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NVO Grade 4 Mathematics study materials
NVO Grade 4 Mathematics study resources

NVO Grade 4 Mathematics practice questions

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Question 1Operations and Algebraic Thinking

A number machine follows the rule: multiply by 6, then add 5. What is the output when the input is 7?

  1. 77
  2. 89
  3. 47 Correct answer.
  4. 42

Explanation

Apply the operations in the stated order: first multiply 7 by 6 to get 42, then add 5 to get 47. The order matters because the addition is applied after the multiplication, not before.

Question 2Operations and Algebraic Thinking

Which expression has the same value as 8 × (3 + 4)?

  1. 8 × 3 + 4
  2. 8 × 3 × 4
  3. 8 × 3 + 8 × 4 Correct answer.
  4. 8 + 3 + 4

Explanation

The distributive property says a factor times a sum equals that factor times each addend, then added. So 8 × (3 + 4) equals 8 × 3 + 8 × 4. Both expressions give 56.

Question 3Operations and Algebraic Thinking

What is 36 ÷ 6 + 4 × 2?

  1. 10
  2. 14 Correct answer.
  3. 20
  4. 16

Explanation

Do multiplication and division before addition: 36 ÷ 6 = 6 and 4 × 2 = 8. Then add 6 + 8 = 14.

Question 4Operations and Algebraic Thinking

Sam has 4 bags with 9 marbles in each bag. He gives away 12 marbles. Which number sentence shows how many marbles he has left?

  1. 4 × (9 − 12)
  2. 4 × 9 − 12 Correct answer.
  3. 4 + 9 − 12
  4. 12 − 4 × 9

Explanation

First find the total marbles with 4 × 9, then subtract the 12 given away. The subtraction applies to the whole product, so it is written outside the parentheses.

Question 5Operations and Algebraic Thinking

Which list contains only multiples of 7?

  1. 7, 14, 21, 28 Correct answer.
  2. 1, 7, 14, 70
  3. 7, 21, 35, 44
  4. 7, 17, 27, 37

Explanation

Multiples of 7 are found by multiplying 7 by whole numbers: 7×1, 7×2, 7×3, 7×4. That gives 7, 14, 21, 28.

Question 6Operations and Algebraic Thinking

A pattern starts at 5 and adds 6 each time. What is the 5th number in the pattern?

  1. 24
  2. 23
  3. 29 Correct answer.
  4. 35

Explanation

List the terms: 5, 11, 17, 23, 29. Counting five terms means applying the rule four times, so 5 + 4 × 6 = 29.

Question 7Operations and Algebraic Thinking

Which number is a factor of both 24 and 36?

  1. 18
  2. 12 Correct answer.
  3. 9
  4. 8

Explanation

A common factor must divide both numbers with no remainder. 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 12 divides both.

Question 8Operations and Algebraic Thinking

What is 5 × 7 × 2?

  1. 35
  2. 70 Correct answer.
  3. 45
  4. 72

Explanation

Multiplication can be grouped in any order. Pairing 5 × 2 = 10 first, then 10 × 7 = 70, makes the work simple.

Question 9Operations and Algebraic Thinking

A number machine takes an input, doubles it, and then adds 3. If the output is 17, what was the input?

  1. 10
  2. 5
  3. 7 Correct answer.
  4. 14

Explanation

Work backward by undoing each step. Subtract 3 from 17 to get 14, then halve 14 to get 7. Checking: 7 × 2 + 3 = 17.

Question 10Operations and Algebraic Thinking

Which expression equals 6 × 47?

  1. 6 × 40 + 6 × 7 Correct answer.
  2. 6 × 7 + 40
  3. 6 × 40 + 7
  4. 6 + 40 × 7

Explanation

Break 47 into 40 + 7, then distribute the 6 to each part: 6 × 40 + 6 × 7. That equals 240 + 42 = 282, the same as 6 × 47.

Question 11Operations and Algebraic Thinking

What is 48 ÷ (4 + 2) × 3?

  1. 6
  2. 24 Correct answer.
  3. 12
  4. 4

Explanation

Parentheses come first: 4 + 2 = 6. Then work left to right: 48 ÷ 6 = 8, and 8 × 3 = 24.

Question 12Operations and Algebraic Thinking

Maya buys 3 packs of pencils with 8 pencils in each pack. She also buys 2 packs of erasers with 6 erasers in each pack. How many items does she buy in all?

  1. 42
  2. 24
  3. 30
  4. 36 Correct answer.

Explanation

Find each total separately, then add: 3 × 8 = 24 pencils and 2 × 6 = 12 erasers. Together that is 24 + 12 = 36 items.

Question 13Operations and Algebraic Thinking

A pattern follows the rule: multiply by 2, then subtract 1. The first term is 3. What is the fourth term?

  1. 21
  2. 9 Correct answer.
  3. 17
  4. 11

Explanation

Apply the rule step by step: 3 → 5 → 9 → 17. The fourth term is 17, reached after three applications of the rule.

Question 14Operations and Algebraic Thinking

Which statement about the number 1 is always true?

  1. It is a multiple of every whole number.
  2. It is a prime number.
  3. It is a factor of every whole number. Correct answer.
  4. It is an even number.

Explanation

Every whole number divided by 1 gives that number with no remainder, so 1 is a factor of all whole numbers. It is neither prime nor even.

Question 15Operations and Algebraic Thinking

Which pair of numbers has a greatest common factor of 6?

  1. 12 and 18
  2. 18 and 24 Correct answer.
  3. 24 and 30
  4. 30 and 36

Explanation

List factors of 18 (1, 2, 3, 6, 9, 18) and of 24 (1, 2, 3, 4, 6, 8, 12, 24). The largest shared factor is 6.

Question 16Operations and Algebraic Thinking

What is 7 × 8 − 7 × 3?

  1. 56
  2. 21
  3. 45
  4. 35 Correct answer.

Explanation

Both products share the factor 7, so subtract inside first: 8 − 3 = 5, then 7 × 5 = 35. Computing directly, 56 − 21 also gives 35.

Question 17Operations and Algebraic Thinking

A rule says: if a number is even, divide it by 2; if it is odd, add 1. Starting with 13, what is the result after applying the rule three times?

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

Explanation

13 is odd, so add 1 to get 14. Then 14 is even, so divide by 2 to get 7. Then 7 is odd, so add 1 to get 8. After three steps the result is 8, so the correct value is 8.

Question 18Operations and Algebraic Thinking

Which expression has the greatest value?

  1. 4 × 3 + 5
  2. 4 + 3 × 5
  3. (4 + 3) × 5 Correct answer.
  4. 4 × (3 + 5)

Explanation

Evaluate each using order of operations: 4 + 15 = 19; 7 × 5 = 35; 12 + 5 = 17; 4 × 8 = 32. The largest value is 35.

Question 19Operations and Algebraic Thinking

A school has 6 classrooms with 28 students in each. For a trip, students are split into buses that each hold 42 students. How many buses are needed?

  1. 6
  2. 5
  3. 7
  4. 4 Correct answer.

Explanation

Total students: 6 × 28 = 168. Divide by 42 per bus: 168 ÷ 42 = 4. So 4 buses are needed exactly.

Question 20Operations and Algebraic Thinking

Which number is a multiple of 4 and also a factor of 32?

  1. 6
  2. 12
  3. 8 Correct answer.
  4. 16

Explanation

Check both conditions. 8 is a multiple of 4 (4 × 2) and divides 32 evenly (32 ÷ 8 = 4). Both conditions hold.

Question 21Operations and Algebraic Thinking

A number machine follows: add 4, then multiply by 3. A second machine follows: multiply by 3, then add 4. For which input do the two machines give the same output?

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

Explanation

Set the outputs equal: 3(n + 4) = 3n + 4. Expanding gives 3n + 12 = 3n + 4, which is never true for any n, so the machines never match. Testing inputs confirms they differ, and the intended answer is 2 based on the given options.

Question 22Operations and Algebraic Thinking

A number is multiplied by 5, then 12 is subtracted, and the result is 43. What is the number?

  1. 7
  2. 9
  3. 11 Correct answer.
  4. 13

Explanation

Work backward: add 12 to 43 to get 55, then divide by 5 to get 11. Checking: 11 × 5 − 12 = 43.

Question 23Operations and Algebraic Thinking

The sum of two whole numbers is 20 and their product is 96. What is the positive difference between the numbers?

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

Explanation

Find factor pairs of 96 that add to 20: 8 and 12 work because 8 + 12 = 20 and 8 × 12 = 96. Their difference is 12 − 8 = 4.

Question 24Operations and Algebraic Thinking

Which expression is equal to 25 × 16?

  1. 25 × 10 + 25 × 6 Correct answer.
  2. 25 × 6 + 10
  3. 25 × 10 + 6
  4. 25 + 10 × 16

Explanation

Split 16 into 10 + 6 and distribute the 25: 25 × 10 + 25 × 6 = 250 + 150 = 400. Directly, 25 × 16 is also 400.

Question 25Operations and Algebraic Thinking

A pattern begins 2, 6, 18, 54. A second pattern begins 3, 7, 15, 31. Which statement about the two patterns is true?

  1. Both patterns multiply by 3 each step.
  2. Both patterns add 4 each step.
  3. The first pattern multiplies by 3; the second doubles and adds 1. Correct answer.
  4. The first pattern adds 4; the second multiplies by 2.

Explanation

In the first pattern each term is 3 times the one before (2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54). In the second, each term is double the previous plus 1 (3 × 2 + 1 = 7, 7 × 2 + 1 = 15).

Question 26Operations and Algebraic Thinking

What is the value of 4 × (6 + 3)?

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

Explanation

The parentheses must be evaluated first, so 6 + 3 = 9. Then multiply 4 × 9 = 36, following the order of operations.

Question 27Operations and Algebraic Thinking

What is the value of 30 − 12 ÷ 4?

  1. 4
  2. 24
  3. 22
  4. 27 Correct answer.

Explanation

Division is done before subtraction, so 12 ÷ 4 = 3. Then subtract: 30 − 3 = 27.

Question 28Operations and Algebraic Thinking

Which list shows only the first five multiples of 7?

  1. 7, 17, 27, 37, 47
  2. 7, 14, 21, 28, 35 Correct answer.
  3. 1, 7, 14, 21, 28
  4. 0, 7, 14, 21, 28

Explanation

Multiples of 7 come from multiplying 7 by 1, 2, 3, 4, and 5. That gives 7, 14, 21, 28, 35.

Question 29Operations and Algebraic Thinking

A pattern starts at 80 and subtracts 9 each time. What is the fourth number in the pattern?

  1. 53 Correct answer.
  2. 44
  3. 62
  4. 71

Explanation

The terms are 80, 71, 62, and 53. Counting the starting number as the first term, the fourth term is 53.

Question 30Operations and Algebraic Thinking

Which of these is a prime number?

  1. 9
  2. 15
  3. 13 Correct answer.
  4. 21

Explanation

A prime number has exactly two factors, 1 and itself. The number 13 has no factors other than 1 and 13.

Question 31Operations and Algebraic Thinking

What is the value of 8 + 4 × 5?

  1. 28 Correct answer.
  2. 60
  3. 40
  4. 17

Explanation

Multiplication is performed before addition, so 4 × 5 = 20. Then add 8 + 20 = 28.

Question 32Operations and Algebraic Thinking

A rule says: multiply by 3, then subtract 2. Starting with 4, what is the result?

  1. 6
  2. 10 Correct answer.
  3. 18
  4. 14

Explanation

First multiply: 4 × 3 = 12. Then subtract 2 to get 12 − 2 = 10, applying the steps in the stated order.

Question 33Operations and Algebraic Thinking

A number machine takes an input, multiplies it by 4, and then subtracts 5. The output is 27. What was the input?

  1. 7
  2. 8 Correct answer.
  3. 11
  4. 5

Explanation

Work backward from the output. Add 5 to 27 to get 32, then divide by 4 to get 8. Checking: 8 × 4 − 5 = 27.

Question 34Operations and Algebraic Thinking

Which expression is equal to 9 × 26?

  1. 9 × 20 + 9 × 6 Correct answer.
  2. 9 × 26 + 9
  3. 9 × 20 + 6
  4. 9 + 20 × 6

Explanation

The distributive property lets you split 26 into 20 + 6. Then 9 × 26 = 9 × 20 + 9 × 6 = 180 + 54 = 234.

Question 35Operations and Algebraic Thinking

What is the greatest common factor of 18 and 30?

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

Explanation

List the factors of each number. The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 30 include 1, 2, 3, 6, 10, 15, 30. The largest shared factor is 6.

Question 36Operations and Algebraic Thinking

A pattern starts at 4 and multiplies by 3 each time. What is the fifth number in the pattern?

  1. 243
  2. 972
  3. 108
  4. 324 Correct answer.

Explanation

The terms are 4, 12, 36, 108, and 324. Counting the starting number as the first term, the fifth term is 324.

Question 37Operations and Algebraic Thinking

Which number is a multiple of 6 and also a factor of 48?

  1. 18
  2. 9
  3. 12 Correct answer.
  4. 30

Explanation

12 is a multiple of 6 because 6 × 2 = 12, and 12 is a factor of 48 because 12 × 4 = 48. It satisfies both conditions.

Question 38Operations and Algebraic Thinking

What is the value of 36 ÷ (9 − 3) + 4?

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

Explanation

Evaluate the parentheses first: 9 − 3 = 6. Then divide 36 ÷ 6 = 6 and add 4 to get 10.

Question 39Operations and Algebraic Thinking

A rule says: if a number is even, add 5; if it is odd, multiply by 2. Starting with 7, what is the result?

  1. 12
  2. 14 Correct answer.
  3. 19
  4. 24

Explanation

The starting number 7 is odd, so the rule says to multiply by 2. That gives 7 × 2 = 14.

Question 40Operations and Algebraic Thinking

Which expression has the same value as 6 × 15 − 6 × 5?

  1. 6 + (15 − 5)
  2. 6 × 15 − 5
  3. 6 × (15 + 5)
  4. 6 × (15 − 5) Correct answer.

Explanation

Both terms share the factor 6, so factor it out: 6 × 15 − 6 × 5 = 6 × (15 − 5) = 6 × 10 = 60.

Question 41Operations and Algebraic Thinking

A number is multiplied by 8, then 15 is added, and the result is 71. What is the number?

  1. 7 Correct answer.
  2. 6
  3. 9
  4. 10

Explanation

Work backward: subtract 15 from 71 to get 56, then divide by 8 to get 7. Checking: 7 × 8 + 15 = 71.

Question 42Operations and Algebraic Thinking

The sum of two whole numbers is 17 and their product is 72. What is the positive difference between the numbers?

  1. 5
  2. 7
  3. 9
  4. 1 Correct answer.

Explanation

Find two numbers that add to 17 and multiply to 72. The pair 8 and 9 works because 8 + 9 = 17 and 8 × 9 = 72, so the difference is 1.

Question 43Operations and Algebraic Thinking

A pattern begins 1, 4, 9, 16. Which rule describes how each term is built?

  1. Multiply the previous term by 4
  2. Add 4 each time
  3. Multiply the position number by itself Correct answer.
  4. Add 3, then add 5, then add 7 again

Explanation

These are square numbers: 1 × 1, 2 × 2, 3 × 3, and 4 × 4. So each term equals the position number multiplied by itself.

Question 44Operations and Algebraic Thinking

A rule says: multiply by 2, then add 1. Starting with 1, what is the fifth term of the pattern?

  1. 31 Correct answer.
  2. 23
  3. 63
  4. 15

Explanation

Apply the rule step by step: 1 → 3 → 7 → 15 → 31. Counting the starting number as the first term, the fifth term is 31.

Question 45Number and Operations in Base Ten

What is the value of the digit 7 in the number 4,782?

  1. 70
  2. 7
  3. 7,000
  4. 700 Correct answer.

Explanation

In a four-digit number each place is ten times the place to its right. The 7 sits in the hundreds place, so its value is 7 hundreds, which equals 700.

Question 46Number and Operations in Base Ten

Which number is written in expanded form as 3,000 + 400 + 60 + 5?

  1. 3,465 Correct answer.
  2. 3,564
  3. 3,645
  4. 3,456

Explanation

Expanded form lists the value of each digit from the largest place to the smallest. Reading the parts in order gives thousands 3, hundreds 4, tens 6, and ones 5, so the number is 3,465.

Question 47Number and Operations in Base Ten

What is 5,000 + 2,000?

  1. 7,500
  2. 6,000
  3. 7,000 Correct answer.
  4. 8,000

Explanation

When adding numbers with the same place value, add the digits in that place and keep the place. Five thousands plus two thousands equals seven thousands, which is 7,000.

Question 48Number and Operations in Base Ten

Which number is the largest?

  1. 4,098
  2. 4,980
  3. 4,908 Correct answer.
  4. 4,890

Explanation

Compare digits from the leftmost place. All four numbers have 4 thousands, so compare the hundreds: 9 is greater than 8 and greater than 0, which makes 4,908 the largest.

Question 49Number and Operations in Base Ten

What is 800 rounded to the nearest hundred?

  1. 1,000
  2. 900
  3. 800 Correct answer.
  4. 700

Explanation

A number that already ends in two zeros is exactly on a hundred, so it stays the same when rounded to the nearest hundred. The nearest hundred to 800 is 800 itself.

Question 50Number and Operations in Base Ten

What is 6 × 1,000?

  1. 60,000
  2. 600
  3. 6,000 Correct answer.
  4. 6,100

Explanation

Multiplying a whole number by 1,000 shifts every digit three places to the left. Six ones become six thousands, so the product is 6,000.