Ray's New Elementary Algebra · Arts. 53–55 · Unit 1: Chapter I: Fundamental rules
4. Addition
Goal: Your student adds similar terms with the same or different signs, and adds polynomials by lining up similar terms.
You'll need
- The book, open to the page
- Pencil and plenty of paper (or a whiteboard)
- A card to cover printed answers
What's in the book
The three cases of addition, each with a rule: similar terms with the same sign; similar terms with unlike signs (with a merchant's gains and losses); and unlike or partly like terms. Each case has worked examples and exercises with printed answers.
The lesson, step by step
Warm-up
Ask: Are 4xy and −3xy similar? Are 2a and 2b? Then: 5 apples and 3 apples make how many? 5 apples and 3 pears?
Case I: same signs
Read the apple example (three pockets with 3, 4 and 5 apples) and the rule:
Add together the coefficients of the several quantities;
to their sum prefix the common sign, and annex the common letter or letters.
Say3a + 4a + 5a is 12a. And −3a, −4a and −5a make −12a: the sign stays.
Case II: unlike signs
Read the merchant example and the rule:
TO ADD LIKE QUANTITIES WHICH HAVE UNLIKE SIGNS,
SayAdd up the plus coefficients, add up the minus ones, subtract the smaller total from the larger, and keep the sign of the larger.
Gains of 3a and 8a, losses of 2a and 5a: 11a − 7a = 4a.
Guided practice
Cover the answers. Your student does these while you watch:
8. Of 2ab, 5ab, 8ab, and 11ab? Ans. 26ab.
9. Of 6a— 4b, 3a+2b, —7a— 8b, and — a+9b? Ans. a — b.
For the second, add the a column and the b column separately.
Case III: unlike terms
Read the rule:
1. Write the quantities to be added, placing those that are similar under each other.
2. Add similar terms, and annex the others, with their proper signs.
Work exercise 2 together, writing the two lines under each other: 6a − 4c + 3b and −2a − 3c − 5b. The sum is 4a − 7c − 2b.
Independent practice
Your student works Case I exercises 7 to 10, Case II exercises 5 to 13, and Case III exercises 3 to 9, checking each against the printed answer.
Check by numbers
Pick one finished problem. Put a = 2, b = 1 into the question and into the answer; both should give the same number. The site's calculator (/homeschool/calculator/) can do this check too, but only after the work is done by hand.
Wrap-up
Your student states the three cases in their own words.
Tip
Lining up similar terms in columns, as the rule says, prevents nearly every mistake in this lesson.
Answers to the book's problems
The book prints the answer after each exercise.
Worked out for this site from the scan. If a number in your copy differs, trust the book. Every answer is in the Key ↗.