Ray's New Practical Arithmetic · Arts. 106–108 · Unit 10: Fractions
55. Higher terms, lowest terms, common denominators
Goal: Your child raises a fraction to a given denominator, reduces a fraction to lowest terms, and brings several fractions to their least common denominator.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case IV (to higher terms), Case V (to lowest terms, using the greatest common divisor) and Case VI (to the least common denominator, using the least common multiple), each with a rule and problems.
The lesson, step by step
Warm-up
Mental: 1/2 = ?/8; 3/4 = ?/12; 6/8 = ?/4.
Case IV
Read:
A fraction is reduced to higher terms by multiplying both terms by the same number.
Divide the required denominator by the denominator of the given fraction.
Multiply both terms of the fraction by the quotient; the result will be the required fraction.
Example: 4/5 to thirtieths: 30 ÷ 5 = 6, so 24/30.
Case V
Read:
Divide both terms of the given fraction by their greatest common divisor.
The resulting fraction will be in its lowest terms.
Example: 18/24: G. C. D. 6, so 3/4.
Case VI
Read:
A common denominator of two or more fractions is a common multiple of their denominators.
Find the L. C. M. of the denominators of the fractions for their least common denominator.
The book's example has denominators 4, 6, 9 and 12: their L. C. M. is 36, so each fraction becomes thirty-sixths.
Guided practice
Do two problems from each case together.
Independent practice
Your child does about six problems from each case. Spend more time on Case V; lowest terms is used everywhere afterward.
Check and wrap-up
Lowest-terms answers are printed. Check Case IV problems by reducing the answer back to lowest terms. Mental: 10/15 in lowest terms? (2/3.)
Tip
Case V begins on p. 141; its rule is at the top of p. 142.