Discover Mathematics P5: Term 2, Unit 8, Lessons 5–8
GoalAdd mixed numbers whose fractions have different denominators, in two ways: parts separately, or as improper fractions.
New words
improper fraction · a fraction with a numerator bigger than the denominator, such as 7/5convert · to change a mixed number into an improper fraction or backsum · the result of adding
Explanation
Method one: add the whole numbers, rewrite the fractions with a common denominator, add them, and change any extra wholes. 3 1/2 + 2 2/3 = (3 + 2) + (3/6 + 4/6) = 5 7/6 = 6 1/6. Method two: change each mixed number to an improper fraction (multiply the whole by the denominator and add the numerator), add the fractions with a common denominator, then change the result back. 1 2/5 = 7/5 and 3 1/2 = 7/2, so 7/5 + 7/2 = 14/10 + 35/10 = 49/10 = 4 9/10. Both methods give the same answer, so you can use one to check the other.
Two ways. The grown-up writes a sum of two mixed numbers with unlike fractions. The child solves it by method one, then by method two, and checks that the answers match. If they do not match, find the slip together. Do three sums.
Practice
1
Work out 2 1/4 + 1 2/3.
2 3/12 + 1 8/12 = 3 11/12.
2
Work out 4 5/6 + 2 3/4.
4 10/12 + 2 9/12 = 6 19/12 = 7 7/12.
3
Work out 1 3/10 + 2 4/5.
1 3/10 + 2 8/10 = 3 11/10 = 4 1/10.
4
Work out 2 1/3 + 1 1/2 with improper fractions.
7/3 + 3/2 = 14/6 + 9/6 = 23/6 = 3 5/6.
5
Youssef walks 2 3/4 km and then rides a bus for 5 1/2 km. How far does he travel?
