☰ Year plan · Mathematics

Unit fractions and mixed numbers

Week 16 · Unit fractions and mixed numbers · 3 lessons
3

Wholes and parts together: mixed numbers

Discover Mathematics P4: Term 2, Unit 9, Lessons 1–4
GoalWrite mixed numbers and fractions greater than 1, and place them on a number line.
New words
mixed number · a whole number and a fraction together, such as 1 3/4fraction greater than 1 · a fraction whose numerator is bigger than its denominator, such as 7/4whole number · 0, 1, 2, 3 and so on
Explanation

When we have more than one whole we can write the amount in two ways. A mixed number puts the wholes and the extra fraction together: 1 3/4 is one whole and 3/4 more. A fraction greater than 1 counts all the pieces: 7/4 is seven quarters. They are the same, because 4/4 is one whole and 7/4 = 4/4 + 3/4 = 1 3/4. To change a mixed number into a fraction, make each whole into pieces and add: 2 1/3 = 3/3 + 3/3 + 1/3 = 7/3, or 2 × 3 + 1 = 7 thirds. To change 11/4 into a mixed number divide: 11 ÷ 4 = 2 R 3, so 11/4 = 2 3/4. On a number line the point 7/4 and the point 1 3/4 are the same point.

01/42/43/44/45/46/47/48/41 3/4
Worked examples
01/42/43/44/45/46/47/48/47/4
Change 7/4 into a mixed number. 4/4 is one whole and 3/4 is left: 7/4 = 1 3/4. On the number line the point is 3 steps after 1.
2 1/31/31/31/31/31/31/31/3
Change 2 1/3 into a fraction. Each whole is 3/3, so two wholes are 6/3. Add 1/3: 6/3 + 1/3 = 7/3. The bar shows seven pieces of 1/3.
Rahma walks 3 1/2 km to her grandmother. Write it as halves: each km is 2/2, so 3 km is 6/2, and 6/2 + 1/2 = 7/2 km. Check: 3 × 2 + 1 = 7.
Class activity

Count in quarters. Start at 0 and count in steps of 1/4 up to 3: 1/4, 2/4, 3/4, 4/4... Say each answer as a fraction and as a mixed number when it is more than 1, for example 5/4 is 1 1/4.

Practice
1
Write 9/4 as a mixed number.
2
Write 3 2/5 as a fraction.
3
How many pieces of 1/6 are in 2 5/6?
4
A jug holds 1 1/2 litres of juice. Write the amount as a fraction of halves.
5
Seif says 2 1/4 = 3/4 because 2 + 1 = 3. What is wrong? Give the right fraction.