Back
The Distributive Property of Multiplication
> ... Math > The Order of Operations and Variables > The Distributive Property of Multiplication

A property is a characteristic about something that is always true. The distributive property of multiplication is a rule that is always true. There are many properties in math that you use regularly, like the commutative property (the property that says that you can multiply in any order, $$2 \times 3 = 3 \times 2$$ ). The distributive property says that you can distribute a number being multiplied into parentheses. The following video will explain in more detail with some examples. Here is an example of the distributive property of multiplication.

$$2 (1 + 3) = (2 \times 1) + (2 \times 3) = 2 + 6 = 8$$

Distributive property of multiplication
More Examples of the Distributive Property of Multiplication

### Practice Problems

Evaluate the following expressions:
1. $$4 \lgroup 3 + 4 \rgroup = ?$$ (
Solution
Solution: $$28$$
Details:
Although this problem can be solved using the Order of Operation, for this lesson, practice solving with the Distributive Property.
Start by distributing the $$4$$ into each number inside the parentheses. Multiply the $$4 × 3$$ and $$4 × 4$$.
$$4\lgroup3 + 4\rgroup$$
$$4\lgroup3\rgroup + 4\lgroup4\rgroup$$

Solve $$4 × 3 = 12$$ and $$4 × 4 = 16$$

$$4\lgroup3\rgroup + 4\lgroup4\rgroup$$
$$12+16$$

Finally add $$12\;\text{plus}\;16 = 28$$.
)
2. $$\lgroup 2 + 9 \rgroup 3 = ?$$ (
Solution
Solution:
$$33$$
)
3. $$-8 \lgroup -2 + 5 \rgroup = ?$$ (
Video Solution
Solution: $$-24$$
Details:

(Video Source | Transcript)
)
4. $$\lgroup -2 + 3 \rgroup \lgroup -6 \rgroup = ?$$ (
Solution)
Solution: $$-6$$
Details:
Solve by using the Distributive Property. Multiply $$-6$$ by each number inside the parentheses.
$$\lgroup-2 + 3\rgroup\lgroup-6\rgroup$$

Continue to multiply $$-2 × -6$$ and $$3 × -6$$.
$$\lgroup-2\rgroup\lgroup-6\rgroup + \lgroup3\rgroup\lgroup-6\rgroup$$

The product, or answer are $$12$$ and $$-18$$.
$$\lgroup12\rgroup + \lgroup-18\rgroup$$

The final step is to add
$$\lgroup12\rgroup + \lgroup-18\rgroup$$

The answer is $$- 6$$.
5. $$\lgroup -9 - 4 \rgroup \lgroup -8 \rgroup = ?$$ (
Video Solution
Solution: 104
Details:

(Video Source | Transcript)
)
6. $$-5 \lgroup -7 - \lgroup -6 \rgroup \rgroup = ?$$ (
Solution
Solution:
$$5$$
)
7. $$\lgroup -5 - \lgroup -9 \rgroup \rgroup 6 = ?$$ (
Solution
Solution:
$$24$$
)

### Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.