Ray's New Higher Arithmetic · Arts. 136–139 · Unit 8: Common Fractions
33. Common denominators
Goal: Your student brings fractions to a common denominator and to the least common denominator.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Common denominator and least common denominator defined, two principles, Case VI (any common denominator, by multiplying both terms by the other denominators) and Case VII (the least common denominator, by the L. C. M.), with examples and printed answers.
The lesson, step by step
Warm-up
Mental: Which is larger, 2/3 or 3/4? How can you be sure?
The idea
Read:
A common denominator of two or more fractions, is a denominator by which they express like parts of a unit.
Only a common multiple of different denominators can become a common denominator.
Case VI
Read:
Multiply both terms of each fraction by the denominators of the other fractions.
The book's example: 1/2, 2/3, 3/4 become 12/24, 16/24, 18/24.
The values of the fractions are unaltered.
Case VII
Read:
Find the L. C. M. of the denominators of the given fractions, for the L. C. D.
Divide this L. C. D. by the denominator of each fraction, and multiply the numerator by the quotient.
The book's example uses denominators 8, 9 and 24, with L. C. D. 72: 5/8 becomes 45/72.
Guided practice
Together, bring 1/2, 2/3, 3/4 to their least common denominator. (6/12, 8/12, 9/12: smaller than 24ths.)
Independent practice
Your student works the examples under both cases. The book prints the answers.
Wrap-up
Ask: Now which is larger, 2/3 or 3/4? (3/4: 9/12 against 8/12.)
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.