Ray's New Elementary Algebra · Arts. 153–154 · Unit 4: Chapter IV: Simple equations
25. Transposition and clearing of fractions
Goal: Your student moves a term across the equals sign by changing its sign, and clears an equation of fractions using the L.C.M.
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
Transposition explained with x − 3 = 5 and x + b = c, then clearing fractions by multiplying by the denominators or their L.C.M., with ten exercises. Answers are printed.
The lesson, step by step
Warm-up
Solve x + 5 = 12 and x − 4 = 9 aloud.
Transposition
Read Art. 153.
Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign be changed.
SayIt is a shortcut for adding or subtracting the same thing on both sides.
Clearing fractions
Read Art. 154 and the rule:
Find the least common multiple of all the denominators, and multiply each term of the equation by it.
Work example 1 together: x/2 + x/3 = 5. Multiply every term by 6: 3x + 2x = 30.
Guided practice
Your student clears exercises 2 and 3 while you watch, naming the L.C.M. aloud before multiplying. Compare with the printed answers.
Watch the minus before a fraction
In exercise 5 a fraction is subtracted. Its whole numerator changes sign when cleared. Do it together.
Independent practice
The remaining exercises (4 to 10). Compare each with the printed answer.
Wrap-up
Ask: Why multiply EVERY term, including the ones with no fraction?
Tip
The forgotten term is the classic error: when clearing fractions, a whole number on the right gets multiplied too.
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 ↗.