Grade 5 Math Practice Test: Order of Operations, Patterns and Unit Conversions

Multiply before subtracting: 3 × 4 = 12, then 18 − 12 = 6. The answer 60 comes from subtracting first, (18 − 3) × 4.

Parentheses first: 8 + 2 = 10. Then 5 × 10 = 50, and 50 − 6 = 44. Ignoring the parentheses gives 5 × 8 + 2 − 6 = 36.

Parentheses: 4 + 2 = 6. Then divide and multiply from left to right: 24 ÷ 6 = 4 and 4 × 2 = 8. Last, 3 + 8 = 11. The answer 5 comes from multiplying 6 × 2 before dividing, which breaks the left-to-right rule.

Work from the inside out: 6 − 4 = 2, then 10 − 2 = 8 inside the brackets, and 2 × 8 = 16. The answer 18 comes from multiplying 2 × 10 before using the brackets.

The sum must be found first, so 9 + 4 goes in parentheses, and then it is multiplied by 6. Without parentheses, 9 + 4 × 6 would multiply 4 × 6 first.

The expression multiplies the whole sum 125 + 38 by 4, so its value is 4 times as large. Adding 4 would be written (125 + 38) + 4.

Compare matching terms: 3 and 6, 6 and 12, 9 and 18. Each number in B is double the one in A, because B adds 6 each time and A adds 3, and 6 is 2 × 3. The difference is not always 3 (for example, 18 − 9 = 9).

The fourth numbers in the patterns are 9 (Pattern A) and 18 (Pattern B), so (9, 18) is one of the pairs. In every pair, the second number is twice the first, and none of the other pairs follows that rule.

1 meter = 100 centimeters, so 4.5 × 100 = 450 centimeters. The answer 4,500 would come from using 1,000, which is the number of millimeters in a meter.

1 yard = 36 inches, so 6 yards = 6 × 36 = 216 inches, and 216 ÷ 9 = 24 pieces. The answer 8 comes from using 12 inches per yard, which is the number of inches in a foot.

1 gallon = 4 quarts = 8 pints = 16 cups, so 5 gallons = 5 × 16 = 80 cups. The answers 20 and 40 are the numbers of quarts and pints, not cups.

The total is 3 × 12 = 36 ounces. Since 1 pound = 16 ounces, 36 ounces = 2 pounds and 4 ounces, which is 214 pounds. The answer 3 pounds wrongly uses 12 ounces per pound.

She runs 4 × 400 = 1,600 meters a day and 1,600 × 5 = 8,000 meters in 5 days. Since 1 kilometer = 1,000 meters, 8,000 meters = 8 kilometers.

Her total cost is 3 × 4 + 2 = $14, and the whole cost must be subtracted from 20, so it goes in parentheses: 20 − 14 = $6. Without parentheses, 20 − 3 × 4 + 2 adds the $2 instead of subtracting it and gives $10.

1 liter = 1,000 milliliters, so 2.5 liters = 2,500 milliliters, and 2,500 ÷ 250 = 10 glasses. The answer 1 comes from forgetting to convert liters to milliliters.