Egypt Primary 6 Mathematics, Week 2: Adding and subtracting fractions with the LCM as the common denominator

GCF, LCM and fraction sums

Week 2 · Writing sums with the GCF; the LCM and fractions with unlike denominators · 3 lessons

Adding and subtracting fractions with the LCM as the common denominator

Discover Mathematics P6: Term 1, Unit 1, Lessons 3–4

GoalAdd and subtract fractions with unlike denominators, simplify, and write a mixed number when needed.

New words

denominator · the bottom number of a fractioncommon denominator · a denominator that two fractions are both written withsimplify · divide the top and bottom by their GCFmixed number · a whole number and a fraction together

Explanation

We can only add or subtract fractions when the pieces have the same size, so the denominators must match. The best common denominator is the LCM of the two denominators. To add 1/4 + 1/6: the LCM of 4 and 6 is 12. Write 1/4 as 3/12 (multiply top and bottom by 3) and 1/6 as 2/12 (multiply by 2). Then add the numerators and keep the denominator: 3/12 + 2/12 = 5/12. Finally, simplify if you can, and if the answer is bigger than 1, write it as a mixed number.

★Remember

Find the LCM of the denominators, rewrite both fractions, add or subtract the tops, then simplify.

Worked examples

1/4 + 1/6. LCM = 12. 1/4 = 3/12 and 1/6 = 2/12, so 1/4 + 1/6 = 5/12. It cannot be simplified because 5 and 12 share only 1.

Step	Work
LCM of 6 and 8	24
Rewrite	5/6 = 20/24, 3/8 = 9/24
Subtract the tops	20/24 − 9/24 = 11/24

5/6 − 3/8. LCM of 6 and 8 is 24. 5/6 = 20/24 and 3/8 = 9/24. So 5/6 − 3/8 = 20/24 − 9/24 = 11/24.

Step	Work
LCM of 10 and 6	30
Add	21/30 + 5/30 = 26/30
Simplify (÷ 2)	13/15

7/10 + 1/6. LCM of 10 and 6 is 30. 7/10 = 21/30 and 1/6 = 5/30. The sum is 26/30. Both 26 and 30 divide by 2, so simplify: 26/30 = 13/15.

Class activity

Fraction pizza. Cut two paper circles, one into 4 equal parts and one into 6 equal parts. Cover 1/4 and 1/6 with 12ths made from a third paper circle cut into 12 parts. Count how many 12ths fit, and write the addition sentence.

Practice

1/3 + 1/4

3/4 − 2/5

5/6 + 3/4. Write the answer as a mixed number.

7/8 − 1/6

Amal uses 2/5 of a bag of flour on Monday and 1/4 of the bag on Tuesday. How much of the bag has she used, and how much is left?