2 Digit Subtraction Games WITH / WITHOUT Regrouping - Free Printable
Educational worksheet: 2 Digit Subtraction Games WITH / WITHOUT Regrouping. Download and print for classroom or home learning activities.
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Step-by-step solution for: 2 Digit Subtraction Games WITH / WITHOUT Regrouping
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Show Answer Key & Explanations
Step-by-step solution for: 2 Digit Subtraction Games WITH / WITHOUT Regrouping
The task involves completing subtraction pyramids where each number in a block is the result of subtracting the two numbers directly below it. Let's solve each pyramid step by step.
---
```
79
/ \
39 ?
/ \ / \
21 ? ? ?
/ \ / \ / \ / \
9 12 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (79):
- \( 79 - 39 = 40 \)
- So, the right block under 79 is 40.
2. Second Level (39):
- \( 39 - 21 = 18 \)
- So, the right block under 39 is 18.
3. Third Level (21):
- \( 21 - 9 = 12 \)
- \( 21 - 12 = 9 \)
- So, the blocks under 21 are 12 and 9.
4. Fourth Level (9 and 12):
- \( 9 - 12 \) is not possible (since we are working with positive numbers only), so we need to recheck the structure. However, based on the pattern, the next level should be filled as follows:
- The missing blocks are derived from the differences:
- \( 12 - 9 = 3 \)
- \( 9 - 12 \) is not valid, so we assume the structure is correct as given.
Final Pyramid:
```
79
/ \
39 40
/ \ / \
21 18 19 21
/ \ / \ / \ / \
9 12 3 9 10 11
```
---
```
78
/ \
41 ?
/ \ / \
19 ? ? ?
/ \ / \ / \ / \
8 11 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (78):
- \( 78 - 41 = 37 \)
- So, the right block under 78 is 37.
2. Second Level (41):
- \( 41 - 19 = 22 \)
- So, the right block under 41 is 22.
3. Third Level (19):
- \( 19 - 8 = 11 \)
- \( 19 - 11 = 8 \)
- So, the blocks under 19 are 11 and 8.
4. Fourth Level (8 and 11):
- \( 8 - 11 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
78
/ \
41 37
/ \ / \
19 22 26 15
/ \ / \ / \ / \
8 11 11 8 15 11
```
---
```
78
/ \
33 ?
/ \ / \
18 ? ? ?
/ \ / \ / \ / \
10 8 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (78):
- \( 78 - 33 = 45 \)
- So, the right block under 78 is 45.
2. Second Level (33):
- \( 33 - 18 = 15 \)
- So, the right block under 33 is 15.
3. Third Level (18):
- \( 18 - 10 = 8 \)
- \( 18 - 8 = 10 \)
- So, the blocks under 18 are 8 and 10.
4. Fourth Level (10 and 8):
- \( 10 - 8 = 2 \)
- \( 8 - 10 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
78
/ \
33 45
/ \ / \
18 15 27 30
/ \ / \ / \ / \
10 8 8 10 19 11
```
---
```
98
/ \
57 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
19 12 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (98):
- \( 98 - 57 = 41 \)
- So, the right block under 98 is 41.
2. Second Level (57):
- \( 57 - 31 = 26 \)
- So, the right block under 57 is 26.
3. Third Level (31):
- \( 31 - 19 = 12 \)
- \( 31 - 12 = 19 \)
- So, the blocks under 31 are 12 and 19.
4. Fourth Level (19 and 12):
- \( 19 - 12 = 7 \)
- \( 12 - 19 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
98
/ \
57 41
/ \ / \
31 26 16 25
/ \ / \ / \ / \
19 12 12 19 7 18
```
---
```
88
/ \
47 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
13 13 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (88):
- \( 88 - 47 = 41 \)
- So, the right block under 88 is 41.
2. Second Level (47):
- \( 47 - 26 = 21 \)
- So, the right block under 47 is 21.
3. Third Level (26):
- \( 26 - 13 = 13 \)
- \( 26 - 13 = 13 \)
- So, the blocks under 26 are 13 and 13.
4. Fourth Level (13 and 13):
- \( 13 - 13 = 0 \)
- \( 13 - 13 = 0 \)
- So, the blocks under 13 are 0 and 0.
Final Pyramid:
```
88
/ \
47 41
/ \ / \
26 21 15 20
/ \ / \ / \ / \
13 13 13 13 0 0
```
---
```
74
/ \
36 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
10 10 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (74):
- \( 74 - 36 = 38 \)
- So, the right block under 74 is 38.
2. Second Level (36):
- \( 36 - 20 = 16 \)
- So, the right block under 36 is 16.
3. Third Level (20):
- \( 20 - 10 = 10 \)
- \( 20 - 10 = 10 \)
- So, the blocks under 20 are 10 and 10.
4. Fourth Level (10 and 10):
- \( 10 - 10 = 0 \)
- \( 10 - 10 = 0 \)
- So, the blocks under 10 are 0 and 0.
Final Pyramid:
```
74
/ \
36 38
/ \ / \
20 16 22 22
/ \ / \ / \ / \
10 10 10 10 0 0
```
---
\[
\boxed{
\begin{array}{c}
\text{Pyramid 1:} \\
\begin{array}{ccccccc}
& & & 79 & & & \\
& & 39 & & 40 & & \\
& 21 & & 18 & & 19 & 21 \\
9 & & 12 & & 3 & & 9 & & 10 & & 11 \\
\end{array} \\
\text{Pyramid 2:} \\
\begin{array}{ccccccc}
& & & 78 & & & \\
& & 41 & & 37 & & \\
& 19 & & 22 & & 26 & 15 \\
8 & & 11 & & 11 & & 8 & & 15 & & 11 \\
\end{array} \\
\text{Pyramid 3:} \\
\begin{array}{ccccccc}
& & & 78 & & & \\
& & 33 & & 45 & & \\
& 18 & & 15 & & 27 & 30 \\
10 & & 8 & & 8 & & 10 & & 19 & & 11 \\
\end{array} \\
\text{Pyramid 4:} \\
\begin{array}{ccccccc}
& & & 98 & & & \\
& & 57 & & 41 & & \\
& 31 & & 26 & & 16 & 25 \\
19 & & 12 & & 12 & & 19 & & 7 & & 18 \\
\end{array} \\
\text{Pyramid 5:} \\
\begin{array}{ccccccc}
& & & 88 & & & \\
& & 47 & & 41 & & \\
& 26 & & 21 & & 15 & 20 \\
13 & & 13 & & 13 & & 13 & & 0 & & 0 \\
\end{array} \\
\text{Pyramid 6:} \\
\begin{array}{ccccccc}
& & & 74 & & & \\
& & 36 & & 38 & & \\
& 20 & & 16 & & 22 & 22 \\
10 & & 10 & & 10 & & 10 & & 0 & & 0 \\
\end{array}
\end{array}
}
\]
---
Pyramid 1:
```
79
/ \
39 ?
/ \ / \
21 ? ? ?
/ \ / \ / \ / \
9 12 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (79):
- \( 79 - 39 = 40 \)
- So, the right block under 79 is 40.
2. Second Level (39):
- \( 39 - 21 = 18 \)
- So, the right block under 39 is 18.
3. Third Level (21):
- \( 21 - 9 = 12 \)
- \( 21 - 12 = 9 \)
- So, the blocks under 21 are 12 and 9.
4. Fourth Level (9 and 12):
- \( 9 - 12 \) is not possible (since we are working with positive numbers only), so we need to recheck the structure. However, based on the pattern, the next level should be filled as follows:
- The missing blocks are derived from the differences:
- \( 12 - 9 = 3 \)
- \( 9 - 12 \) is not valid, so we assume the structure is correct as given.
Final Pyramid:
```
79
/ \
39 40
/ \ / \
21 18 19 21
/ \ / \ / \ / \
9 12 3 9 10 11
```
---
Pyramid 2:
```
78
/ \
41 ?
/ \ / \
19 ? ? ?
/ \ / \ / \ / \
8 11 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (78):
- \( 78 - 41 = 37 \)
- So, the right block under 78 is 37.
2. Second Level (41):
- \( 41 - 19 = 22 \)
- So, the right block under 41 is 22.
3. Third Level (19):
- \( 19 - 8 = 11 \)
- \( 19 - 11 = 8 \)
- So, the blocks under 19 are 11 and 8.
4. Fourth Level (8 and 11):
- \( 8 - 11 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
78
/ \
41 37
/ \ / \
19 22 26 15
/ \ / \ / \ / \
8 11 11 8 15 11
```
---
Pyramid 3:
```
78
/ \
33 ?
/ \ / \
18 ? ? ?
/ \ / \ / \ / \
10 8 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (78):
- \( 78 - 33 = 45 \)
- So, the right block under 78 is 45.
2. Second Level (33):
- \( 33 - 18 = 15 \)
- So, the right block under 33 is 15.
3. Third Level (18):
- \( 18 - 10 = 8 \)
- \( 18 - 8 = 10 \)
- So, the blocks under 18 are 8 and 10.
4. Fourth Level (10 and 8):
- \( 10 - 8 = 2 \)
- \( 8 - 10 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
78
/ \
33 45
/ \ / \
18 15 27 30
/ \ / \ / \ / \
10 8 8 10 19 11
```
---
Pyramid 4:
```
98
/ \
57 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
19 12 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (98):
- \( 98 - 57 = 41 \)
- So, the right block under 98 is 41.
2. Second Level (57):
- \( 57 - 31 = 26 \)
- So, the right block under 57 is 26.
3. Third Level (31):
- \( 31 - 19 = 12 \)
- \( 31 - 12 = 19 \)
- So, the blocks under 31 are 12 and 19.
4. Fourth Level (19 and 12):
- \( 19 - 12 = 7 \)
- \( 12 - 19 \) is not possible, so we assume the structure is correct as given.
Final Pyramid:
```
98
/ \
57 41
/ \ / \
31 26 16 25
/ \ / \ / \ / \
19 12 12 19 7 18
```
---
Pyramid 5:
```
88
/ \
47 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
13 13 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (88):
- \( 88 - 47 = 41 \)
- So, the right block under 88 is 41.
2. Second Level (47):
- \( 47 - 26 = 21 \)
- So, the right block under 47 is 21.
3. Third Level (26):
- \( 26 - 13 = 13 \)
- \( 26 - 13 = 13 \)
- So, the blocks under 26 are 13 and 13.
4. Fourth Level (13 and 13):
- \( 13 - 13 = 0 \)
- \( 13 - 13 = 0 \)
- So, the blocks under 13 are 0 and 0.
Final Pyramid:
```
88
/ \
47 41
/ \ / \
26 21 15 20
/ \ / \ / \ / \
13 13 13 13 0 0
```
---
Pyramid 6:
```
74
/ \
36 ?
/ \ / \
? ? ? ?
/ \ / \ / \ / \
10 10 ? ? ? ?
```
#### Step-by-Step Solution:
1. Top Level (74):
- \( 74 - 36 = 38 \)
- So, the right block under 74 is 38.
2. Second Level (36):
- \( 36 - 20 = 16 \)
- So, the right block under 36 is 16.
3. Third Level (20):
- \( 20 - 10 = 10 \)
- \( 20 - 10 = 10 \)
- So, the blocks under 20 are 10 and 10.
4. Fourth Level (10 and 10):
- \( 10 - 10 = 0 \)
- \( 10 - 10 = 0 \)
- So, the blocks under 10 are 0 and 0.
Final Pyramid:
```
74
/ \
36 38
/ \ / \
20 16 22 22
/ \ / \ / \ / \
10 10 10 10 0 0
```
---
Final Answer:
\[
\boxed{
\begin{array}{c}
\text{Pyramid 1:} \\
\begin{array}{ccccccc}
& & & 79 & & & \\
& & 39 & & 40 & & \\
& 21 & & 18 & & 19 & 21 \\
9 & & 12 & & 3 & & 9 & & 10 & & 11 \\
\end{array} \\
\text{Pyramid 2:} \\
\begin{array}{ccccccc}
& & & 78 & & & \\
& & 41 & & 37 & & \\
& 19 & & 22 & & 26 & 15 \\
8 & & 11 & & 11 & & 8 & & 15 & & 11 \\
\end{array} \\
\text{Pyramid 3:} \\
\begin{array}{ccccccc}
& & & 78 & & & \\
& & 33 & & 45 & & \\
& 18 & & 15 & & 27 & 30 \\
10 & & 8 & & 8 & & 10 & & 19 & & 11 \\
\end{array} \\
\text{Pyramid 4:} \\
\begin{array}{ccccccc}
& & & 98 & & & \\
& & 57 & & 41 & & \\
& 31 & & 26 & & 16 & 25 \\
19 & & 12 & & 12 & & 19 & & 7 & & 18 \\
\end{array} \\
\text{Pyramid 5:} \\
\begin{array}{ccccccc}
& & & 88 & & & \\
& & 47 & & 41 & & \\
& 26 & & 21 & & 15 & 20 \\
13 & & 13 & & 13 & & 13 & & 0 & & 0 \\
\end{array} \\
\text{Pyramid 6:} \\
\begin{array}{ccccccc}
& & & 74 & & & \\
& & 36 & & 38 & & \\
& 20 & & 16 & & 22 & 22 \\
10 & & 10 & & 10 & & 10 & & 0 & & 0 \\
\end{array}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of online subtraction worksheet for 2nd.