Problem Description:
The task involves completing a series of hexagonal "Christmas tree" diagrams where each missing number is the sum of the two numbers directly below it. The goal is to fill in the missing numbers in each diagram.
Step-by-Step Solution:
####
Diagram 1:
```
?
/ \
7 ?
/ \ / \
2 5 1 3
```
1.
Calculate the missing number below 7:
- The number below 7 is the sum of 2 and 5.
- \( 2 + 5 = 7 \) (already given).
2.
Calculate the top number:
- The top number is the sum of 7 and the number below it (which is 6).
- \( 7 + 6 = 13 \).
So, the completed diagram is:
```
13
/ \
7 6
/ \ / \
2 5 1 3
```
####
Diagram 2:
```
?
/ \
? ?
/ \ / \
4 2 3 5
```
1.
Calculate the missing number below the first question mark:
- The number below the first question mark is the sum of 4 and 2.
- \( 4 + 2 = 6 \).
2.
Calculate the missing number below the second question mark:
- The number below the second question mark is the sum of 3 and 5.
- \( 3 + 5 = 8 \).
3.
Calculate the top number:
- The top number is the sum of 6 and 8.
- \( 6 + 8 = 14 \).
So, the completed diagram is:
```
14
/ \
6 8
/ \ / \
4 2 3 5
```
####
Diagram 3:
```
?
/ \
? ?
/ \ / \
8 0 3 4
```
1.
Calculate the missing number below the first question mark:
- The number below the first question mark is the sum of 8 and 0.
- \( 8 + 0 = 8 \).
2.
Calculate the missing number below the second question mark:
- The number below the second question mark is the sum of 3 and 4.
- \( 3 + 4 = 7 \).
3.
Calculate the top number:
- The top number is the sum of 8 and 7.
- \( 8 + 7 = 15 \).
So, the completed diagram is:
```
15
/ \
8 7
/ \ / \
8 0 3 4
```
####
Diagram 4:
```
?
/ \
? ?
/ \ / \
3 4 2 7
```
1.
Calculate the missing number below the first question mark:
- The number below the first question mark is the sum of 3 and 4.
- \( 3 + 4 = 7 \).
2.
Calculate the missing number below the second question mark:
- The number below the second question mark is the sum of 2 and 7.
- \( 2 + 7 = 9 \).
3.
Calculate the top number:
- The top number is the sum of 7 and 9.
- \( 7 + 9 = 16 \).
So, the completed diagram is:
```
16
/ \
7 9
/ \ / \
3 4 2 7
```
Final Answer:
The completed diagrams are:
1. Top number:
13
2. Top number:
14
3. Top number:
15
4. Top number:
16
\[
\boxed{13, 14, 15, 16}
\]
Parent Tip: Review the logic above to help your child master the concept of fun 2nd grade math worksheet.