Ray's New Higher Arithmetic · Arts. 140–141 · Unit 8: Common Fractions
34. Adding and subtracting fractions
Goal: Your student adds and subtracts fractions and mixed numbers, reducing the answer to lowest terms.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Addition of fractions (definition, principle, rule, remarks, 11 examples) and subtraction of fractions (definition, rule, remarks on mixed numbers including borrowing a unit, and examples to about 23, among them word problems about a share of a ship and a farm). Answers are printed.
The lesson, step by step
Warm-up
Mental: 1/2 + 1/4; 3/4 − 1/2; 1 − 3/8.
Adding
Read:
Addition of Fractions is the process of uniting two or more fractional numbers in one sum.
Reduce the fractions to a common denominator, add their numerators, and write the sum over the common denominator.
Remind your student: like parts of like units only.
Mixed numbers
The book adds the whole numbers and the fractions separately, then puts them together. Work 2⅓ + 3¾ = 5 + 13/12 = 6 1/12.
Subtracting
Read:
Subtraction of Fractions is the process of finding the difference between two fractional numbers.
Reduce the fractions to a common denominator, and write the difference of their numerators over the common denominator.
When the fraction below is bigger, take a unit from the whole number. Work 7¼ − 2⅔: write 7 3/12 − 2 8/12; take a unit from the 7 to make 6 15/12; then 6 15/12 − 2 8/12 = 4 7/12.
Independent practice
Your student works a good selection of the addition examples and the subtraction examples, including the word problems near the end.
Check
Answers are printed; the small fractions in the scan can be hard to read, so use a clear copy.
Wrap-up
Ask: Why must fractions have the same denominator before adding? (Only like parts can be added, just as only like units can.)
Afterwards
Split addition and subtraction over two days if needed.
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.