Week 9 · Multiplying decimals, first steps · 3 lessons
3
Tenths times tenths, and estimating products
Discover Mathematics P5: Term 1, Unit 5, Lessons 1–4
GoalMultiply tenths by tenths with a grid model and estimate decimal products.
New words
grid model · a square cut into 100 equal small squares to show hundredthsestimate · a close answer found by rounding
Explanation
What is 0.3 × 0.4? It means 3 tenths of 4 tenths. Draw a square grid of 100 small squares as one whole. Each column is one tenth of the whole. Shade 4 tenths in one direction and 3 tenths in the other. The overlap is 3 columns by 4 rows, which is 12 small squares out of 100, so 0.3 × 0.4 = 0.12. The rule: multiply 3 × 4 = 12, then count the decimal places in both factors (1 + 1 = 2) and give the product that many places: 0.12. The product is smaller than both factors because we take a part of a part. To estimate, round to numbers that are easy to multiply: 4.8 × 0.5 is close to 5 × 0.5 = 2.5.
Worked examples
Work out 0.3 × 0.4 with the grid. The shaded rectangle is 3 squares wide and 4 squares tall, which is 12 of the 100 squares. So 0.3 × 0.4 = 0.12. Check with the rule: 3 × 4 = 12 and two decimal places.
Work out 0.6 × 0.5. 6 × 5 = 30 and there are two decimal places, so the product is 0.30, which is 0.3. On the grid 6 columns by 5 rows is 30 squares, which is 30 hundredths = 3 tenths. Half of 0.6 is 0.3.
Work out 1.2 × 0.4. 12 × 4 = 48 and two decimal places make 0.48. Estimate: 1 × 0.4 = 0.4, and 0.48 is close. And 4.8 × 0.5: estimate 5 × 0.5 = 2.5. Exact: 48 × 5 = 240, one + one decimal places make 2.40 = 2.4, close to 2.5.
Class activity
Paper grid. Draw a 10 by 10 grid on squared paper. Shade a rectangle for 0.7 × 0.6 (7 columns by 6 rows). Count the shaded squares and write the product as a decimal. Do the same for 0.5 × 0.5 and 0.9 × 0.2. Notice that each product is smaller than both factors.
