Mixed numbers: like denominators, common denominators and models
Week 18 · Mixed numbers · 3 lessons
1
Mixed numbers with like denominators
Discover Mathematics P5: Term 2, Unit 8, Lessons 1–4
GoalAdd and subtract mixed numbers that have the same denominator, regrouping a whole when needed.
New words
mixed number · a whole number and a fraction together, such as 2 3/8regroup · to change 1 whole into parts of the same size as the fraction, such as 1 = 6/6improper fraction · a fraction at least as big as 1, such as 10/8
Explanation
A mixed number such as 2 3/8 means 2 wholes and 3 eighths. To add mixed numbers with the same denominator, add the whole numbers, add the fractions, and then change any extra wholes: 2 3/8 + 1 7/8 = 3 10/8 = 3 + 1 2/8 = 4 2/8 = 4 1/4. To subtract, subtract the fractions and then the wholes. If the first fraction is too small, regroup one whole into parts of the same size: 5 1/6 − 2 5/6 cannot take 5/6 from 1/6, so write 5 1/6 as 4 7/6 (because 1 = 6/6 and 6/6 + 1/6 = 7/6). Then 4 7/6 − 2 5/6 = 2 2/6 = 2 1/3.
Regrouping practice. Cut a sheet of paper into 6 strips and call each strip 1/6, and use 5 whole sheets. Show 5 1/6 with the sheets and one strip. To take away 2 5/6, you must cut one whole sheet into strips. Do it and count what is left. Explain to the grown-up why 5 1/6 became 4 7/6.
Practice
1
Work out 3 2/5 + 1 1/5.
4 3/5.
2
Work out 2 5/6 + 3 4/6 and simplify.
5 9/6 = 6 3/6 = 6 1/2.
3
Work out 6 7/8 − 2 3/8.
4 4/8 = 4 1/2.
4
Work out 5 1/4 − 2 3/4 by regrouping.
5 1/4 = 4 5/4. 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2.
5
A rope is 4 3/10 m long. Ahmed cuts off 1 7/10 m. How much is left?
