✖️ Multiply Decimals by Whole Numbers
Grade 5 Math - Complete Notes & Formulae
Key Concepts
- To multiply a decimal by a whole number, multiply normally as if there's no decimal.
- Count how many decimal places are in the decimal number.
- Place the decimal point in the answer so it has the same number of decimal places.
1️⃣ Steps to Multiply a Decimal by a Whole Number
- 1 Ignore the decimal and multiply both numbers.
- 2 Count decimal places in the decimal number (not the whole number).
- 3 Insert the decimal point so the answer has the same number of decimal places as the original decimal.
Example: \(4.7 \times 3\)
- Ignore decimal: \(47 \times 3 = 141\)
- Put decimal point after one place: \(14.1\) (since \(4.7\) has 1 decimal place)
- Final answer: \(4.7 \times 3 = 14.1\)
Example: \(2.64 \times 5\)
- Ignore decimal: \(264 \times 5 = 1320\)
- Put decimal after two digits: \(13.20\) (since \(2.64\) has 2 decimal places)
- Final answer: \(2.64 \times 5 = 13.2\)
2️⃣ Visual Model: Using Blocks or Grids
- Model decimals using base-10 blocks (1 = whole, 0.1 = rod, 0.01 = small cube).
- Multiply the model shape/group by the whole number (e.g., draw the model 4 times for \(4 \times 0.25\)).
- Count up the total to find the answer visually.
3️⃣ Distributive Property
Distributive property helps break multiplication into smaller, simpler parts:
To multiply \(n \times (a + b)\), do: \(n \times a + n \times b\).
To multiply \(n \times (a + b)\), do: \(n \times a + n \times b\).
- \(3 \times 2.5 = 3 \times (2 + 0.5) = 3 \times 2 + 3 \times 0.5 = 6 + 1.5 = 7.5\)
- \(5 \times 1.7 = 5 \times (1 + 0.7) = 5 + 3.5 = 8.5\)
4️⃣ Multiplying by Multi-Digit Whole Numbers
- Line up numbers as for traditional multiplication.
- Ignore decimal, multiply normally.
- Count decimal places in the decimal factor.
- After multiplying, insert the decimal point with the SAME number of decimal digits as the decimal number.
Example: \(4.2 \times 16\)
- Ignore decimal: \(42 \times 16 = 672\)
- One decimal place in \(4.2\), so place decimal in product: \(67.2\)
- Answer: \(4.2 \times 16 = 67.2\)
Example: \(2.17 \times 32\)
- Ignore decimal: \(217 \times 32 = 6944\)
- Two decimal places, so \(69.44\)
- Answer: \(2.17 \times 32 = 69.44\)
5️⃣ Estimating Products
- Round the decimal and whole number to the nearest easy value (whole, tenth, etc).
- Multiply the rounded values mentally.
Estimate \(6.78 \times 4 \approx 7 \times 4 = 28\)
Estimate \(1.57 \times 12 \approx 2 \times 10 = 20\)
A good estimate makes checking work much easier!
6️⃣ Word Problem Example
Emma buys 3 books. Each book costs \$5.75. How much did she pay?
Solution: \(5.75 \times 3 = 17.25\) (Ignore decimal, \(575 \times 3 = 1725\), insert decimal after 2 digits→17.25)\
Solution: \(5.75 \times 3 = 17.25\) (Ignore decimal, \(575 \times 3 = 1725\), insert decimal after 2 digits→17.25)\
7️⃣ Multiplying Three or More Numbers
- Multiply the numbers in any order.
- Put decimal in answer so that total number of decimal places equals the sum of all decimal digits among all factors.
Solve: \(0.2 \times 4 \times 5\)
First: \(0.2 \times 4 = 0.8\)
Then: \(0.8 \times 5 = 4\)
Final answer: 4
First: \(0.2 \times 4 = 0.8\)
Then: \(0.8 \times 5 = 4\)
Final answer: 4
8️⃣ Quick Reference Table
| Task | Step/Rule |
|---|---|
| Multiply decimal by whole | Ignore decimal, multiply, put decimal at correct place |
| Use distributive property | Break decimal into whole + part, multiply each, then add |
| Estimate | Round, then multiply mentally |
| Visual method | Draw groups using blocks/area model |
9️⃣ Practice
- \(0.9 \times 6 =\) _____
- \(1.34 \times 9 =\) _____
- \(2.5 \times 24 =\) _____
- Estimate: \(5.8 \times 7 \approx\) _____
- Word problem: Each pencil costs \$0.75. If you buy 13 pencils, what’s the total?
Answers:
1) 5.4
2) 12.06
3) 60
4) \(6 \times 7 = 42\)
5) \(0.75 \times 13 = 9.75\)
1) 5.4
2) 12.06
3) 60
4) \(6 \times 7 = 42\)
5) \(0.75 \times 13 = 9.75\)