Distributive property in multiplication
Theory
The distributive property splits one factor into easy parts. Multiply each part by the same number, then add the partial products. You can also split to a friendly number, like \(99 = 100 - 1\).
The distributive property lets you split one factor into easy parts, multiply each part, then add the results.
Split by place value: \(34 = 30 + 4\), so \(7 \times 34 = 7 \times 30 + 7 \times 4\).
Multiply each part by the same number, then add the partial products.
You can also split down to a friendly number over subtraction: \(99 = 100 - 1\), so \(7 \times 99 = 7 \times 100 - 7 \times 1\).
Split by place value, or split to a friendly number and take a bit off.
| Number | Split | Products |
|---|---|---|
| \(47\) | \(40 + 7\) | \(6 \times 40 + 6 \times 7\) |
| \(99\) | \(100 - 1\) | \(7 \times 100 - 7 \times 1\) |
| \(98\) | \(100 - 2\) | \(5 \times 100 - 5 \times 2\) |
How to use the distributive property
- Split one factor. Break it into a tens part and a ones part, or into a friendly number.
- Multiply each part. Multiply every piece by the same factor.
- Add or subtract. Join the partial products for the answer.
Split \(47\) into \(40 + 7\).
| \(6 \times 40\) | \(=\) | \(240\) |
| \(6 \times 7\) | \(=\) | \(42\) |
| \(240 + 42\) | \(=\) | \(282\) |
The box holds \(5\).
| \(45\) | \(=\) | \(40 + 5\) |
\(99 = 100 - 1\).
| \(7 \times 100\) | \(=\) | \(700\) |
| \(700 - 7\) | \(=\) | \(693\) |
\(98 = 100 - 2\).
| \(5 \times 100\) | \(=\) | \(500\) |
| \(5 \times 2\) | \(=\) | \(10\) |
| \(500 - 10\) | \(=\) | \(490\) |
Common pitfalls
Frequently asked questions
What is the distributive property?
A way to multiply by splitting one factor into parts. \(7 \times 34 = 7 \times 30 + 7 \times 4\), then add the results.
How do you split a number by place value?
Break it into tens and ones. \(34 = 30 + 4\), so each part is easy to multiply on its own.
Can you split over subtraction?
Yes. For numbers near a round number, split down: \(99 = 100 - 1\), so \(7 \times 99 = 700 - 7 = 693\).
Why not split 45 into 4 and 5?
Because the \(4\) in \(45\) stands for \(40\). Splitting into \(40 + 5\) keeps the value; \(4 + 5\) is far too small.
Do you add or subtract the partial products?
Add when you split into a sum like \(40 + 7\); subtract when you split to a friendly number like \(100 - 1\).