Ray's New Elementary Algebra · Arts. 113–127 · Unit 3: Chapter III: Algebraic fractions

17. What an algebraic fraction is

Goal: Your student can name the kinds of fractions and explains what multiplying or dividing the numerator or denominator does to a fraction's value.

⏱ About 35 minutes · 6 steps

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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

Definitions: fraction, entire and mixed quantities, improper, simple, compound and complex fractions, numerator and denominator; the two ways to look at a fraction (3 apples shared among 4 boys); and Propositions I to VI on changing the terms. No exercises.

The lesson, step by step

  1. Warm-up

    Draw a line and split it into 4 equal parts. Ask your student to show 3/4 of it.

  2. Definitions

    Read Arts. 113 to 120.

    A Fraction is an expression representing one or more of the equal parts into which a unit is supposed to be divided.

    A Complex Fraction is one that has a fraction either in its numerator or denominator, or in both.

    Write a few examples of each kind and have your student name them.

  3. Two ways to see a fraction

    Read Art. 121 (3 apples shared among 4 boys). Say: 3/4 is three of the quarters of one apple, or a quarter of three apples. Act it out with paper circles if you like.

  4. Propositions I to IV

    Read Arts. 122 to 125. Test each with 2/5: double the numerator (4/5, twice as big); halve the numerator; double the denominator (2/10, half as big); halve the denominator.

    Have your student state each one in words after testing it.

  5. Propositions V and VI

    Read Arts. 126 and 127.

    Multiplying both terms of a fraction by the same number or quantity, changes the form of a fraction, but does not alter its value.

    SayThis one rule is behind reducing, common denominators and almost everything else in this chapter.

  6. Wrap-up

    Ask: What happens to a/b if we multiply the numerator by 3 and the denominator by 3? Why?

Afterwards

Before the next session, have your student write Propositions V and VI in the rule notebook.

Tip

Use plain numbers to test every proposition. Students trust a rule they have checked themselves.

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