Ray's New Practical Arithmetic · Arts. 109–111 · Unit 10: Fractions
56. Adding fractions
Goal: Your child adds fractions with the same and with different denominators, and adds mixed numbers.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Addition of fractions, Case I (common denominator) and Case II (different denominators), with rules, remarks on mixed numbers, and problems with answers.
The lesson, step by step
Warm-up
Mental: 1/5 + 2/5? 1/2 + 1/4? 1/3 + 1/6?
Case I
Read:
Addition of Fractions is the process of finding the sum of two or more fractional numbers.
Add the numerators; under the sum write the common denominator.
Example from the book: 1 fifth, 2 fifths and 3 fifths make 6 fifths, which is 1 1/5.
Tidy the answer
Read:
The result, if an improper fraction, must be reduced to an integer, or a mixed number (Art. 105).
The result must be reduced to its lowest terms (Art. 107).
Case II
Read:
When the fractions have not a common denominator.
Reduce the fractions to a common denominator.
Example: 1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12.
Mixed numbers
Read:
Integers and fractions may be added separately and their sums then united.
Example: 2 1/2 + 3 3/4: whole numbers 5, fractions 5/4 = 1 1/4, total 6 1/4.
Independent practice
Your child does about eight Case I and eight Case II problems, including some mixed numbers.
Check and wrap-up
Answers are printed after the problems. Mental: 3/4 + 3/4? (1 1/2.)