Ray's New Higher Arithmetic · Arts. 143–144 · Unit 8: Common Fractions
36. Dividing fractions and complex fractions
Goal: Your student divides with fractions by inverting the divisor, and simplifies complex fractions.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Division of fractions in three cases, the rule (multiply by the divisor inverted), the reason for inverting, 25 examples with answers, then reducing complex fractions to simple ones (Art. 144) with 10 examples.
The lesson, step by step
Warm-up
Mental: How many halves in 3? How many quarters in 3/4?
The idea
Read:
Division of Fractions is finding the quotient when the dividend or divisor is fractional, or when both are fractional.
Multiply the dividend by the divisor with its terms inverted.
Why invert
The book's first method brings both fractions to a common denominator and divides the numerators: 3/4 ÷ 2/3 = 9/12 ÷ 8/12 = 9 ÷ 8 = 9/8. Then:
The same result is obtained by multiplying the dividend by the divisor, with its terms inverted.
Mixed numbers
Read:
Mixed numbers must be reduced to improper fractions. Use cancellation when applicable.
Complex fractions
A complex fraction has a fraction in one or both terms. Read:
Divide the numerator by the denominator, as in division of fractions.
Work (2½)/(3¾) = 5/2 ÷ 15/4 = 5/2 × 4/15 = 2/3.
Independent practice
Your student works a selection of the 25 division examples and the complex fraction examples.
Check
Answers are printed.
Wrap-up
Ask: Is 6 ÷ 1/2 bigger or smaller than 6? (Bigger: 12. There are 12 halves in 6.)
Tip
The scan's small printed fractions are often hard to read. Keep the paper book or a clear copy of the page open when your student works the examples.