4th Grade Multiplying Multi-Digit Numbers Worksheet Answer Key (PDF)
This 4th grade multi digit multiplication worksheet answers covers multiplying multi-digit numbers (Common Core 4.NBT.B.5), with a free PDF to print.
Key takeaway: This answer key helps fourth grade students and parents check multi-digit multiplication and see each partial product.
- Topic: Multiplying Multi-Digit Numbers (4th grade)
- Content: Step-by-step answers to 20 worksheet problems
- Standards: 4.NBT.B.5
- Answers: Every step shown, with the method to review
- Format: Free printable PDF, US Letter, black and white
This answer key helps fourth grade students and parents check multi-digit multiplication and see each partial product. Each solution lists the partial products in order, adds them, and gives the final answer, so an error can be traced to a single step.
The key covers all 20 problems, including the area models in problems 5, 8, 11, and 12 and the mistake explanation in problem 20. Also, word problem answers include units. Then, if your answer differs, check whether you included every partial product and placed zeros correctly. Also, plan about 15 minutes to compare and fix your work.
Grade 4 · Common Core State Standards: 4.NBT.B.5
4th grade multi digit multiplication worksheet answers: worksheet problems 1 to 10
1 – Multiples of 10
3 tens times 4 is 12 tens, which is 120.
120
2 – Tens times tens
Basic fact: \(7 \times 5 = 35\). Two zeros are attached.
\(3,500\)
3 – Hundreds
Basic fact: \(6 \times 4 = 24\). Two zeros are attached.
\(2,400\)
4 – Thousands
Basic fact: \(8 \times 5 = 40\). Three zeros are attached to 40, giving 40,000.
\(40,000\)
5 – Area model: 47 × 6
\(40 \times 6 = 240\) and \(7 \times 6 = 42\).
\(240 + 42 = 282\)
282
6 – Partial products: 58 × 7
\(50 \times 7 = 350\) and \(8 \times 7 = 56\).
\(350 + 56 = 406\)
406
7 – Three-digit number
\(300 \times 4 = 1{,}200\), \(20 \times 4 = 80\), \(6 \times 4 = 24\).
\(1{,}200 + 80 + 24 = 1{,}304\)
\(1,304\)
8 – Four-digit number
\(3{,}000 + 600 + 120 + 27 = 3{,}747\)
\(3,747\)
9 – Zero in the number
\(4{,}000 \times 6 = 24{,}000\), \(800 \times 6 = 4{,}800\), \(0 \times 6 = 0\), \(5 \times 6 = 30\).
\(24{,}000 + 4{,}800 + 0 + 30 = 28{,}830\)
\(28,830\)
10 – Two-digit by two-digit
\(23 \times 10 = 230\) and \(23 \times 4 = 92\).
\(230 + 92 = 322\)
322
Worksheet problems 11 and up
11 – Area model: 36 × 24
\(600 + 120 + 120 + 24 = 864\)
864
12 – Area model: 45 × 62
\(60 \times 40 = 2{,}400\), \(2 \times 40 = 80\), \(60 \times 5 = 300\), \(2 \times 5 = 10\).
\(2{,}400 + 80 + 300 + 10 = 2{,}790\)
\(2,790\)
13 – Bigger partial products
\(78 \times 50 = 3{,}900\) and \(78 \times 3 = 234\).
\(3{,}900 + 234 = 4{,}134\)
\(4,134\)
14 – Use a property
Group the factors that make a friendly number: \((4 \times 25) \times 17\).
\(4 \times 25 = 100\), and \(100 \times 17 = 1{,}700\).
\(1,700\)
15 – Peach baskets
\(28 \times 45\): \(20 \times 45 = 900\) and \(8 \times 45 = 360\).
\(900 + 360 = 1{,}260\)
\(1,260\) peaches
16 – Stadium seats
\(8 imes 1{,}000 = 8{,}000\), \(8 imes 200 = 1{,}600\), \(8 imes 70 = 560\), \(8 imes 5 = 40\).
\(8{,}000 + 1{,}600 + 560 + 40 = 10{,}200\)
\(10,200\) seats
17 – Road trip miles
\(300 \times 6 = 1{,}800\), \(40 \times 6 = 240\), \(7 \times 6 = 42\).
\(1{,}800 + 240 + 42 = 2{,}082\)
\(2,082\) miles
18 – Baseball card packs
\(47 \times 12\): \(47 \times 10 = 470\) and \(47 \times 2 = 94\).
\(470 + 94 = 564\)
564 cards
Worksheet problem 19 and after
19 – Theater seats
Total seats: \(24 \times 38\): \(20 \times 38 = 760\) and \(4 \times 38 = 152\), so \(760 + 152 = 912\).
Left: \(912 – 150 = 762\).
762 seats
20 – Find the mistake
Liam forgot to attach the two zeros from 30 and 50. \(3 \times 5 = 15\) is 15 hundreds, not 15.
Correct: \(30 \times 50 = 1{,}500\).
\(1,500\)
Key facts behind this 4th grade multi digit multiplication worksheet answers
- 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.
- Then, 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.
Common mistakes with this 4th grade multi digit multiplication worksheet answers
- Students check only the final product. If it is wrong, compare each partial product with the key to find the first difference.
- Students skip the area model boxes in the key. Also, each box is one partial product, and counting boxes shows whether any are missing.
- Students copy the key for problem 14 without seeing the property. Instead, notice that 4 times 25 is 100, which makes the rest easy.
- Students forget units in word problems. Also, answers include peaches, seats, miles, cards, or seats left. Slow down at that step and check it twice.
How to use these solutions
- Add the partial products in a different order to check. Also, if the sum is the same, the work is probably right.
- Redo each missed problem with an area model if you used the standard algorithm, or the other way around. Then, matching answers show understanding.
- Parents can ask the child to explain why the answer to 30 times 50 has two more zeros than 3 times 5.
Download the 4th grade multi digit multiplication worksheet answers as a PDF with the button below and keep it with your notes.
4th grade multi digit multiplication worksheet answers: frequently asked questions
What are the partial products for 62 times 45?
They are 60 times 40, which is 2,400, 60 times 5, which is 300, 2 times 40, which is 80, and 2 times 5, which is 10. Also, adding 2,400, 300, 80, and 10 gives 2,790. Checking with an estimate of 60 times 45 gives 2,700.
How does the property in problem 14 make the work easier?
Multiplication can be done in any order, so you can multiply 4 times 25 first to get 100. Then 100 times 17 is 1,700. Choosing a pair that makes a friendly number is faster than going left to right.
How many seats are left in problem 19?
The theater has 24 times 38, which is 912 seats. After reserving 150 for the school group, 912 minus 150 leaves 762 seats. This problem has two steps, a multiplication and then a subtraction.
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