Basic Mathematics

The Distributive Property

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The Distributive Property

This is the distributive prpoerty:

A × ( B + C) = (A × B) + (A × C)

The product of a number and a sum can be written as the sum of two products.

A × (B + C)	=	(A × B) + (A × C)
3 × (5 + 4)	=	(3 × 5) + (3 × 4)
3 × 9	=	15 + 12
27	=	27

The Distributive Property

The distributive property also applies to subtraction:

A × (B − C) = (A × B) − (A × C)

The product of a number and a difference can be written as the difference of two products.

A × (B − C)	=	(A × B) − (A × C)
3 × (6 − 4)	=	(3 × 6) − (3 × 4)
3 × 2	=	18 − 12
6	=	6

The Distributive Property

Using the distributive property sometimes offers a short cut to finding the missing number in an equation.

What number belongs in the box to make the number sentence true?

3 × (14 + 17) = (3 × 14) + (3 × □)
3 × (14 + 17) = (3 × 14) + (3 × 17)

There is no need to find the product of 3 × (14 + 17). The distributive property shows that the missing factor is 17.

The Distributive Property

Click on the example of the distributive property.

3 × (4 × 5) = (3 × 4) × 5

4 + 3 = 3 + 4

3 + (4 + 5) = (3 + 4) + 5

3 × (4 + 5) = (3 × 4) + (3 × 5)

None of these

Question 1 of 8

3 × (4 × 5) = (3 × 4) × 5 shows the associative property of multiplication. Try again.

4 + 3 = 3 + 4 shows the commutative property of addition. Try again.

3 + (4 + 5) = (3 + 4) + 5 shows the associative property of addition. Try again.

3 × (4 + 5) = (3 × 4) + (3 × 5) shows the product of a number and a sum equal to the sum of two products.

One number sentence shows the distributive property of multiplication over addition. Try again.

The distributive property says that A × (B + C) = (A × B) + (A × C).

The Distributive Property

Click on the equivalent expression.

(5 − 4) × 3

Question 2 of 8

(5 − 4) × 3 = 1 × 3
1 × 3 is not equal to 5 − (4 × 3). Try again.

(5 + 4) × 3 = (5 × 3) + (4 × 3) is an example of the distributive property.

(5 − 4) × 3 = 1 × 3
1 × 3 is not equal to (1 × 3) − (1 × 3). Try again.

(5 − 4) × 3 = 1 × 3
1 × 3 is not equal to (5 × 3) − 4. Try again.

One of these is an example of the distributive property of multiplication over subtraction. Try again.

The distributive property says that (A − B) × C = (A × C) − (B × C).

The Distributive Property

Click on the equivalent expression.

5 × 15

Question 3 of 8

5 × 15 is not equal to (15 ÷ 3) + (15 ÷ 2).
5 × 15 = 5 × (10 + 5). Try again.

5 × 15 = 5 × (10 + 5) = (5 × 10) + (5 × 5)
This is an example of the distributive property.

5 × 15 is not equal to 5 ÷ 15.
5 × 15 = 5 × (10 + 5). Try again.

5 × 15 is not equal to (15 × 5) + (15 × 5).
5 × 15 = 5 × (10 + 5). Try again.

One of these is an example of the distributive property. Try again.

Think of 5 × 15 as 5 × (10 + 5). Then apply the distributive property.

The Distributive Property

Click on the equivalent expression.

25 × 2

Question 4 of 8

25 × 2 is not equal to (25 × 2) + (25 × 2).
25 × 2 = (20 + 5) × 2. Try again.

25 × 2 = (20 + 5) × 2 = (20 × 2) + (5 × 2)
This is an example of the distributive property.

25 × 2 is not equal to 20 + (5 × 2).
25 × 2 = (20 + 5) × 2. Try again.

25 × 2 is not equal to (20 × 2) + 5.
25 × 2 = (20 + 5) × 2. Try again.

One of these is an example of the distributive property. Try again.

Think of 25 × 2 as (20 + 5) × 2. Then apply the distributive property.

The Distributive Property

Click on the number that belongs in the box.

96 × 3 = (90 × 3) + ( ⃞ × 3)

Question 5 of 8

96 × 3 is not equal to (90 × 3) + (16 × 3).
96 × 3 = (90 + 6) × 3. Try again.

96 × 3 is not equal to (90 × 3) + (90 × 3).
96 × 3 = (90 + 6) × 3. Try again.

96 × 3 is not equal to (90 × 3) + (3×3).
96 × 3 = (90 + 6) × 3. Try again.

96 × 3 = (90 + 6) × 3 = (90 × 3) + (6 × 3)
This is an example of the distributive property.

One of these numbers makes a true number sentence. Try again.

Think of 96 × 3 as (90 + 6) × 3. Then apply the distributive property.

The Distributive Property

Click on the number that belongs in both boxes.

7 × 35 = (⃞ × 30) + (⃞ × 5)

Question 6 of 8

7 × 35 is not equal to (210 × 30) + (210 × 5).
7 × 35 = 7 × (30 + 5). Try again.

7 × 35 is not equal to (14 × 30) + (14 × 5).
7 × 35 = 7 × (30 + 5). Try again.

7 × 35 is not equal to (35 × 30) + (35 × 5).
7 × 35 = 7 × (30 + 5). Try again.

7 × 35 = 7 × (30 + 5) = (7 × 30) + (7 × 5)
This is an example of the distributive property.

One of these numbers makes a true number sentence. Try again.

Think of 7 × 35 as 7 × (30 + 5). Then apply the distributive property.

The Distributive Property

Click on the number that belongs in the box.

2 × (⃞ − 11) = (2 × 35) − (2 × 11)

Question 7 of 8

2 × (70 − 11) = 2 × 59. 2 × 59 is not equal to (2 × 35) − (2 × 11). Try again.

2 × (22 − 11) = 2 × 11. 2 × 11 is not equal to (2 × 35) − (2 × 11). Try again.

2 × (11 − 11) = 2 × 0. 2 × 0 is not equal to (2 × 35) − (2 × 11). Try again.

2 × (35 − 11) = (2 × 35) − (2 × 11) is an example of the distributive property.

One of these numbers makes a true number sentence. Try again.

The distributive property says that A × (B − C) = (A × B) − (A × C).

The Distributive Property

Click on the number that belongs in both boxes.

(12 − 2) × 4 = (12 × ⃞) − (2 × ⃞)

Question 8 of 8

(12 − 2) × 4 = 10 × 4
10 × 4 is not equal to (12 × 24) − (2 × 24). Try again.

(12 − 2) × 4 = (12 × 4) − (2 × 4) is an example of the distributive property.

(12 − 2) × 4 = 10 × 4
10 × 4 is not equal to (12 × 8) − (2 × 8). Try again.

(12 − 2) × 4 = 10 × 4
10 × 4 is not equal to (12 × 2) − (2 × 2). Try again.

One of these numbers makes a true number sentence. Try again.

The distributive property says that (A − B) × C = (A × C) − (B × C).

The Distributive Property