Ray's New Higher Arithmetic · Arts. 124–129 · Unit 8: Common Fractions
31. Reading, writing and the principles of fractions
Goal: Your student finds reciprocals, reads and writes fractions, and knows how multiplying or dividing either term changes a fraction's value.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Reciprocals, similar and dissimilar fractions, numeration and notation of fractions with ten fractions to write in figures (no answers printed), and the general principles: how a fraction is multiplied, divided, or left unchanged.
The lesson, step by step
Warm-up
Ask: Which is bigger, 3/8 or 3/5? Why?
Reciprocals and like fractions
Read:
The Reciprocal of a number is 1 divided by that number.
Similar Fractions are those that have the same denominator.
Ask: The reciprocal of 5? (1/5.) Of 1/5? (5.)
Reading and writing
Read the rule for reading:
Read the number of parts taken as expressed by the numerator
then name the size of the parts. Your student writes the ten fractions on the page in figures, beginning:
Seven eighths
Four elevenths
The principles
Read:
A Fraction is multiplied, 1st. By multiplying the numerator.
A Fraction is divided, 1st. By dividing the numerator.
The value of a Fraction is not changed, 1st. By multiplying both terms by the same number.
The book's second ways: multiplying a fraction by dividing its denominator, and dividing it by multiplying its denominator.
Try them
Start with 4/12. Multiply it by 2 two ways: double the numerator (8/12) or halve the denominator (4/6). Divide it by 2 two ways: halve the numerator (2/12) or double the denominator (4/24). Show that 8/12 = 4/6 and 2/12 = 4/24.
Wrap-up
Ask: What can you do to both terms without changing the value? (Multiply or divide both by the same number.)
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.
Answers to the book's problems
Fractions to write: 7/8, 4/11, 5/13, 1/17, 3/29, 8/21, 9/42, 19/93, 13/100, 24/115.
Worked out for this site from the scan. If a number in your copy differs, trust the book.