Ray's New Practical Arithmetic · Arts. 112–114 · Unit 10: Fractions
57. Subtracting fractions
Goal: Your child subtracts fractions and mixed numbers, borrowing a whole when needed.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Subtraction of fractions, Case I (common denominator) and Case II (different denominators), with rules, a borrowing example with mixed numbers, and problems.
The lesson, step by step
Warm-up
Mental: 5/7 − 2/7? 1 − 1/3? 1/2 − 1/4?
Case I
Read:
Subtraction of Fractions is the process of finding the difference between two fractional numbers.
From the greater numerator subtract the less; under the remainder write the common denominator.
Example: 5/7 − 2/7 = 3/7.
Borrowing
Show a mixed-number example like the book's: 3 1/4 − 3/4. 3/4 can't come from 1/4, so borrow 1 from the 3: 2 5/4 − 3/4 = 2 2/4 = 2 1/2.
Case II
Read:
When the fractions have not a common denominator.
Reduce the fractions to a common denominator.
Example: 3/4 − 2/3 = 9/12 − 8/12 = 1/12.
Independent practice
Your child does about eight problems from each case.
Check and wrap-up
Many answers are printed; for the rest, check by adding the answer to the number subtracted. Mental: 1 − 5/8? (3/8.)
Tip
Some problems on these pages have no printed answer. Checking by addition is the book's own proof and teaches more than an answer key would.