✖️ Multiply Decimals (Grade 5)
Complete Notes & Formulae — All Methods & Models
Key Concepts
- To multiply decimals, ignore the decimals and multiply as whole numbers.
- Count total decimal places in both numbers; that’s how many places in the answer.
- Visual methods (area and grid models) help see why decimal place value matters.
1️⃣ Steps: Multiplying Two Decimals
Standard Algorithm:
- 1 Ignore the decimals. Multiply as normal.
- 2 Count the total number of decimal places in both factors.
- 3 Insert the decimal in your answer so there are that many decimal places.
Example: \(0.43 \times 0.7\)
- Ignore decimals: \(43 \times 7 = 301\)
- Total decimal places: 2 (in \(0.43\)) + 1 (in \(0.7\)) = 3
- Final answer: \(0.301\) (insert decimal so answer has 3 decimal places)
Example: \(1.24 \times 3.5\)
- Ignore decimals: \(124 \times 35 = 4,340\)
- Decimal places: 2 + 1 = 3
- Answer: \(4.340 \rightarrow 4.34\) (trailing zero dropped)
2️⃣ Grid & Area Models (Visual)
- Draw a 10x10 grid (100 squares = 1 whole; each square = 0.01)
- Shade rows for the first decimal (e.g., 0.7 = 7 rows), columns for the second (e.g., 0.4 = 4 columns); overlapping area = product.
- Great for understanding how partial products add up for decimals less than 1.
Example: \(0.6 \times 0.3\)
Shade 6 rows (for 0.6); 3 columns (for 0.3), overlap = \(0.18\) of the grid.
So \(0.6 \times 0.3 = 0.18\)
Shade 6 rows (for 0.6); 3 columns (for 0.3), overlap = \(0.18\) of the grid.
So \(0.6 \times 0.3 = 0.18\)
3️⃣ Where Does the Decimal Point Go?
- Count the total number of decimal places in both numbers.
- After multiplying, put the decimal point in the product, starting from the right (so there are that many decimal digits).
- Example: \(0.27 \times 0.5\):
27 x 5 = 135, 2 decimal places in \(0.27\), 1 in \(0.5\) → 3 total
So, \(0.135\)
4️⃣ Estimate Products of Decimals
- Round each decimal to a whole or easy fraction (0, 0.5, 1) to estimate quickly.
- Multiply these rounded values for a quick check.
Estimate: \(0.53 \times 0.78 \approx 0.5 \times 0.8 = 0.4\)
Estimate: \(3.27 \times 1.8 \approx 3 \times 2 = 6\)
Estimate: \(3.27 \times 1.8 \approx 3 \times 2 = 6\)
5️⃣ Multiplying Decimals Using Area Models
- Draw a rectangle; write each decimal in expanded (place value) form.
- Find partial products for each part, then add together for final answer.
- This splits larger decimals, e.g., \(1.4 \times 2.3 = (1 + 0.4)\times(2 + 0.3)\).
Example: \(1.2 \times 3.4\)
\((1+0.2)\times(3+0.4)\)
\(1 \times 3 = 3,\) \(1 \times 0.4 = 0.4,\) \(0.2 \times 3 = 0.6,\) \(0.2 \times 0.4 = 0.08\)
Add: \(3 + 0.4 + 0.6 + 0.08 = 4.08\)
\((1+0.2)\times(3+0.4)\)
\(1 \times 3 = 3,\) \(1 \times 0.4 = 0.4,\) \(0.2 \times 3 = 0.6,\) \(0.2 \times 0.4 = 0.08\)
Add: \(3 + 0.4 + 0.6 + 0.08 = 4.08\)
6️⃣ Quick Table: Decimal Place Value
| Decimal Example | Decimal Places (in left number) | Decimal Places (in right number) | Total in product |
|---|---|---|---|
| 0.5 × 0.4 | 1 | 1 | 2 (\(0.20\)) |
| 1.2 × 0.07 | 1 | 2 | 3 (\(0.084\)) |
| 2.35 × 1.8 | 2 | 1 | 3 (\(4.230\) → 4.23) |
7️⃣ Practice Problems
- \(0.6 \times 0.3 =\) _____
- \(2.5 \times 0.4 =\) _____
- \(1.07 \times 0.8 =\) _____
- \(0.13 \times 0.05 =\) _____
- Estimate: \(3.47 \times 1.98 \approx\) _____
Answers:
1) 0.18 2) 1.00 3) 0.856 4) 0.0065 5) \(3.5 \times 2 = 7\)
1) 0.18 2) 1.00 3) 0.856 4) 0.0065 5) \(3.5 \times 2 = 7\)