Fact Family Worksheets - Math Monks - Free Printable

Problem Explanation:

The task involves completing "Fact Family Triangles," which are sets of related addition and subtraction equations using three numbers. Each triangle provides a sum (top number) and two other numbers (bottom numbers). The goal is to create four equations: two addition equations and two subtraction equations, using these three numbers.

General Approach:

1. Identify the Numbers: Each triangle has a top number (the sum) and two bottom numbers.
2. Form Addition Equations:
- Add the two bottom numbers to get the top number.
- Rearrange the addition equation by swapping the order of the addends.
3. Form Subtraction Equations:
- Subtract one of the bottom numbers from the top number to get the other bottom number.
- Repeat the subtraction with the other bottom number.

Solution for Each Triangle:

#### a.
- Numbers: Top = 8, Bottom = 2, 6
- Addition Equations:
- \( 2 + 6 = 8 \)
- \( 6 + 2 = 8 \)
- Subtraction Equations:
- \( 8 - 2 = 6 \)
- \( 8 - 6 = 2 \)

#### b.
- Numbers: Top = 17, Bottom = 12, 5
- Addition Equations:
- \( 12 + 5 = 17 \)
- \( 5 + 12 = 17 \)
- Subtraction Equations:
- \( 17 - 12 = 5 \)
- \( 17 - 5 = 12 \)

#### c.
- Numbers: Top = 20, Bottom = 2, 18
- Addition Equations:
- \( 2 + 18 = 20 \)
- \( 18 + 2 = 20 \)
- Subtraction Equations:
- \( 20 - 2 = 18 \)
- \( 20 - 18 = 2 \)

#### d.
- Numbers: Top = 16, Bottom = 7, 9
- Addition Equations:
- \( 7 + 9 = 16 \)
- \( 9 + 7 = 16 \)
- Subtraction Equations:
- \( 16 - 7 = 9 \)
- \( 16 - 9 = 7 \)

#### e.
- Numbers: Top = 18, Bottom = 7, 11
- Addition Equations:
- \( 7 + 11 = 18 \)
- \( 11 + 7 = 18 \)
- Subtraction Equations:
- \( 18 - 7 = 11 \)
- \( 18 - 11 = 7 \)

#### f.
- Numbers: Top = 5, Bottom = 1, 4
- Addition Equations:
- \( 1 + 4 = 5 \)
- \( 4 + 1 = 5 \)
- Subtraction Equations:
- \( 5 - 1 = 4 \)
- \( 5 - 4 = 1 \)

#### g.
- Numbers: Top = 11, Bottom = 9, 2
- Addition Equations:
- \( 9 + 2 = 11 \)
- \( 2 + 9 = 11 \)
- Subtraction Equations:
- \( 11 - 9 = 2 \)
- \( 11 - 2 = 9 \)

#### h.
- Numbers: Top = 9, Bottom = 3, 6
- Addition Equations:
- \( 3 + 6 = 9 \)
- \( 6 + 3 = 9 \)
- Subtraction Equations:
- \( 9 - 3 = 6 \)
- \( 9 - 6 = 3 \)

#### i.
- Numbers: Top = 12, Bottom = 6, 6
- Addition Equations:
- \( 6 + 6 = 12 \)
- \( 6 + 6 = 12 \) (Note: Both additions are the same)
- Subtraction Equations:
- \( 12 - 6 = 6 \)
- \( 12 - 6 = 6 \) (Note: Both subtractions are the same)

Final Answer:

\[
\boxed{
\begin{array}{lll}
\text{a.} & 2 + 6 = 8, & 6 + 2 = 8, \\
& 8 - 2 = 6, & 8 - 6 = 2 \\
\text{b.} & 12 + 5 = 17, & 5 + 12 = 17, \\
& 17 - 12 = 5, & 17 - 5 = 12 \\
\text{c.} & 2 + 18 = 20, & 18 + 2 = 20, \\
& 20 - 2 = 18, & 20 - 18 = 2 \\
\text{d.} & 7 + 9 = 16, & 9 + 7 = 16, \\
& 16 - 7 = 9, & 16 - 9 = 7 \\
\text{e.} & 7 + 11 = 18, & 11 + 7 = 18, \\
& 18 - 7 = 11, & 18 - 11 = 7 \\
\text{f.} & 1 + 4 = 5, & 4 + 1 = 5, \\
& 5 - 1 = 4, & 5 - 4 = 1 \\
\text{g.} & 9 + 2 = 11, & 2 + 9 = 11, \\
& 11 - 9 = 2, & 11 - 2 = 9 \\
\text{h.} & 3 + 6 = 9, & 6 + 3 = 9, \\
& 9 - 3 = 6, & 9 - 6 = 3 \\
\text{i.} & 6 + 6 = 12, & 6 + 6 = 12, \\
& 12 - 6 = 6, & 12 - 6 = 6 \\
\end{array}
}
\]