Example Of The Distributive Property

Definition of the distributive property

When we have expressions of the course a (b + c), the distributive belongings helps the states to solve them with the following process:

1. Multiply each number within the parentheses by the number outside the parentheses.

2. Add all the products.

You lot may wonder why we don't follow the order of operations that tells us to evaluate what's inside the parentheses first. The answer is that there are times when we have variables and different terms within the parentheses.

In those cases, we cannot perform operations on those terms, and then we must apply the distributive belongings to simplify the problems.

Distributive holding in multiplication with addition

Information technology does non matter that we use the distributive property or follow the lodge of operations, we will always go far at the same answer. In the following instance, we merely follow the social club of operations past simplifying what is inside the parentheses first.

$latex 5\left( {4+3} \right)=5\left( 7 \right)$

$latex =35$

Using the distributive property, we practice the following:

1. We multiply or distribute the outside term to the terms within the parentheses.

2. We combine like terms.

3. We solve the equation.

$latex 5\left( {4+iii} \right)=5\left( 4 \correct)+5\left( three \correct)$

$latex =20+15$

$latex =35$

Try solving the following do

Simplify the expression $latex 10(3+4+ane)$.

Choose an respond

$latex 60$

$latex 70$

$latex 80$

$latex 90$

Distributive holding in multiplication with subtraction

Like to the operation to a higher place, we perform the distributive belongings of multiplication with subtraction following the same rules, except that nosotros are finding the difference instead of the sum.

$latex 7\left( {7-3} \right)=7\left( vii \correct)-vii\left( 3 \correct)$

$latex =49-21$

$latex =28$

Note that it does not matter if the operator is a plus or a minus. We e'er keep the 1 in parentheses.

Try solving the post-obit exercise

Simplify the expression $latex 6(12-7)$.

Choose an answer

$latex 28$

$latex thirty$

$latex 32$

$latex 38$

Distributive holding with variables

The distributive holding is especially useful when nosotros accept to simplify equations in which nosotros have unknown values.

Using the distributive property with variables, nosotros can solve forxpast following these steps:

1. Multiply or distribute the outside terms to the inside terms.

2. Combine like terms.

iii. Organize the terms and then that the constants and variables are on opposite sides of the equal sign.

4. Solve the equation and simplify if possible.

$latex 5\left( {10-2} \right)=20$

$latex five\left( x \right)-5\left( 2 \right)=twenty$

$latex 5x-10=xx$

$latex 5x-10+ten=20+10$

$latex 5x=20+10$

$latex 5x=thirty$

$latex x=6$

Endeavour solving the following practise

Discover the value of x in the equation $latex half dozen(2x-5)=vi$.

Cull an reply

$latex x=1$

$latex x=3$

$latex x=-2$

$latex x=ii$

Distributive property with exponents

Exponents are a annotation that tell usa how many times a number is multiplied by itself. When nosotros take parentheses and exponents, we tin make facilitate the simplification of expressions past using the distributive property.

1. Aggrandize the equation

ii. Multiply or distribute the showtime numbers of a set, the outer numbers of a prepare, the inner numbers of a set, and the last numbers of a fix.

3. Combine similar terms.

4. Solve the equation and simplify if possible.

$latex {{\left( {4x+3} \right)}^{2}}$

$latex =\left( {4x+three} \correct)\left( {4x+three} \correct)$

$latex =16{{x}^{2}}+12x+12x+ix$

$latex =16{{10}^{2}}+24x+ix$

Distributive holding with fractions

The distributive property tin likewise be used to simplify fractions. Solving algebraic expressions with fractions looks more hard than it really is. With the following steps, we can facilitate this:

1. Place the fractions and utilise the distributive property to eventually convert them to integers.

2. For all fractions, nosotros find the least common multiple. That is, the smallest number that the denominators volition fit into. This will let united states of america to add the fractions.

3. Multiply each term in the equation past the least common multiple.

4. Place the variables and the constants on opposite sides of the equal sign.

5. Combine like terms.

vi. Solve the equation and simplify if possible.

$latex x+five=\frac{x}{4}+\frac{i}{2}$

$latex 4\left( {x+v} \right)=iv\left( {\frac{x}{four}+\frac{1}{2}} \right)$

$latex 4x+twenty=x+2$

$latex 4x-x=2-xx$

$latex 3x=-18$

$latex x=-6$

Try solving the post-obit exercise

Find the value of x in the equation $latex ten-3=\frac{x}{6}+\frac{1}{3}$.

Choose an answer

$latex 10=2$

$latex ten=-ii$

$latex x=-4$

$latex ten=iv$