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Type: Multiple-Choice
Category: Rational and Irrational Numbers
Level: Grade 11
Standards: HSN-RN.B.3
Author: nsharp1
Created: 5 years ago

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Rational and Irrational Numbers Question

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For the rational numbers

$a_1, a_2 !=0$ , prove that their sum is also a rational number.

$" Statement "$	$" Reason "$
$1. a_1, a_2 in QQ$	$1. "Given"$
$2. a_1 = p_1/q_1, a_2 = p_2/q_2, \ \ \ " where " p_1, p_2, q_1, q_2 in ZZ$	$2. ""$
$3. a_1 + a_2 = p_1/q_1 + p_2/q_2$	$3. "Addition Property of Equality"$
$4. a_1 +a_2 = p_1/q_1 (q_2/q_2) + p_2/q_2 (q_1/q_1)$	$4. "Multiplicative Identity Property"$
$5. a_1 + a_2 = (p_1 q_2 + p_2 q_1) / (q_1 q_2)$	$5. "Distributive Property"$
$6. p_1q_2, \ p_2q_1, \ q_1q_2 in ZZ$	$6. ""$
$7. p_1q_2 + p_2q_1 in ZZ$	$7. "Integers are closed under addition"$
$8. a_1 + a_2 = (p_1 q_2 + p_2 q_1) / (q_1 q_2) in QQ$	$8. "Definition of rational numbers"$

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

What is the missing reason in step 2?

Given
Division Property of Equality
Definition of rational numbers
Any number can be rewritten in another form