4th Grade Multiplying Multi-Digit Numbers Test Solutions and Scoring (PDF)

1. \(6 \times 3 = 18\), then attach two zeros. \(1,800\)
2. \(8 \times 7 = 56\), then attach three zeros. \(56,000\)

Scoring: 1 point for each answer.

\(1{,}500 + 60 + 300 + 12 = 1{,}872\)

\(1,872\)

Scoring: 1 point for the four correct partial products. 1 point for 1,872.

\(3{,}000 \times 5 = 15{,}000\), \(800 \times 5 = 4{,}000\), \(60 \times 5 = 300\), \(2 \times 5 = 10\).

\(15{,}000 + 4{,}000 + 300 + 10 = 19{,}310\)

\(19,310\)

Scoring: 1 point for correct partial products. 1 point for 19,310.

\(2{,}400 + 280 + 480 + 56 = 3{,}216\)

\(3,216\)

Scoring: 1 point for correct partial products. 1 point for 3,216.

Associative and commutative properties: \(5 \times 18 \times 20 = (5 \times 20) \times 18\).

\(5 \times 20 = 100\), and \(100 \times 18 = 1{,}800\).

\(1,800\)

Scoring: 1 point for a valid regrouping. 1 point for 1,800.

Estimate: \(50 \times 30 = 1{,}500\).

Exact: \(48 \times 30 = 1{,}440\) and \(48 \times 1 = 48\), so \(1{,}440 + 48 = 1{,}488\).

about \(1,500\); exactly \(1,488\)

Scoring: 1 point for the estimate. 1 point for the exact product.

1. \(24 \times 38 = 24 \times 30 + 24 \times 8 = 720 + 192 = 912\). 912 muffins
2. \(24 \times 45 = 24 \times 40 + 24 \times 5 = 960 + 120 = 1{,}080\). \(1,080\) muffins
3. \(912 + 1{,}080 = 1{,}992\). \(1,992\) muffins

Scoring: 1 point for each part.

1. The 2 in 23 is 2 tens, so the partial product is \(46 \times 20 = 920\), not \(46 \times 2 = 92\).
2. \(920 + 138 = 1{,}058\). \(1,058\)
3. \(50 \times 20 = 1{,}000\). The product should be close to 1,000, so 230 is too small.

Scoring: 1 point for each part.

All seats: \(9 \times 1{,}250 = 11{,}250\) (\(9 \times 1{,}000 = 9{,}000\), \(9 \times 250 = 2{,}250\)).

Open: \(11{,}250 – 2{,}400 = 8{,}850\).

\(8,850\) seats

Scoring: 1 point for 11,250. 1 point for 8,850.