Question

a. what are the other three members of this fact family? select all that apply.
a. 9+11=11+9
c. 9+2=11
e. 2-9=2+(-9)
g. 11-9=2
b. 11+2=9
d. 9-2=-(2-9)
f. 2+9=11
h. 2+9+11=0
b. draw four number line models to illustrate each of the number facts in part (a). identify the number fact that corresponds to the question mark in each graph.

Explanation:

Step1: Analyze Fact Family Basics

A fact family with numbers 2, 9, 11 (since \(9 + 2 = 11\)) includes addition (commutative) and subtraction (inverse) facts.

• Addition: \(a + b = c\), \(b + a = c\)
• Subtraction: \(c - a = b\), \(c - b = a\)

Step2: Evaluate Each Option

• Option A: \(9 + 11 = 11 + 9\) – Involves 9, 11, but not 2. Incorrect.
• Option B: \(11 + 2 = 9\) – \(11 + 2 = 13

eq 9\). Incorrect.

• Option C: \(9 + 2 = 11\) – Correct (addition fact).
• Option D: \(9 - 2 = -(2 - 9)\) – Simplify: \(9 - 2 = 7\), \(-(2 - 9) = 7\), but this is not a fact family with 2, 9, 11 (focuses on sign, not sum/difference). Incorrect.
• Option E: \(2 - 9 = 2 + (-9)\) – Just rewriting subtraction, not a fact family member. Incorrect.
• Option F: \(2 + 9 = 11\) – Correct (commutative addition: \(9 + 2 = 2 + 9 = 11\)).
• Option G: \(11 - 9 = 2\) – Correct (subtraction: \(11 - 9 = 2\), inverse of \(9 + 2 = 11\)).
• Option H: \(2 + 9 + 11 = 0\) – \(2 + 9 + 11 = 22

eq 0\). Incorrect.

Answer:

C. \(9 + 2 = 11\), F. \(2 + 9 = 11\), G. \(11 - 9 = 2\)