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

4th Grade math test solutions: Multiplying Multi-Digit Numbers – Maths PDF

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This multiply test answers for 4th Grade covers multiplying multi-digit numbers (Common Core 4.NBT.B.5), with a free PDF to print.

Use this answer key to score the test. Each solution lists the partial products, and the scoring note tells how the points are awarded. Total: 20 points.

Grade 4 · Common Core State Standards: 4.NBT.B.5

Multiply test answers: worked solutions

Question 1 – Mental math [2 pts]

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

Scoring: 1 point for each answer.

Question 2 – Area model [2 pts]

1,500 + 60 + 300 + 12 = 1,872.

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

\(1,872\)

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

Question 3 – Four digits by one [2 pts]

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

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

\(19,310\)

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

Question 4 – Two digits by two [2 pts]

Partial products for 67 × 48.

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

\(3,216\)

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

Question 5 – Properties [2 pts]

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.

Question 6 – Estimate and solve [2 pts]

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.

Question 7 – Muffin boxes [3 pts]

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

Scoring: 1 point for each part.

Question 8 – Find the mistake [3 pts]

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

Scoring: 1 point for each part.

Question 9 – Stadium sections [2 pts]

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.

Total score

Total

20 points

Key facts behind this multiply test answers

Key facts

Partial products are the answers to each smaller multiplication; add them for the final product.
Distributive property: 6 × 47 = 6 × 40 + 6 × 7.
A 2-digit by 2-digit problem has four partial products in an area model.
For multiples of 10, multiply the basic facts and attach all the zeros: 30 × 40 = 1,200.
Estimate first by rounding to check that the product makes sense.

How to use this multiply test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 4 chapters: Grade 4 math.

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