In some cases the Distributive Property of Multiplication over Addition or Distributive Property of Multiplication over Subtraction can be used to obtain an answer quickly. Represent the following operations using one of the distributive properties and also
give the answer.
801 ¡ñ 30 + 4 ¡ñ 30
65 ¡ñ 20 ¨C 5 ¡ñ 20
for the first one I assume they want you to factor out ¡ñ 30 and add 801+4
for the second, I assume they want you to first factor out ¡ñ 20 then do the combination--not 100% sure.
a) 801 ¡ñ 30 + 4 ¡ñ 30
b) 65 ¡ñ 20 ¨C 5 ¡ñ 20
Just a dark circle in between each number
801 30 +4 30
65 20 -5 20
To represent the operations using the distributive properties, we can rewrite them as:
1. 801 × 30 + 4 × 30
2. 65 × 20 - 5 × 20
Now, let's use the distributive properties to simplify the expressions step by step:
1. 801 × 30 + 4 × 30
= (801 + 4) × 30 (Distributive Property of Multiplication over Addition)
= 805 × 30 (Addition)
= 24,150
Therefore, the answer to the first expression is 24,150.
2. 65 × 20 - 5 × 20
= (65 - 5) × 20 (Distributive Property of Multiplication over Subtraction)
= 60 × 20 (Subtraction)
= 1,200
So, the answer to the second expression is 1,200.
To use the Distributive Property of Multiplication over Addition or Subtraction, you need to apply the multiplication to each term within the parentheses and then perform the addition or subtraction.
Let's start with the first operation:
801 × 30 + 4 × 30
Using the Distributive Property, we can rewrite this as:
(801 + 4) × 30
Now we can simplify the expression within the parentheses:
805 × 30
And finally, we multiply:
24,150
So the answer to the first operation is 24,150.
Now let's move on to the second operation:
65 × 20 - 5 × 20
Again, applying the Distributive Property, we have:
(65 - 5) × 20
Simplifying the expression within the parentheses:
60 × 20
Multiplying:
1,200
Therefore, the answer to the second operation is 1,200.