Rational and Irrational Numbers Question
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For the rational numbers [math]a_1, a_2 !=0[/math], prove that their sum is also a rational number.
| [math] " Statement " [/math] | [math] " Reason "[/math] |
| [math]1. a_1, a_2 in QQ[/math] | [math]1. "Given"[/math] |
| [math]2. a_1 = p_1/q_1, a_2 = p_2/q_2, \ \ \ " where " p_1, p_2, q_1, q_2 in ZZ[/math] | [math]2. ""[/math] |
| [math]3. a_1 + a_2 = p_1/q_1 + p_2/q_2[/math] | [math]3. "Addition Property of Equality"[/math] |
| [math]4. a_1 +a_2 = p_1/q_1 (q_2/q_2) + p_2/q_2 (q_1/q_1) [/math] | [math]4. "Multiplicative Identity Property"[/math] |
| [math]5. a_1 + a_2 = (p_1 q_2 + p_2 q_1) / (q_1 q_2)[/math] | [math]5. "Distributive Property"[/math] |
| [math]6. p_1q_2, \ p_2q_1, \ q_1q_2 in ZZ[/math] | [math]6. ""[/math] |
| [math]7. p_1q_2 + p_2q_1 in ZZ[/math] | [math]7. "Integers are closed under addition"[/math] |
| [math]8. a_1 + a_2 = (p_1 q_2 + p_2 q_1) / (q_1 q_2) in QQ[/math] | [math]8. "Definition of rational numbers"[/math] |
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
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