Question

Explain how you know whether to add or subtract when you use the Distributive property to multiply

Answer 1

The distributive property of multiplication over addition can be used when you multiply a number by a sum. The distributive property lets you multiply a sum by multiplying each addend separately and then add the products:

$a\cdot (b+c)=a\cdot b+a\cdot c.$

The distributive property of multiplication over subtraction can be used when you multiply a number by a difference. The property states that the product of a number and the difference of two other numbers is equal to the difference of the products:

$a\cdot (b-c)=a\cdot b-a\cdot c.$

Therefore, you can see what sign is in the brackets, if sign is "+", then you have to add, if sign is "-", then you have to subtract.

Answer 2

The addition or subtraction in the distribution property depends on the sign between the two real numbers in the expression.

Further explanation:

The distributive property states that if a number $a$ is multiplied with the sum of the two numbers $b$ and $c$ then the result is same as if the numbers are multiplied separately.

$\fbox{\begin\\\ \math a(b+c)=(a\cdot b)+(a\cdot c)\\\end{minispace}}$          ....(1)

The distributive property states that if a number $a$ is multiplied with the difference of the two numbers $b$ and $c$ then the result is same as if the numbers are multiplied separately.

$\fbox{\begin\\\ \math a(b-c)=(a\cdot b)-(a\cdot c)\\\end{minispace}}$             ....(2)

For example: Consider $5$ as $a$, $6$ as $b$ and $2$ as $c$.

Substitute $5$ for $a$, $6$ for $b$ and $2$ as $c$ in the equation (1) as follows:

$\begin{aligned}5(6+2)&=(5\cdot 6)+(5\cdot 2)\\5\cdot 8&=30+10\\40&=40\end{aligned}$  

Now, substitute $5$ for $a$, $6$ for $b$ and $2$ as $c$ in the equation (2) as follows,

$\begin{aligned}5(6-2)&=(5\cdot 6)-(5\cdot 2)\\5\cdot 4&=30-10\\20&=20\end{aligned}$

Therefore, the addition or subtraction in the distributive property is based on the sign between the two real numbers. If the sign between the real number is positive then the numbers are added and if the sign between the real number is negative then the numbers are subtracted.

Learn more:

1. A problem on triangle brainly.com/question/7437053.

2. A problem on triangle brainly.com/question/2992432.

3. A problem on circle brainly.com/question/1506955

Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Real numbers

Keywords: Distributive property, a(b+c)=ab+ac, a(b-c)=ab-ac, real numbers, positive value, negative value, multiply, add, sum, difference.