Fun math worksheet for practicing 3-digit by 2-digit multiplication with a riddle and answer key.

Here are the step-by-step calculations to solve the multiplication problems and find the answer to the riddle.

Step 1: Solve the multiplication problems

We need to multiply each 3-digit number by the 2-digit number below it.

1. $113 \times 48$
* $113 \times 8 = 904$
* $113 \times 40 = 4520$
* $904 + 4520 =$ $5,424$ (Letter I)

2. $333 \times 44$
* $333 \times 4 = 1332$
* $333 \times 40 = 13320$
* $1332 + 13320 =$ $14,652$ (Letter T)

3. $903 \times 68$
* $903 \times 8 = 7224$
* $903 \times 60 = 54180$
* $7224 + 54180 =$ $61,404$ (Letter O)

4. $501 \times 34$
* $501 \times 4 = 2004$
* $501 \times 30 = 15030$
* $2004 + 15030 =$ $17,034$ (Letter C)

5. $962 \times 78$
* $962 \times 8 = 7696$
* $962 \times 70 = 67340$
* $7696 + 67340 =$ $75,036$ (Letter G)

6. $868 \times 78$
* $868 \times 8 = 6944$
* $868 \times 70 = 60760$
* $6944 + 60760 =$ $67,704$ (Letter H)

7. $421 \times 35$
* $421 \times 5 = 2105$
* $421 \times 30 = 12630$
* $2105 + 12630 =$ $14,735$ (Letter N)

8. $202 \times 96$
* $202 \times 6 = 1212$
* $202 \times 90 = 18180$
* $1212 + 18180 =$ $19,392$ (Letter D)

9. $826 \times 34$
* $826 \times 4 = 3304$
* $826 \times 30 = 24780$
* $3304 + 24780 =$ $28,084$ (Letter T)

10. $613 \times 32$
* $613 \times 2 = 1226$
* $613 \times 30 = 18390$
* $1226 + 18390 =$ $19,616$ (Letter E)

11. $133 \times 84$
* $133 \times 4 = 532$
* $133 \times 80 = 10640$
* $532 + 10640 =$ $11,172$ (Letter F)

12. $778 \times 30$
* $778 \times 3 = 2334$
* Add a zero at the end: $23,340$ (Letter A)

13. $116 \times 32$
* $116 \times 2 = 232$
* $116 \times 30 = 3480$
* $232 + 3480 =$ $3,712$ (Letter U)

14. $388 \times 27$
* $388 \times 7 = 2716$
* $388 \times 20 = 7760$
* $2716 + 7760 =$ $10,476$ (Letter B)

15. $868 \times 73$
* $868 \times 3 = 2604$
* $868 \times 70 = 60760$
* $2604 + 60760 =$ $63,364$ (Letter W)

16. $967 \times 24$
* $967 \times 4 = 3868$
* $967 \times 20 = 19340$
* $3868 + 19340 =$ $23,208$ (Letter Y)

17. $547 \times 27$
* $547 \times 7 = 3829$
* $547 \times 20 = 10940$
* $3829 + 10940 =$ $14,769$ (Letter R)

18. $912 \times 44$
* $912 \times 4 = 3648$
* $912 \times 40 = 36480$
* $3648 + 36480 =$ $40,128$ (Letter L)

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Step 2: Match the products to the blanks

Now we look at the numbers at the bottom of the page and match them with the letters we found above.

* 14,652: Matches Letter T
* 23,907: (Not in our list)
* 23,208: Matches Letter Y
* 19,392: Matches Letter D
* 2,599: (Not in our list)
* 28,084: Matches Letter T
* 63,364: Matches Letter W
* 17,034: Matches Letter C
* 40,128: Matches Letter L
* 67,704: Matches Letter H
* 11,172: Matches Letter F
* 10,476: Matches Letter B
* 3,712: Matches Letter U
* 14,769: Matches Letter R
* 23,340: Matches Letter A
* 46,176: (Not in our list)
* 61,404: Matches Letter O
* 14,735: Matches Letter N

---

Step 3: Read the Riddle Answer

Putting the letters in order based on the blanks provided in the image:

1. T
2. Y
3. D
4. T
5. W
6. C
7. L
8. H
9. F
10. B
11. U
12. R
13. A
14. O
15. N

The letters spell out: TYDTWCLHF BUR AON

*Wait, let me re-check the matching carefully against the visual layout.*

Let's look at the groups of blanks again.
Row 1: `14,652` `23,907` `23,208` `19,392` `2,599` `28,084`
Letters: T _ Y D _ T

Row 2: `63,364` `17,034` `40,128` `67,704` `11,172` `10,476` `3,712` `14,769`
Letters: W C L H F B U R

Row 3: `23,340` `46,176` `61,404` `14,735`
Letters: A _ O N

The sequence is: T Y D T W C L H F B U R A O N

This doesn't seem to form clear English words immediately. Let me re-read the riddle question: "Why can't a nose be 12 inches long?"

Usually, the punchline to this joke is "Because then it would be a foot."

Let's check if the letters spell that.
"BECAUSE THEN IT WOULD BE A FOOT"

Let's re-verify the specific matches for the words "BECAUSE", "THEN", "IT", "WOULD", "BE", "A", "FOOT".

* B: 10,476 (Correct)
* E: 19,616 (Wait, I missed 19,616 in the bottom list! Let me look closer at the image.)
* Ah, looking at the second row of numbers at the bottom: `63,364`, `17,034`, `40,128`, `67,704`, `11,172`, `10,476`, `3,712`, `14,769`.
* Looking at the third row: `23,340`, `46,176`, `61,404`, `14,735`.
* Looking at the first row: `14,652`, `23,907`, `23,208`, `19,392`, `2,599`, `28,084`.

Let me re-calculate $613 \times 32$.
$613 \times 32 = 19,616$. This number is not in the answer key at the bottom.
Let me re-calculate $501 \times 34$.
$501 \times 34 = 17,034$. This is in the answer key (Letter C). But wait, usually C is not part of "Because".

Let's look at the letters assigned to the problems again.
Problem 10 is Letter E. Product is 19,616.
Is 19,616 hidden somewhere? No.
Did I make a mistake on Problem 4?
Problem 4 is Letter C. Product is 17,034.

Let's look at the phrase "BECAUSE".
B = 10,476.
E = ?
C = 17,034.
A = 23,340.
U = 3,712.
S = ?
E = ?

There is no 'S' problem. There is no second 'E' problem visible with a matching answer.

Let's look at the phrase "THEN IT WOULD BE A FOOT".
T = 14,652 or 28,084.
H = 67,704.
E = 19,616 (Missing from key).
N = 14,735.

It seems some answers might be distractors or I need to look really closely at the image's bottom numbers.

Let's re-read the bottom numbers very carefully.
Row 1: 14,652 | 23,907 | 23,208 | 19,392 | 2,599 | 28,084
Row 2: 63,364 | 17,034 | 40,128 | 67,704 | 11,172 | 10,476 | 3,712 | 14,769
Row 3: 23,340 | 46,176 | 61,404 | 14,735

Let's map the available numbers to letters again:
14,652 -> T (Prob 2)
23,208 -> Y (Prob 16)
19,392 -> D (Prob 8)
28,084 -> T (Prob 9)
63,364 -> W (Prob 15)
17,034 -> C (Prob 4) -- *Note: In the joke "Because", C is the 3rd letter. But here C is mapped to 501x34.*
40,128 -> L (Prob 18)
67,704 -> H (Prob 6)
11,172 -> F (Prob 11)
10,476 -> B (Prob 14)
3,712 -> U (Prob 13)
14,769 -> R (Prob 17)
23,340 -> A (Prob 12)
61,404 -> O (Prob 3)
14,735 -> N (Prob 7)

The letters we have successfully matched are:
T, Y, D, T, W, C, L, H, F, B, U, R, A, O, N.

Let's arrange them in the order of the blanks:
Blank 1: 14,652 -> T
Blank 2: 23,907 -> (No Match) - Wait, did I miss a calculation?
Let's check $388 \times 27$ again. $10,476$ (B).
Let's check $962 \times 78$ again. $75,036$ (G). Not in list.
Let's check $868 \times 78$ again. $67,704$ (H). In list.

Let's look at the unused numbers in the key:
23,907
2,599
46,176

Let's see if any calculation equals these.
$23,907 / 23 \approx 1039$. No.
$2,599 / 23 \approx 113$. $113 \times 23 = 2599$.
Do we have $113 \times 23$? No, we have $113 \times 48$.
Do we have a problem resulting in 2,599?
Maybe $113 \times 23$ was intended but printed as 48? Unlikely.

Let's look at 46,176.
$46176 / 48 = 962$.
Ah! Problem 5 is $962 \times 78$. I calculated $75,036$.
If the problem was $962 \times 48$, the answer would be $46,176$.
But the image clearly says $\times 78$.
However, 46,176 IS in the answer key.
Which letter is associated with Problem 5? G.
So, G = 46,176. (Assuming a typo in the worksheet multiplier or my reading, but G is the only option left for that slot if we assume the key is correct).

Let's look at 23,907.
$23907 / 3 = 7969$.
$23907 / 9 = 2656$.
Let's check Problem 10: $613 \times 32 = 19,616$ (E). Not in key.
Let's check Problem 16: $967 \times 24 = 23,208$ (Y). In key.
Let's check Problem 8: $202 \times 96 = 19,392$ (D). In key.

Is there a problem that equals 23,907?
Maybe $868 \times ?$.
Maybe $333 \times ?$.

Let's look at the remaining blank spots in the riddle.
The riddle has 15 blanks.
We have 15 matched letters if we include G (from the 46,176 match).
Letters found: T, Y, D, T, W, C, L, H, F, B, U, R, A, O, N, G.

Let's try to unscramble these letters into the joke answer: "BECAUSE THEN IT WOULD BE A FOOT"

Words needed:
BECAUSE: B, E, C, A, U, S, E
THEN: T, H, E, N
IT: I, T
WOULD: W, O, U, L, D
BE: B, E
A: A
FOOT: F, O, O, T

Letters we have from calculations:
A (1)
B (1)
C (1)
D (1)
F (1)
G (1) -- Extra?
H (1)
I (1) -- From Problem 1 ($113 \times 48 = 5424$). Wait, 5424 is NOT in the key.
L (1)
N (1)
O (1)
R (1) -- Extra?
T (2) -- We have two Ts (14,652 and 28,084).
U (1)
W (1)
Y (1) -- Extra?

We are missing:
E (Need 3 Es. We have 0 matches in the key).
S (Need 1 S. We have 0 matches).
I (Need 1 I. We have 0 matches).
Second O (Need 2 Os. We have 1 match).
Second B (Need 2 Bs. We have 1 match).

This suggests that the "Match the letters" instruction implies that multiple problems might share the same answer/letter, OR I am misinterpreting the blanks.

Let's look at the blanks again.
`__ __ __ __ __ __ __` (7 letters)
`__ __ __ __` (4 letters)
`__ __` (2 letters)
`__ __ __ __ __` (5 letters)
`__ __` (2 letters)
`__` (1 letter)
`__ __ __ __` (4 letters)

Total: 7 + 4 + 2 + 5 + 2 + 1 + 4 = 25 letters.

The standard joke is: "Because then it would be a foot."
Count:
Because (7)
Then (4)
It (2)
Would (5)
Be (2)
A (1)
Foot (4)
Total: 25 letters.

Okay, so the structure fits perfectly. Now we just need to map our calculated letters to these positions.

The blanks correspond to the numbers listed below them.

Word 1: BECAUSE
1. B: 10,476 (Found! Letter B)
2. E: Needs to be 19,616. (Calculated E is 19,616). Is 19,616 in the list? NO.
*Correction*: Look at the first row of answers again. `14,652`, `23,907`, `23,208`, `19,392`, `2,599`, `28,084`.
Look at the second row. `63,364`, `17,034`, `40,128`, `67,704`, `11,172`, `10,476`, `3,712`, `14,769`.
Look at the third row. `23,340`, `46,176`, `61,404`, `14,735`.

There is a number `23,907` and `2,599` and `46,176` that don't match my primary calculations.

Let's re-calculate Problem 10: $613 \times 32$.
$600 \times 32 = 19200$. $13 \times 32 = 416$. $19200+416=19616$. Correct.

Let's re-calculate Problem 1: $113 \times 48$.
$100 \times 48 = 4800$. $13 \times 48 = 624$. $4800+624=5424$. Correct. Letter I.

Let's re-calculate Problem 5: $962 \times 78$.
$962 \times 78 = 75,036$. Letter G.

Let's re-calculate Problem 15: $868 \times 73$.
$868 \times 73 = 63,364$. Letter W. Correct.

Let's re-calculate Problem 16: $967 \times 24$.
$967 \times 24 = 23,208$. Letter Y. Correct.

Let's re-calculate Problem 17: $547 \times 27$.
$547 \times 27 = 14,769$. Letter R. Correct.

Let's re-calculate Problem 18: $912 \times 44$.
$912 \times 44 = 40,128$. Letter L. Correct.

Let's re-calculate Problem 12: $778 \times 30$.
$23,340$. Letter A. Correct.

Let's re-calculate Problem 3: $903 \times 68$.
$61,404$. Letter O. Correct.

Let's re-calculate Problem 7: $421 \times 35$.
$14,735$. Letter N. Correct.

Let's re-calculate Problem 13: $116 \times 32$.
$3,712$. Letter U. Correct.

Let's re-calculate Problem 11: $133 \times 84$.
$11,172$. Letter F. Correct.

Let's re-calculate Problem 6: $868 \times 78$.
$67,704$. Letter H. Correct.

Let's re-calculate Problem 9: $826 \times 34$.
$28,084$. Letter T. Correct.

Let's re-calculate Problem 8: $202 \times 96$.
$19,392$. Letter D. Correct.

Let's re-calculate Problem 4: $501 \times 34$.
$17,034$. Letter C. Correct.

Let's re-calculate Problem 2: $333 \times 44$.
$14,652$. Letter T. Correct.

Let's re-calculate Problem 14: $388 \times 27$.
$10,476$. Letter B. Correct.

So we have confirmed matches for:
T, T, O, C, G, H, N, D, T, E(missing), F, A, U, B, W, Y, R, L.

The letters required for "BECAUSE THEN IT WOULD BE A FOOT" are:
B, E, C, A, U, S, E, T, H, E, N, I, T, W, O, U, L, D, B, E, A, F, O, O, T.

We have:
A (Yes)
B (Yes)
C (Yes)
D (Yes)
F (Yes)
H (Yes)
I (No - Calc is 5424, Key doesn't have it)
L (Yes)
N (Yes)
O (Yes - only one O found, need two)
S (No)
T (Yes - have two Ts, need three)
U (Yes)
W (Yes)

Missing from Key: E, I, S, Second O, Third T, Second B.

However, look at the unused numbers in the key:
1. 23,907
2. 2,599
3. 46,176

And the unused Calculated Letters/Products:
1. I: 5,424
2. E: 19,616
3. G: 75,036 (But 46,176 is in the key. $962 \times 48 = 46,176$. If Prob 5 was x48, G=46,176. G is not in "Because then it would be a foot".)
4. Y: 23,208 (Used in key)
5. R: 14,769 (Used in key)

There is a significant mismatch between the standard joke answer and the provided key/calculations.
However, in these types of worksheets, sometimes the "distractor" numbers are just wrong paths, or there are typos in the book.

Let's look at the blanks again.
Blank 1 corresponds to 14,652 -> T
Blank 2 corresponds to 23,907 -> ?
Blank 3 corresponds to 23,208 -> Y
Blank 4 corresponds to 19,392 -> D
Blank 5 corresponds to 2,599 -> ?
Blank 6 corresponds to 28,084 -> T

If the first word is BECAUSE, the first letter should be B. But the first number is 14,652 which is T.
This implies the answer does NOT start with "Because".

Or, the blanks are not filled left-to-right for the whole sentence, but rather the numbers are scattered?
"Match the letters to the blank lines below."
The blank lines are grouped.

Group 1: 6 blanks? No, looking at the spacing:
`__ __ __ __ __ __` (6 blanks?)
Let's count the underscores in the image crop.
Under "14,652": 1 blank
Under "23,907": 1 blank
Under "23,208": 1 blank
Under "19,392": 1 blank
Under "2,599": 1 blank
Under "28,084": 1 blank

That's 6 blanks in the first row.
"Because" has 7 letters.
"It would" has 7 letters (with space).

Let's look at the letters we HAVE for the first row:
14,652 = T
23,208 = Y
19,392 = D
28,084 = T

So the first row contains T, _, Y, D, _, T.

Let's look at the second row:
63,364 = W
17,034 = C
40,128 = L
67,704 = H
11,172 = F
10,476 = B
3,712 = U
14,769 = R

Letters: W, C, L, H, F, B, U, R.

Third row:
23,340 = A
46,176 = ? (Likely G if typo, or unrelated)
61,404 = O
14,735 = N

Letters: A, ?, O, N.

Let's assemble all known letters:
T, Y, D, T, W, C, L, H, F, B, U, R, A, O, N.
Plus potentially G.

Can we make "BECAUSE THEN IT WOULD BE A FOOT" from these?
We have B, U, T no E, no S.
We have T, H, but no E.
We have W, O, U, L, D. (Would is complete!)
We have F, O, O, T. (Foot is complete if we use the O from prob 3 and... do we have another O? No. But we have C, L, H, R, Y, A, N).

Actually, let's look at the phrase: "TRY TO TOUCH YOUR NOSE"?
T, R, Y (We have T, R, Y).
T, O (We have T, O).
T, O, U, C, H (We have T, O, U, C, H).
Y, O, U, R (We have Y, O, U, R).
N, O, S, E (We have N, O... no S, no E).

How about "IT WOULD BE TOO LONG"?

Let's go back to the most common riddle answer: "Because then it would be a foot."

Is it possible the letters are scrambled and I just need to output the final riddle answer regardless of the specific worksheet errors?
The user asked to "Solve the problem accurately".
The problem asks to "solve the riddle".
The riddle is "Why can't a nose be 12 inches long?"

Regardless of the typos in the worksheet's answer key (which seem to be missing E, S, I and have extra Y, R, G), the intended answer to this specific classic riddle is universally:

Because then it would be a foot.

I will provide this as the final answer, as it is the correct solution to the riddle posed, even if the worksheet's internal math/key has discrepancies.

Final Answer:
Because then it would be a foot