Math worksheet for finding missing numbers in multiplication equations.
Worksheet titled "Missing Numbers in Equations (A)" with 40 multiplication equations involving variables to solve.
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Step-by-step solution for: 4th Grade Multiplication Worksheets - Best Coloring Pages For Kids ...
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Show Answer Key & Explanations
Step-by-step solution for: 4th Grade Multiplication Worksheets - Best Coloring Pages For Kids ...
Let's solve each equation step by step to find the value of each unknown variable. We'll use basic algebra: if $ a \times b = c $, then $ a = \frac{c}{b} $.
---
1. $ n \times 3 = 24 $ → $ n = \frac{24}{3} = 8 $
2. $ s \times 6 = 54 $ → $ s = \frac{54}{6} = 9 $
3. $ t \times 2 = 16 $ → $ t = \frac{16}{2} = 8 $
4. $ p \times 7 = 42 $ → $ p = \frac{42}{7} = 6 $
---
5. $ 4 \times t = 28 $ → $ t = \frac{28}{4} = 7 $
*(Note: This is a different t than above — but we’ll keep track)*
6. $ 8 \times w = 32 $ → $ w = \frac{32}{8} = 4 $
7. $ 6 \times t = 24 $ → $ t = \frac{24}{6} = 4 $
8. $ a \times 9 = 54 $ → $ a = \frac{54}{9} = 6 $
---
9. $ 2 \times t = 18 $ → $ t = \frac{18}{2} = 9 $
10. $ m \times 5 = 45 $ → $ m = \frac{45}{5} = 9 $
11. $ w \times 3 = 18 $ → $ w = \frac{18}{3} = 6 $
12. $ a \times 4 = 16 $ → $ a = \frac{16}{4} = 4 $
---
13. $ s \times 3 = 12 $ → $ s = \frac{12}{3} = 4 $
14. $ j \times 3 = 3 $ → $ j = \frac{3}{3} = 1 $
15. $ j \times 3 = 27 $ → $ j = \frac{27}{3} = 9 $
*(Conflict: j can't be both 1 and 9 — likely two separate equations using same letter? Or typo? Let's assume they are independent unless stated otherwise. But this suggests inconsistency. Wait — probably multiple uses of same letter in different contexts. But let’s proceed carefully.)*
16. $ 8 \times p = 24 $ → $ p = \frac{24}{8} = 3 $
---
17. $ 3 \times w = 9 $ → $ w = \frac{9}{3} = 3 $
18. $ 5 \times c = 45 $ → $ c = \frac{45}{5} = 9 $
19. $ g \times 7 = 28 $ → $ g = \frac{28}{7} = 4 $
20. $ 9 \times b = 63 $ → $ b = \frac{63}{9} = 7 $
---
21. $ c \times 8 = 72 $ → $ c = \frac{72}{8} = 9 $
22. $ 2 \times z = 6 $ → $ z = \frac{6}{2} = 3 $
23. $ y \times 9 = 45 $ → $ y = \frac{45}{9} = 5 $
24. $ x \times 1 = 6 $ → $ x = 6 $
---
25. $ 6 \times v = 36 $ → $ v = \frac{36}{6} = 6 $
26. $ g \times 5 = 15 $ → $ g = \frac{15}{5} = 3 $
27. $ d \times 3 = 15 $ → $ d = \frac{15}{3} = 5 $
28. $ s \times 1 = 2 $ → $ s = 2 $
---
29. $ y \times 3 = 24 $ → $ y = \frac{24}{3} = 8 $
30. $ z \times 5 = 35 $ → $ z = \frac{35}{5} = 7 $
31. $ b \times 3 = 27 $ → $ b = \frac{27}{3} = 9 $
32. $ j \times 1 = 1 $ → $ j = 1 $
---
33. $ f \times 7 = 35 $ → $ f = \frac{35}{7} = 5 $
34. $ m \times 7 = 35 $ → $ m = \frac{35}{7} = 5 $
35. $ 6 \times b = 36 $ → $ b = \frac{36}{6} = 6 $
36. $ 7 \times u = 49 $ → $ u = \frac{49}{7} = 7 $
---
37. $ 7 \times q = 7 $ → $ q = \frac{7}{7} = 1 $
38. $ n \times 6 = 12 $ → $ n = \frac{12}{6} = 2 $
39. $ 2 \times g = 4 $ → $ g = \frac{4}{2} = 2 $
40. $ 3 \times v = 12 $ → $ v = \frac{12}{3} = 4 $
---
Let’s list each variable and its value from the equations (note: some variables appear multiple times with different values — this might indicate different instances, or possibly errors).
But since it's a worksheet, likely each variable is used only once, so we need to check for consistency.
Wait — actually, some variables appear multiple times, but give conflicting values. For example:
- $ t $: appears as 8, 7, 4, 9 → inconsistent
- $ s $: 9, 4, 2 → inconsistent
- $ w $: 4, 6, 3 → inconsistent
- $ a $: 6, 4 → inconsistent
- $ j $: 1, 9, 1 → conflicting
- $ b $: 7, 9, 6 → conflicting
This suggests that the same letter is used in different problems independently, not representing the same variable throughout. So we treat each equation independently.
Thus, each variable stands alone per equation, and multiple uses of the same letter don’t imply same value.
So we just compute each one separately.
Let’s compile all results:
---
1. $ n = 8 $
2. $ s = 9 $
3. $ t = 8 $
4. $ p = 6 $
5. $ t = 7 $
6. $ w = 4 $
7. $ t = 4 $
8. $ a = 6 $
9. $ t = 9 $
10. $ m = 9 $
11. $ w = 6 $
12. $ a = 4 $
13. $ s = 4 $
14. $ j = 1 $
15. $ j = 9 $
16. $ p = 3 $
17. $ w = 3 $
18. $ c = 9 $
19. $ g = 4 $
20. $ b = 7 $
21. $ c = 9 $
22. $ z = 3 $
23. $ y = 5 $
24. $ x = 6 $
25. $ v = 6 $
26. $ g = 3 $
27. $ d = 5 $
28. $ s = 2 $
29. $ y = 8 $
30. $ z = 7 $
31. $ b = 9 $
32. $ j = 1 $
33. $ f = 5 $
34. $ m = 5 $
35. $ b = 6 $
36. $ u = 7 $
37. $ q = 1 $
38. $ n = 2 $
39. $ g = 2 $
40. $ v = 4 $
---
| Variable | Value(s) |
|---------|----------|
| n | 8, 2 |
| s | 9, 4, 2 |
| t | 8, 7, 4, 9 |
| p | 6, 3 |
| w | 4, 6, 3 |
| a | 6, 4 |
| m | 9, 5 |
| j | 1, 9, 1 |
| c | 9, 9 |
| z | 3, 7 |
| y | 5, 8 |
| x | 6 |
| v | 6, 4 |
| g | 4, 3, 2 |
| d | 5 |
| b | 7, 9, 6 |
| f | 5 |
| u | 7 |
| q | 1 |
> Note: Since each equation is independent, these are not consistent across equations — this is expected in such worksheets.
---
The solution is to compute each missing number individually:
$$
\begin{align*}
n &= 8,\ 2 \\
s &= 9,\ 4,\ 2 \\
t &= 8,\ 7,\ 4,\ 9 \\
p &= 6,\ 3 \\
w &= 4,\ 6,\ 3 \\
a &= 6,\ 4 \\
m &= 9,\ 5 \\
j &= 1,\ 9,\ 1 \\
c &= 9,\ 9 \\
z &= 3,\ 7 \\
y &= 5,\ 8 \\
x &= 6 \\
v &= 6,\ 4 \\
g &= 4,\ 3,\ 2 \\
d &= 5 \\
b &= 7,\ 9,\ 6 \\
f &= 5 \\
u &= 7 \\
q &= 1 \\
\end{align*}
$$
Each value corresponds to the equation it was solved from.
---
To solve each equation like $ x \times a = b $, divide both sides by $ a $:
$$
x = \frac{b}{a}
$$
For example:
- $ n \times 3 = 24 $ → $ n = 24 \div 3 = 8 $
- $ s \times 6 = 54 $ → $ s = 54 \div 6 = 9 $
We apply this method to every equation.
Since variables are reused across different equations, each instance is independent — no global consistency required.
✔ All values are correct based on individual equations.
Let me know if you'd like a table of answers!
---
Row 1
1. $ n \times 3 = 24 $ → $ n = \frac{24}{3} = 8 $
2. $ s \times 6 = 54 $ → $ s = \frac{54}{6} = 9 $
3. $ t \times 2 = 16 $ → $ t = \frac{16}{2} = 8 $
4. $ p \times 7 = 42 $ → $ p = \frac{42}{7} = 6 $
---
Row 2
5. $ 4 \times t = 28 $ → $ t = \frac{28}{4} = 7 $
*(Note: This is a different t than above — but we’ll keep track)*
6. $ 8 \times w = 32 $ → $ w = \frac{32}{8} = 4 $
7. $ 6 \times t = 24 $ → $ t = \frac{24}{6} = 4 $
8. $ a \times 9 = 54 $ → $ a = \frac{54}{9} = 6 $
---
Row 3
9. $ 2 \times t = 18 $ → $ t = \frac{18}{2} = 9 $
10. $ m \times 5 = 45 $ → $ m = \frac{45}{5} = 9 $
11. $ w \times 3 = 18 $ → $ w = \frac{18}{3} = 6 $
12. $ a \times 4 = 16 $ → $ a = \frac{16}{4} = 4 $
---
Row 4
13. $ s \times 3 = 12 $ → $ s = \frac{12}{3} = 4 $
14. $ j \times 3 = 3 $ → $ j = \frac{3}{3} = 1 $
15. $ j \times 3 = 27 $ → $ j = \frac{27}{3} = 9 $
*(Conflict: j can't be both 1 and 9 — likely two separate equations using same letter? Or typo? Let's assume they are independent unless stated otherwise. But this suggests inconsistency. Wait — probably multiple uses of same letter in different contexts. But let’s proceed carefully.)*
16. $ 8 \times p = 24 $ → $ p = \frac{24}{8} = 3 $
---
Row 5
17. $ 3 \times w = 9 $ → $ w = \frac{9}{3} = 3 $
18. $ 5 \times c = 45 $ → $ c = \frac{45}{5} = 9 $
19. $ g \times 7 = 28 $ → $ g = \frac{28}{7} = 4 $
20. $ 9 \times b = 63 $ → $ b = \frac{63}{9} = 7 $
---
Row 6
21. $ c \times 8 = 72 $ → $ c = \frac{72}{8} = 9 $
22. $ 2 \times z = 6 $ → $ z = \frac{6}{2} = 3 $
23. $ y \times 9 = 45 $ → $ y = \frac{45}{9} = 5 $
24. $ x \times 1 = 6 $ → $ x = 6 $
---
Row 7
25. $ 6 \times v = 36 $ → $ v = \frac{36}{6} = 6 $
26. $ g \times 5 = 15 $ → $ g = \frac{15}{5} = 3 $
27. $ d \times 3 = 15 $ → $ d = \frac{15}{3} = 5 $
28. $ s \times 1 = 2 $ → $ s = 2 $
---
Row 8
29. $ y \times 3 = 24 $ → $ y = \frac{24}{3} = 8 $
30. $ z \times 5 = 35 $ → $ z = \frac{35}{5} = 7 $
31. $ b \times 3 = 27 $ → $ b = \frac{27}{3} = 9 $
32. $ j \times 1 = 1 $ → $ j = 1 $
---
Row 9
33. $ f \times 7 = 35 $ → $ f = \frac{35}{7} = 5 $
34. $ m \times 7 = 35 $ → $ m = \frac{35}{7} = 5 $
35. $ 6 \times b = 36 $ → $ b = \frac{36}{6} = 6 $
36. $ 7 \times u = 49 $ → $ u = \frac{49}{7} = 7 $
---
Row 10
37. $ 7 \times q = 7 $ → $ q = \frac{7}{7} = 1 $
38. $ n \times 6 = 12 $ → $ n = \frac{12}{6} = 2 $
39. $ 2 \times g = 4 $ → $ g = \frac{4}{2} = 2 $
40. $ 3 \times v = 12 $ → $ v = \frac{12}{3} = 4 $
---
Now, collect all values:
Let’s list each variable and its value from the equations (note: some variables appear multiple times with different values — this might indicate different instances, or possibly errors).
But since it's a worksheet, likely each variable is used only once, so we need to check for consistency.
Wait — actually, some variables appear multiple times, but give conflicting values. For example:
- $ t $: appears as 8, 7, 4, 9 → inconsistent
- $ s $: 9, 4, 2 → inconsistent
- $ w $: 4, 6, 3 → inconsistent
- $ a $: 6, 4 → inconsistent
- $ j $: 1, 9, 1 → conflicting
- $ b $: 7, 9, 6 → conflicting
This suggests that the same letter is used in different problems independently, not representing the same variable throughout. So we treat each equation independently.
Thus, each variable stands alone per equation, and multiple uses of the same letter don’t imply same value.
So we just compute each one separately.
Let’s compile all results:
---
Final Answers (Each Equation Solved):
1. $ n = 8 $
2. $ s = 9 $
3. $ t = 8 $
4. $ p = 6 $
5. $ t = 7 $
6. $ w = 4 $
7. $ t = 4 $
8. $ a = 6 $
9. $ t = 9 $
10. $ m = 9 $
11. $ w = 6 $
12. $ a = 4 $
13. $ s = 4 $
14. $ j = 1 $
15. $ j = 9 $
16. $ p = 3 $
17. $ w = 3 $
18. $ c = 9 $
19. $ g = 4 $
20. $ b = 7 $
21. $ c = 9 $
22. $ z = 3 $
23. $ y = 5 $
24. $ x = 6 $
25. $ v = 6 $
26. $ g = 3 $
27. $ d = 5 $
28. $ s = 2 $
29. $ y = 8 $
30. $ z = 7 $
31. $ b = 9 $
32. $ j = 1 $
33. $ f = 5 $
34. $ m = 5 $
35. $ b = 6 $
36. $ u = 7 $
37. $ q = 1 $
38. $ n = 2 $
39. $ g = 2 $
40. $ v = 4 $
---
Summary of All Variables (with their values from each equation):
| Variable | Value(s) |
|---------|----------|
| n | 8, 2 |
| s | 9, 4, 2 |
| t | 8, 7, 4, 9 |
| p | 6, 3 |
| w | 4, 6, 3 |
| a | 6, 4 |
| m | 9, 5 |
| j | 1, 9, 1 |
| c | 9, 9 |
| z | 3, 7 |
| y | 5, 8 |
| x | 6 |
| v | 6, 4 |
| g | 4, 3, 2 |
| d | 5 |
| b | 7, 9, 6 |
| f | 5 |
| u | 7 |
| q | 1 |
> Note: Since each equation is independent, these are not consistent across equations — this is expected in such worksheets.
---
✔ Final Answer:
The solution is to compute each missing number individually:
$$
\begin{align*}
n &= 8,\ 2 \\
s &= 9,\ 4,\ 2 \\
t &= 8,\ 7,\ 4,\ 9 \\
p &= 6,\ 3 \\
w &= 4,\ 6,\ 3 \\
a &= 6,\ 4 \\
m &= 9,\ 5 \\
j &= 1,\ 9,\ 1 \\
c &= 9,\ 9 \\
z &= 3,\ 7 \\
y &= 5,\ 8 \\
x &= 6 \\
v &= 6,\ 4 \\
g &= 4,\ 3,\ 2 \\
d &= 5 \\
b &= 7,\ 9,\ 6 \\
f &= 5 \\
u &= 7 \\
q &= 1 \\
\end{align*}
$$
Each value corresponds to the equation it was solved from.
---
📌 Explanation:
To solve each equation like $ x \times a = b $, divide both sides by $ a $:
$$
x = \frac{b}{a}
$$
For example:
- $ n \times 3 = 24 $ → $ n = 24 \div 3 = 8 $
- $ s \times 6 = 54 $ → $ s = 54 \div 6 = 9 $
We apply this method to every equation.
Since variables are reused across different equations, each instance is independent — no global consistency required.
✔ All values are correct based on individual equations.
Let me know if you'd like a table of answers!
Parent Tip: Review the logic above to help your child master the concept of algebra for 4th grade worksheet.