three times the sum of a number and six.'

Question 42Operations and Algebraic Thinking

A taxi charges $3 to start plus $2 per mile. Which expression gives the cost of a ride of m miles?

  1. 3 + 2m Correct answer.
  2. 3m + 2m
  3. 2 + 3m
  4. 5m

Explanation

The start fee of $3 is paid once, and the $2 charge is paid for each mile, giving 2m. Adding them gives 3 + 2m.

Question 43Operations and Algebraic Thinking

A number machine follows 'add 8, then divide by 2.' A second machine reverses it. What does the reverse machine do?

  1. subtract 8, then multiply by 2
  2. subtract 2, then divide by 8
  3. multiply by 2, then subtract 8 Correct answer.
  4. divide by 2, then add 8

Explanation

To reverse a sequence, undo each step in the opposite order. The last step, dividing by 2, is undone first by multiplying by 2; then the adding of 8 is undone by subtracting 8.

Question 44Operations and Algebraic Thinking

Which value of x makes 4x + 7 = 35 true?

  1. 9
  2. 7 Correct answer.
  3. 8
  4. 10

Explanation

Subtract 7 from both sides to get 4x = 28, then divide by 4 to get x = 7. Checking: 4 × 7 + 7 = 35.

Question 45Operations and Algebraic Thinking

A number n is multiplied by 6 and then 9 is subtracted, giving 27. Which equation matches this situation?

  1. 6n + 9 = 27
  2. 6(n − 9) = 27
  3. 6n − 9 = 27 Correct answer.
  4. 9n − 6 = 27

Explanation

Multiplying n by 6 gives 6n, and subtracting 9 from that gives 6n − 9. Setting it equal to 27 gives 6n − 9 = 27, so n = 6.

Question 46Operations and Algebraic Thinking

Two expressions are 4(2x + 5) and 8x + 20. A student says they are equal only when x = 3. Which statement is correct?

  1. They are equal for every value of x because 4(2x + 5) expands to 8x + 20. Correct answer.
  2. They are equal only when x = 0.
  3. They are never equal for any value of x.
  4. They are equal only when x = 3, as the student says.

Explanation

The distributive property gives 4(2x + 5) = 8x + 20, so the two expressions are equivalent. Equivalent expressions have the same value for every x, not just one value.

Question 47Operations and Algebraic Thinking

A pattern of squares uses 1 square in figure 1, 4 in figure 2, 9 in figure 3, and 16 in figure 4. Which expression gives the number of squares in figure n?

  1. n + 3
  2. n × n Correct answer.
  3. 2n + 1
  4. 4n − 3

Explanation

The counts 1, 4, 9, and 16 are the squares of the figure numbers: 1², 2², 3², 4². So figure n uses n × n squares, which is n².

Question 48Operations and Algebraic Thinking

A store sells notebooks for $3 each and pens for $2 each. Maya buys 4 notebooks and some pens, spending $20 in all. Which equation finds p, the number of pens?

  1. 3 × 4 + 2 + p = 20
  2. 3 × 4 + 2p = 20 Correct answer.
  3. 3p + 2 × 4 = 20
  4. 2 × 4 + 3p = 20

Explanation

The notebooks cost 3 × 4 = $12, and the pens cost 2p dollars. Their total is $20, so 3 × 4 + 2p = 20, which gives p = 4.

Question 49Operations and Algebraic Thinking

The expression 2 + 3 × (4 + 2)² has what value?

  1. 900
  2. 38
  3. 110 Correct answer.
  4. 74

Explanation

First the parentheses: 4 + 2 = 6. Then the exponent: 6² = 36. Then multiply 3 × 36 = 108, and finally add 2 + 108 = 110.

Question 50Operations and Algebraic Thinking

A number machine uses the rule 'multiply by 3, then add 2.' A second machine is built to undo the first machine exactly. When the first machine's output is used as the input of the second machine, the original number comes back. Which rule describes the second machine?

  1. Divide by 3, then subtract 2
  2. Subtract 2, then multiply by 3
  3. Subtract 2, then divide by 3 Correct answer.
  4. Add 2, then divide by 3

Explanation

To undo a rule, reverse each step in the opposite order. The first machine multiplies by 3 and then adds 2, so the undo machine must first subtract 2 and then divide by 3. Checking with an input of 4: the first machine gives 3 × 4 + 2 = 14, and the undo rule gives (14 − 2) ÷ 3 = 4, which returns the original number.