5th Grade Multiplying and Dividing Decimals Test Solutions and Scoring (PDF)

(a) \(6 \times 9 = 54\); 2 decimal places: \(0.54\).

(b) \(42 \times 35 = 1{,}470\); 2 decimal places: \(14.70\), so \(14.7\).

Scoring: 1 point for each correct product.

(a) \(0.7 \times 0.5\).

(b) \(7 \times 5 = 35\) squares, so \(0.35\).

Scoring: 1 point for the sentence with 0.7 and 0.5 (either order); 1 point for 0.35.

(a) \(84 \div 7 = 12\), so \(1.2\).

(b) \(576 \div 8 = 72\), so \(0.72\).

Scoring: 1 point for each correct quotient.

(a) \(90 \div 3 = 30\) (multiply both by 10): \(30\).

(b) \(360 \div 8 = 45\) (multiply both by 100): \(45\).

Scoring: 1 point for each correct quotient.

(a) \(6 \times 0.5 = 3\), so the product should be close to 3. Since 0.5 is less than 1, the product is less than 6.2, so 31 is too large.

(b) \(62 \times 5 = 310\); 2 decimal places gives \(3.10\): \(3.1\).

Scoring: 1 point for a valid estimate near 3 with the explanation; 1 point for 3.1.

\(25 \times 32 = 800\); 2 decimal places gives \(8.00\).

The grapes cost $8.00.

Scoring: 1 point for multiplying 2.5 by 3.20 correctly; 1 point for $8.00 with the dollar sign.

(a) \(12.6 \div 0.9 = 126 \div 9 = 14\): 14 pieces.

(b) \(14 \times 1.75 = 24.50\): $24.50.

Scoring: (a) 1 point for setting up the division 12.6 / 0.9, 1 point for 14. (b) 1 point for $24.50.

(a) Notebooks: \(3 \times 2.85 = 8.55\). Pens: \(2 \times 1.35 = 2.70\). Total: \(8.55 + 2.70 = 11.25\): $11.25.

(b) \(20 – 11.25 = 8.75\): $8.75.

Scoring: (a) 1 point for finding both costs, 1 point for the total. (b) 1 point for the change.

(a) \(46 \times 35 = 1{,}610\); 2 decimal places gives \(16.10\): 16.1 square feet.

(b) \(7.14 \div 2.1 = 71.4 \div 21 = 3.4\): 3.4 feet.

Scoring: 1 point for each correct answer with units.