K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will be able to add fractions with different denominators.

Teacher planning

Time required for lesson

1.5 hours


  • Students will need their math books, pencils and paper
  • Teachers will need colored markers or chalk and fraction pie circles with pieces for 6/6 and 8/8


Students will need to know how to simplify fractions, add fractions with like denominators, write numbers as Product of Primes, and Multiply Fractions.


  1. On the board write the fraction problems: 1/5+3/5 (vertical), 3/4*1/5 (horizontal), 5/6-3/8 (vertical), and 5/9+7/15 (vertical). Also, write the numbers 7, 10 and 24.
  2. Review fractions: “We know how to do the first two problems. When we add or subtract fractions with the bottoms the same, we do the top and keep the bottom. 1/5+3/5=4/5. When we multiply fractions we do the top AND the bottom. 3/4*1/5=3/20.”
  3. Review Prime factors: “Remember factors can be written in any order! 7 is a prime number. The only multiplication problem we can write is 1*7. 10 is not prime so we can write the problems 2*5 and 1*10. 24 is not prime but there are many problems we can write. 2*12, 3*8, 4*6, and 1*24. If we write 24 as the product of primes we get only one problem 2*2*2*3.”
  4. Fraction pies: “When we look at 5/6-3/8 we see a problem. The bottoms are not the same so we cannot keep the bottom. If we try to use some pie pieces to make a circle and use some pieces from the 6/6 pie and some pieces from the 8/8 pie, we can’t make a flat circle with the mixed pieces. We have to make the bottoms (pie pieces) the same size.”
  5. Multiply by one: “Any time you multiply by one the result is the same number.”
  6. Choosing the fraction to multiply by: “5/6-3/8 have bottoms of 6 and 8. The prime factors of 6 are 2*3 and the prime factors of 8 are 2*2*2. Write these factors before the 6 and 8 in the problem. Mark out what is the same in both numbers (2) and mark them out. Then take the remaining numbers and multiply the other fraction by the fraction with that number on top and bottom.”
                  5  *  4  =  20    2*3       6  *  4  =  24            - 3  *  3  =   9   2*2*2      8  *  3  =  24                          11                          24
  7. Repeat with 5/9+7/15. (3’s are marked out.)
  8. Assign the appropriate number of problems from their math book. Monitor their work carefully to ensure mastery.


Students will solve 9 out of 12 problems on the test for adding and subtracting fractions with unlike denominations.

Supplemental information

Fractions: rtf | jpg


This is an algebraic method of adding fractions. It works well in the high school class for adding fractions with quadratic denominators. I have adapted the method for students who have problems doing basic math.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 5

        • 5.NOF.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 +...

North Carolina curriculum alignment

Mathematics (2004)

Grade 5

  • Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
    • Objective 1.02: Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).
      • Develop and analyze strategies for adding and subtracting numbers.
      • Estimate sums and differences.
      • Judge the reasonableness of solutions.