Math Fact: Relationship Between Addition & Subtraction | Worksheet ... - Free Printable

Problem Explanation:

The task involves working with fact families. A fact family is a group of math facts using the same numbers, typically involving addition and subtraction. For example, if you have three numbers (e.g., 4, 5, and 9), the fact family includes all possible addition and subtraction equations that can be formed using these numbers.

#### Key Points:
1. Each triangle contains three numbers.
2. Using these three numbers, you need to create:
- Two addition equations.
- Two subtraction equations.

#### General Rules:
- For any three numbers \( a \), \( b \), and \( c \) where \( a + b = c \):
- Addition: \( a + b = c \) and \( b + a = c \).
- Subtraction: \( c - a = b \) and \( c - b = a \).

Solution:

#### Triangle 1: Numbers (4, 5, 9)
1. Addition:
- \( 4 + 5 = 9 \)
- \( 5 + 4 = 9 \)

2. Subtraction:
- \( 9 - 4 = 5 \)
- \( 9 - 5 = 4 \)

#### Triangle 2: Numbers (7, 6, 13)
1. Addition:
- \( 7 + 6 = 13 \)
- \( 6 + 7 = 13 \)

2. Subtraction:
- \( 13 - 7 = 6 \)
- \( 13 - 6 = 7 \)

#### Triangle 3: Numbers (6, 4, 10)
1. Addition:
- \( 6 + 4 = 10 \)
- \( 4 + 6 = 10 \)

2. Subtraction:
- \( 10 - 6 = 4 \)
- \( 10 - 4 = 6 \)

#### Triangle 4: Numbers (5, 7, 12)
1. Addition:
- \( 5 + 7 = 12 \)
- \( 7 + 5 = 12 \)

2. Subtraction:
- \( 12 - 5 = 7 \)
- \( 12 - 7 = 5 \)

#### Triangle 5: Numbers (8, 9, 17)
1. Addition:
- \( 8 + 9 = 17 \)
- \( 9 + 8 = 17 \)

2. Subtraction:
- \( 17 - 8 = 9 \)
- \( 17 - 9 = 8 \)

#### Triangle 6: Numbers (8, 7, 15)
1. Addition:
- \( 8 + 7 = 15 \)
- \( 7 + 8 = 15 \)

2. Subtraction:
- \( 15 - 8 = 7 \)
- \( 15 - 7 = 8 \)

#### Triangle 7: Numbers (10, 6, 16)
1. Addition:
- \( 10 + 6 = 16 \)
- \( 6 + 10 = 16 \)

2. Subtraction:
- \( 16 - 10 = 6 \)
- \( 16 - 6 = 10 \)

#### Triangle 8: Numbers (2, 6, 8)
1. Addition:
- \( 2 + 6 = 8 \)
- \( 6 + 2 = 8 \)

2. Subtraction:
- \( 8 - 2 = 6 \)
- \( 8 - 6 = 2 \)

#### Triangle 9: Numbers (3, 7, 10)
1. Addition:
- \( 3 + 7 = 10 \)
- \( 7 + 3 = 10 \)

2. Subtraction:
- \( 10 - 3 = 7 \)
- \( 10 - 7 = 3 \)

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Triangle 1:} \\
4 + 5 = 9, \quad 5 + 4 = 9 \\
9 - 4 = 5, \quad 9 - 5 = 4 \\
\\
\text{Triangle 2:} \\
7 + 6 = 13, \quad 6 + 7 = 13 \\
13 - 7 = 6, \quad 13 - 6 = 7 \\
\\
\text{Triangle 3:} \\
6 + 4 = 10, \quad 4 + 6 = 10 \\
10 - 6 = 4, \quad 10 - 4 = 6 \\
\\
\text{Triangle 4:} \\
5 + 7 = 12, \quad 7 + 5 = 12 \\
12 - 5 = 7, \quad 12 - 7 = 5 \\
\\
\text{Triangle 5:} \\
8 + 9 = 17, \quad 9 + 8 = 17 \\
17 - 8 = 9, \quad 17 - 9 = 8 \\
\\
\text{Triangle 6:} \\
8 + 7 = 15, \quad 7 + 8 = 15 \\
15 - 8 = 7, \quad 15 - 7 = 8 \\
\\
\text{Triangle 7:} \\
10 + 6 = 16, \quad 6 + 10 = 16 \\
16 - 10 = 6, \quad 16 - 6 = 10 \\
\\
\text{Triangle 8:} \\
2 + 6 = 8, \quad 6 + 2 = 8 \\
8 - 2 = 6, \quad 8 - 6 = 2 \\
\\
\text{Triangle 9:} \\
3 + 7 = 10, \quad 7 + 3 = 10 \\
10 - 3 = 7, \quad 10 - 7 = 3 \\
\end{array}
}
\]