Grade 4 Math Questions With Answers

A set of grade 4 math questions on operations on numbers, converting units, algebraic expressions, evaluation of algebraic expressions, and word problems are presented along with step-by-step solutions and explanations.

Questions and Solutions

  1. Place Value: The cost of buying a tall building is one hundred twenty one million dollars. Write this number in standard form using digits.
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    Problem: Write one hundred twenty-one million in standard form.

    Explanation: One hundred twenty-one million is written as 121 followed by six zeros for the thousands and units periods.

    \(\$121,000,000\).

  2. Fractions: Order from greatest to least the fractions: 1/3 , 1/6 , 1/2 , 1/7.
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    Problem: Order from greatest to least: \(\dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{2}, \dfrac{1}{7}\)

    Explanation: For unit fractions (numerator of 1), the fraction with the smallest denominator is the largest value. Sorting from greatest to least:

    \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{7}\).

  3. Subtraction: When you subtract 1,995 from 4,008, the answer is equal to:
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    Problem: \(4,008 - 1,995\)

    Explanation: Subtract column by column with regrouping or find the difference: \(4,008 - 1,995 = 2,013\).

  4. Measurement: How many milliliters in one liter?
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    Problem: Milliliters in one liter

    Explanation: By definition, \(1 \text{ l} = 1000 \text{ ml}\).

  5. Rounding: Round 312.92 to the nearest whole number.
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    Problem: Round \(312.92\) to the nearest whole number.

    Explanation: Look at the tenths digit, which is 9. Since 9 is greater than or equal to 5, round up the whole number from 312 to 313.

  6. Mental Math: If you add 1,000 to 29,898, you obtain:
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    Problem: \(29,898 + 1,000\)

    Explanation: Increase the thousands digit by 1, resulting in \(30,898\).

  7. Decimals: Convert 5/10 to decimal.
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    Problem: Convert \(\dfrac{5}{10}\) to a decimal.

    Explanation: Dividing 5 by 10 gives \(0.5\).

  8. Word Problem: There are 61 boxes of pencils in a store. There are 14 pencils in each box. How many pencils are in the store?
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    Problem: Total pencils in 61 boxes with 14 pencils each.

    Explanation: Multiply boxes by pencils per box: \(61 \times 14 = 854\) pencils.

  9. Word Problem: There are 24 hours in one day, and 3,600 seconds in one hour. How many seconds are in one day?
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    Problem: Seconds in one day given 24 hours/day and 3,600 seconds/hour.

    Explanation: Multiply hours per day by seconds per hour: \(24 \times 3600 = 86,400\) seconds.

  10. Word Problem: Julia read a book in 20 days. She read 16 pages every day for the first 15 days, and 18 pages everyday for the last 5 days. How many pages did Julia read?
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    Problem: Total pages read over 20 days.

    Explanation: Calculate pages read in first 15 days (\(16 \times 15 = 240\)) plus pages read in last 5 days (\(18 \times 5 = 90\)). Total = \(240 + 90 = 330\) pages.

  11. Division Word Problem: 64 sweets are put in boxes that contain 8 sweets each. How many boxes are needed?
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    Problem: Boxes needed for 64 sweets with 8 sweets per box.

    Explanation: Divide total sweets by sweets per box: \(64 \div 8 = 8\) boxes.

  12. Division Remainder: If 6 children share 145 sweets equally, how many sweets will remain?
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    Problem: Remainder of \(145 \div 6\)

    Explanation: \(6 \times 24 = 144\). The remainder is \(145 - 144 = 1\) sweet remaining.

  13. Multiplication Property: Which of these is the same as \(8 \times 9\)?
    1. \(4 \times 4 \times 9\)
    2. \(2 \times 4 \times 9\)
    3. \(3 \times 4 \times 9\)
    4. \(2 \times 2 \times 9\)
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    Problem: Equivalent expression for \(8 \times 9\)

    Explanation: Since \(8 = 2 \times 4\), the expression \(8 \times 9\) can be rewritten as \((2 \times 4) \times 9\).

    Therefore, the correct option is B.

  14. Algebraic Equation: What is \(n\) if \(9 \times n = 108\)?
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    Problem: Solve for \(n\) in \(9 \times n = 108\)

    Explanation: Divide both sides by 9: \(n = 108 \div 9 = 12\).

  15. Order of Operations: What is the value of (14 + 5) - (5 - 2)?
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    Problem: \((14 + 5) - (5 - 2)\)

    Explanation: Evaluate parentheses: \((14 + 5) = 19\) and \((5 - 2) = 3\). Then subtract: \(19 - 3 = 16\).

  16. Order of Operations: Evaluate the expression: 2 × (14 + 5) - 7 =
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    Problem: \(2 \times (14 + 5) - 7\)

    Explanation: Evaluate parentheses: \(14 + 5 = 19\). Multiply by 2: \(2 \times 19 = 38\). Subtract 7: \(38 - 7 = 31\).

  17. Algebra Evaluation: What is the value of 23 - (10 - a) if \(a = 5\)?
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    Problem: Evaluate \(23 - (10 - a)\) when \(a = 5\)

    Explanation: Substitute 5 for \(a\): \(23 - (10 - 5) = 23 - 5 = 18\).

  18. Algebraic Substitution: If z + y = 20 and \(y = 5\), what is \(z\)?
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    Problem: If \(z + y = 20\) and \(y = 5\), find \(z\).

    Explanation: Substitute 5 for \(y\): \(z + 5 = 20\), so \(z = 20 - 5 = 15\).

  19. Algebraic Equation: What is S if 6 × 4 = 3 × S?
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    Problem: Solve for \(S\) in \(6 \times 4 = 3 \times S\)

    Explanation: Calculate the left side: \(6 \times 4 = 24\). Then \(3 \times S = 24\), so \(S = 24 \div 3 = 8\).

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