Ray's New Higher Arithmetic · Arts. 107–123 · Unit 8: Common Fractions
30. What a fraction is
Goal: Your student names the terms of a fraction, explains what each term tells, and sorts fractions into proper, improper, mixed, simple, complex and compound.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Fraction defined, common and decimal fractions, the denominator and numerator, three things every fraction implies, two ways of reading 4/5, the value of a fraction, and the classes of fractions by value and form.
The lesson, step by step
Warm-up
Cut a sheet of paper into 5 equal strips. Hand over 4. Ask: What part of the sheet do you have?
The idea
Read:
A Fraction is an expression for one or more of the equal parts of a divided whole.
The Denominator is the number below the line.
The Numerator is the number above the line.
The book's note: the denominator names the parts; the numerator numbers them.
Two readings
The book says 4/5 can mean 4 fifths of one thing, or 1 fifth of 4 things. Show both: 4 of the 5 strips, and a fifth of 4 whole sheets. They are the same amount.
Value
Read:
The value of a fraction is its relation to a unit.
A fraction is also an indicated division: 3/4 means 3 ÷ 4.
Classes of fractions
Read and give an example of each:
one whose numerator is less than its denominator.
(proper)
one whose numerator is equal to, or greater than, its denominator.
(improper)
a number composed of an integer and a fraction.
(mixed)
one which has one or both of its terms fractional.
(complex)
a fraction of a fraction.
(compound)
Practice
You write ten fractions of mixed kinds; your student labels each. Include 7/7, 2½/3 and 2/3 of 3/4.
Wrap-up
Read:
An Integer may be expressed as a fraction by writing 1 under it as a denominator.
Ask: Write 9 as a fraction. (9/1.)
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.