Discover Mathematics P5: Term 2, Unit 9, Lessons 5–8
GoalMultiply two mixed numbers with an area model and with improper fractions.
New words
area model · a rectangle cut into boxes whose areas are addedpartial product · the product of one part of each numberestimate · a close answer found with easy numbers
Explanation
Two mixed numbers can be multiplied with an area model. Draw a rectangle whose sides are the two numbers, and split each side into its whole part and its fraction part. That makes four boxes. For 2 1/2 × 1 1/3 the boxes are 2 × 1 = 2, 2 × 1/3 = 2/3, 1/2 × 1 = 1/2 and 1/2 × 1/3 = 1/6. Add them with a common denominator of 6: 2 + 4/6 + 3/6 + 1/6 = 2 + 8/6 = 3 1/3. The second way is to change both numbers into improper fractions: 5/2 × 4/3 = 20/6 = 10/3 = 3 1/3. Same answer. Before you start, estimate with easy numbers (2 1/2 is about 3 and 1 1/3 is about 1, so the answer is about 3) to check that your answer is sensible.
2 1/2 × 1 1/3 = 2 + 2/3 + 1/2 + 1/6 = 3 1/3
1
1/3
2
2
2/3
1/2
1/2
1/6
Worked examples
2
1/4
3
6
3/4
1/3
2/3
1/12
Work out 3 1/3 × 2 1/4 with an area model. 3 × 2 = 6, 3 × 1/4 = 3/4, 1/3 × 2 = 2/3, 1/3 × 1/4 = 1/12. With denominator 12: 6 + 9/12 + 8/12 + 1/12 = 6 + 18/12 = 7 1/2.
Check it with improper fractions: 3 1/3 = 10/3 and 2 1/4 = 9/4. 10/3 × 9/4 = 90/12 = 15/2 = 7 1/2. Both ways give 7 1/2.
Estimate first, then work out 1 3/4 × 2 2/5. 1 3/4 is about 2 and 2 2/5 is about 2, so the answer is about 4. Exactly: 7/4 × 12/5 = 84/20 = 21/5 = 4 1/5. This is close to the estimate.
Class activity
Rectangle on squared paper. On squared paper draw a rectangle 2 1/2 squares long and 1 1/2 squares wide (cut half squares by drawing a diagonal or counting two halves as one). Mark the four boxes with a pencil, write the area of each, and add them. Check with improper fractions: 5/2 × 3/2.
Practice
1
Work out 1 1/2 × 2 1/3.
3/2 × 7/3 = 21/6 = 7/2 = 3 1/2.
2
Work out 2 1/4 × 1 1/3.
9/4 × 4/3 = 36/12 = 3.
3
Work out 3 1/2 × 2 1/2.
7/2 × 5/2 = 35/4 = 8 3/4.
4
Copy the area model and fill the four boxes for 2 1/2 × 2 1/2. Then add them.
