3
Models for mixed numbers with unlike denominators
Discover Mathematics P5: Term 2, Unit 8, Lessons 1–4
GoalUse bar models to add and subtract mixed numbers when the fraction parts have different denominators.
New words
bar model · a drawing of bars that shows the sizes of the partswhole · a complete barfraction part · the part of a mixed number that is less than a whole
Explanation
Draw each mixed number as whole bars plus a part of a bar. To add 1 1/2 + 1 1/3, draw 1 whole and 1/2 in the first row, 1 whole and 1/3 in the second. The wholes together are 2. The parts 1/2 and 1/3 need the same size pieces: sixths. 1/2 = 3/6 and 1/3 = 2/6, so together they are 5/6. The total is 2 5/6. To subtract, start from the larger mixed number and take away the whole bars first, then the fraction. If you do not have enough of the fraction, cut one whole bar into pieces of the right size.
Worked examples
Add 1 1/2 + 1 1/3. Wholes: 1 + 1 = 2. Parts: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Answer: 2 5/6.
Add 2 1/2 + 1 1/4. Wholes: 3. Parts: 2/4 + 1/4 = 3/4. Answer: 3 3/4.
Subtract 3 1/2 − 1 1/3. Wholes: 3 − 1 = 2. Parts: 1/2 − 1/3 = 3/6 − 2/6 = 1/6. Answer: 2 1/6.
Class activity
Bar drawing. On squared paper draw 2 1/3 + 1 1/2 using bars where one whole is 6 squares long. Cut the bars to show thirds (2 squares) and halves (3 squares). Count the squares for the total and write it as a mixed number.
Practice
1
Work out 1 1/4 + 2 1/2 with a model.
Wholes 3. Parts 1/4 + 2/4 = 3/4. Answer 3 3/4.
2
Work out 2 2/3 + 1 1/6.
Wholes 3. Parts 4/6 + 1/6 = 5/6. Answer 3 5/6.
3
Work out 4 3/4 − 1 1/2.
Wholes 3. Parts 3/4 − 2/4 = 1/4. Answer 3 1/4.
4
Work out 3 1/2 − 1 2/3. Cut a whole into sixths.
3 3/6 − 1 4/6 = 2 9/6 − 1 4/6 = 1 5/6.
5
Work out 2 1/3 + 1 1/2 with a model and check with an estimate.
Wholes 3. Parts 2/6 + 3/6 = 5/6. Answer 3 5/6. Estimate: 2 + 2 = 4, which is close.