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.
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.
\(\$121,000,000\).
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:
\(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{7}\).
Problem: \(4,008 - 1,995\)
Explanation: Subtract column by column with regrouping or find the difference: \(4,008 - 1,995 = 2,013\).
Problem: Milliliters in one liter
Explanation: By definition, \(1 \text{ l} = 1000 \text{ ml}\).
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.
Problem: \(29,898 + 1,000\)
Explanation: Increase the thousands digit by 1, resulting in \(30,898\).
Problem: Convert \(\dfrac{5}{10}\) to a decimal.
Explanation: Dividing 5 by 10 gives \(0.5\).
Problem: Total pencils in 61 boxes with 14 pencils each.
Explanation: Multiply boxes by pencils per box: \(61 \times 14 = 854\) pencils.
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.
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.
Problem: Boxes needed for 64 sweets with 8 sweets per box.
Explanation: Divide total sweets by sweets per box: \(64 \div 8 = 8\) boxes.
Problem: Remainder of \(145 \div 6\)
Explanation: \(6 \times 24 = 144\). The remainder is \(145 - 144 = 1\) sweet remaining.
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.
Problem: Solve for \(n\) in \(9 \times n = 108\)
Explanation: Divide both sides by 9: \(n = 108 \div 9 = 12\).
Problem: \((14 + 5) - (5 - 2)\)
Explanation: Evaluate parentheses: \((14 + 5) = 19\) and \((5 - 2) = 3\). Then subtract: \(19 - 3 = 16\).
Problem: \(2 \times (14 + 5) - 7\)
Explanation: Evaluate parentheses: \(14 + 5 = 19\). Multiply by 2: \(2 \times 19 = 38\). Subtract 7: \(38 - 7 = 31\).
Problem: Evaluate \(23 - (10 - a)\) when \(a = 5\)
Explanation: Substitute 5 for \(a\): \(23 - (10 - 5) = 23 - 5 = 18\).
Problem: If \(z + y = 20\) and \(y = 5\), find \(z\).
Explanation: Substitute 5 for \(y\): \(z + 5 = 20\), so \(z = 20 - 5 = 15\).
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 \(S = 24 \div 3 = 8\).