Adding and subtracting fractions with unlike denominators
الأسبوع 17 · جمع الكسور مختلفة المقام وطرحها · 3 دروس
3
Fraction stories to solve
Discover Mathematics P5: Term 2, Unit 7, Lessons 4–6
GoalSolve story problems that need adding or subtracting fractions with unlike denominators.
New words
whole · the full amount, written as 1part and whole · a part is a fraction of a whole; parts together make the wholewhat is left · the whole minus the parts already used
Explanation
In a fraction story the whole is 1. If you know two parts, you add them to find how much was used. To find what is left, subtract the used part from 1, and write 1 as a fraction with the right denominator (for example 1 = 20/20). Read the question twice, draw a bar for the whole, and mark the parts. Then choose add or subtract, solve with a common denominator, simplify, and write the answer as a sentence with the name of the thing (a book, a tank, a rope).
Worked examples
Karim reads 2/5 of a book on Monday and 1/4 on Tuesday. 2/5 + 1/4 = 8/20 + 5/20 = 13/20 of the book is read. What is left is 1 − 13/20 = 20/20 − 13/20 = 7/20.
A water tank is 3/4 full. Then 1/6 of the whole tank is used. How full is it now? 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
Salma paints 1/3 of a wall blue and 1/2 of it yellow. Painted: 1/3 + 1/2 = 2/6 + 3/6 = 5/6. Left unpainted: 1 − 5/6 = 1/6.
Class activity
Story workshop. Pick one of the situations (a book, a juice bottle, a garden bed, a rope). Write a story with two fractions that have different denominators and ask two questions: how much is used, and how much is left. Swap with the grown-up and solve each other’s stories, drawing a bar for each.
Practice
1
Ola walks 1/2 km to school and 2/5 km to the shop. How far does she walk in all?
1/2 + 2/5 = 5/10 + 4/10 = 9/10 km.
2
A recipe needs 3/4 cup of sugar but Mariam has only 2/3 cup. How much more does she need?
3/4 − 2/3 = 9/12 − 8/12 = 1/12 cup.
3
Mina gives 1/5 of his stickers to Hana and 1/2 to Nour. What fraction does he keep?
