Distributive of multiplication over addition show five examples
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Answer:
The distributive property of multiplication over addition is applied when you multiply a value by a sum. For example, suppose you want to multiply 5 by the sum of 10 + 3. As we have like terms, we usually first add the numbers and then multiply by 5. 5(10 + 3) = 5(13) = 65.
Also known as the distributive law of multiplication, it’s one of the most commonly used properties in mathematics.
When you distribute something, you are dividing it into parts. In math, the distributive property helps simplify difficult problems because it breaks down expressions into the sum or difference of two numbers.
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Definition of distributive property
Distributive property of addition
Distributive property of subtraction
Distributive property of variables
Distributive property of exponents
Distributive property of fractions
Engaging ways to teach distributive property
Distributive property definition
For expressions in the form of a(b+c), the distributive property shows us how to solve them by:
Multiplying the number immediately outside parentheses with those inside
Adding the products together
What is the distributive property
What about PEMDAS? What happened to first evaluating what’s inside parentheses?
If your students are wondering why you aren’t following the order of operations you’ve taught them in the past, they’re not wrong.
However, when algebraic expressions have parentheses containing variables — a quantity that may change within the context of a mathematical problem, usually represented by a single letter — performing that operation isn’t possible.
Distributive property of multiplication over addition
Regardless of whether you use the distributive property or follow the order of operations, you’ll arrive at the same answer. In the first example below, we simply evaluate the expression according to the order of operations, simplifying what was in parentheses first.
Distributive property of addition
Using the distributive law, we:
Multiply, or distribute, the outer term to the inner terms.
Combine like terms.
Solve the equation.
Distributive property multiplication
Let’s use a real-life scenario to help make this clearer. Imagine one student and her two friends each have seven strawberries and four clementines. How many pieces of fruit do all three students have in total?
In their lunch bags — or, the parentheses — they each have 7 strawberries and 4 clementines. To know the total number of pieces of fruit, they need to multiply the whole thing by 3.
When you break it down, you’re multiplying 7 strawberries and 4 clementines by 3 students. So, you end up with 21 strawberries and 12 clementines, for a total of 33 pieces of fruit.
Distributive property of multiplication over subtraction
Similar to the operation above, performing the distributive property with subtraction follows the same rules — except you’re finding the difference instead of the sum.
Distributive property problems
Note: It doesn’t matter if the operation is plus or minus. Keep whichever one is in the parentheses.
Distributive property with variables
Remember what we said about algebraic expressions and variables? The distributive property allows us to simplify equations when dealing with unknown values.
Using the distributive law with variables involved, we can isolate x:
Multiply, or distribute, the outer term to the inner terms.
Combine like terms.
Arrange terms so constants and variables are on opposite sides of the equals sign.
Solve the equation and simplify, if needed.
How to do distributive property
Note: When isolating variables (see step three) what you do to one side you must do to the other. In order to eliminate 12 on the left side, you must add twelve to both the left and right sides. The same goes for multiplication and division: to isolate x, divide each side by 4.