21. Adding and subtracting fractions

The lesson, step by step

1. Warm-up

   Find the least common denominator of 1/ab, 1/bc and 1/ac. (abc.)

2. Same denominator

   Read Art. 137, examples 1 and 2. Say: a/m + b/m = (a + b)/m, just as 3 fifths and 2 fifths make 5 fifths.

3. The rules

   Reduce the fractions, if necessary, to a common denominator; add the numerators together, and write their sum over the common denominator.

   Reduce the fractions, if necessary, to a common denominator; subtract the numerator of the subtrahend from the numerator of the minuend, and write the remainder over the common denominator.

4. Work one together

   Addition exercise 12: (a − b)/ab + (b − c)/bc + (c − a)/ac. Over abc the numerators are c(a − b), a(b − c) and b(c − a). Multiply out: ac − bc + ab − ac + bc − ab = 0. The answer is 0, as printed.

5. Guided practice

   Your student does addition exercises 4 and 6 and subtraction exercises 1 and 2 while you watch. In subtraction, put the second numerator in parentheses before changing its signs.

6. Independent practice

   The remaining addition and subtraction exercises. Mixed quantities (exercise 13 onward) may be added separately or turned into fractions first.

7. Check

   Pick one answer and check it with numbers (a = 2, b = 3, c = 5). After working by hand, your student may confirm on the site's calculator (/homeschool/calculator/).

8. Wrap-up

   Ask your student to explain exercise 12's answer of 0 in their own words.