Expand using distributive property

Expand using distributive property DEFAULT

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Current timeTotal duration

Distributive property with variables

Video transcript

Sours: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-distributive-property/v/distributive-property-with-variables-exercise

Using the Distributive Property to Expand Algebraic Expressions

1. Original problem:$7(5+3)=$____ $+$____a. Distribute the 7$7(5+3)=$ $7*5$$ + $$7*3$&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;..&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;.2. Original problem:$6a+6b=$______$(a+b)$a. Factor out the 6$6a+6b=$ $6$$(a+b)$&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;..&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;.3. Original problem:$2x + 3($$x$$- 4 +$$2x$$) + (x)$a.Simplify what we can in the parentheses$2x+\color{#f15a23}{3(}\color{blue}{3x}-4\color{#f15a23})\color{#4a&#;}{+(x)}$b.Use the distributive property to remove the parentheses$2x + $$9x$$-4 + x$c.Combine like terms$\color{blue}{2x + 9x} $$- 12 + 2$$ -2x $d. Solution$\color{red}{9x}$&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;..&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;&#;.4. Original problem:$\dfrac{x + 1}{5n} + \dfrac{x}{5n}$a. Since the fractions have a common denominator we can add them.$\dfrac{(x + 1) + (x)}{5n}$b. Rearrange the terms.$\dfrac{(x + ^-2x) + (1+4)}{5n}$c. Now we can combine like terms$\color{red}{\dfrac{5-x}{5n}}$
Sours: https://www.frontporchmath.com/topics/algebra/playing-with-variables/using-distributive-property-expand-algebraic-expressions-video/
  1. Msp codes 2019
  2. Samsung flex notebook
  3. Bates family updates 2020

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Current timeTotal duration

The distributive property & equivalent expressions

Video transcript

Sours: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-factoring/v/factoring-algebraic-expressions
The Distributive Property - Math with Mr. J

Distributive Property: 5 Clear Examples to Use in Class

What is the distributive property? 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.

According to this principle, multiplying the total of two addends by a number will give us the exact same result as multiplying each addend individually by the number and then adding them together.

Understanding distributive property

For expressions in the form of a(b+c), the distributive propertyshows us how to solve them by:

  • Multiplying the number immediately outside parentheses with those inside
  • Adding the products together

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.

Using the distributive law, we:

  1. Multiply, or distribute, the outer term to the inner terms.
  2. Combine like terms.
  3. Solve the equation.

Let’s use a real-life scenario as an example of the distributive property.

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.

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:

  1. Multiply, or distribute, the outer term to the inner terms.
  2. Combine like terms.
  3. Arrange terms so constants and variables are on opposite sides of the equals sign.
  4. Solve the equation and simplify, if needed.

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.

Distributive property with exponents

An exponent is a shorthand notation indicating how many times a number is multiplied by itself. When parentheses and exponents are involved, using the distributive property can make simplifying the expression much easier.

  1. Expand the equation.
  2. Multiply (distribute) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set.
  3. Combine like terms.
  4. Solve the equation and simplify, if needed.

Note: For step two, use the FOIL (first, outer, inner, last) technique to distribute each expression.

Distributive property with fractions

Solving algebraic expressions with fractions looks more complicated than it is. Follow the steps outlined below to see how it’s done.

Hopefully, this step-by-step process helps your students understand how and why the distributive property can come in handy when simplifying fractions and complex numbers.

  1. Identify the fractions. Using the distributive property, you’ll eventually turn them into integers.
  2. For all fractions, find the lowest common multiple (LCM) — the smallest number that both denominators can fit neatly into. This will allow you to add fractions.
  3. Multiply every term in the equation by the LCM.
  4. Isolate variables adding or subtracting like terms on both sides of the equals sign.
  5. Combine like terms.
  6. Solve the equation and simplify, if needed.

Note: In steps two and three, we find the LCM and use it to multiply the fractions in order to simplify and get rid of them. Need a quick refresher? See our blog post on how to multiply fractions.

A variety of properties

Apart from distributive property, there are other commonly used properties such as the associative property and Commutative property.

Let's look at the associative property:

The associative property refers to grouping elements together. This rule states that how numbers (or whole numbers) are grouped within a math problem will not change the product.

Example in addition:

a + (b +c) = (a + b) + c or 2 + (3 + 4) = (2 + 3) + 4

Example in multiplication:

5×4×2 = (5 x 4) x 2 = 20 x 2 = 40

This property works with multiplication, addition, subtraction, and division.

Exploring distributive property in different ways

1. Prodigy

Prodigy is an adaptive, game-based learning math platform loved by more than one million teachers million students around the world! It offers curriculum-aligned content from every major math topic in 1st to 8th grade, including how to:

  • Use the distributive property to expand and solve expressions
  • Fill in the missing numbers in equivalent expressions using the distributive property

Using Prodigy Math Game helps students learn and practice math beyond fact fluency and into DoK levels two and three. With questions like the one above, students will master the distributive property in no time at all enjoy our variety of guides and worksheets..

Interested in supplementing math lessons with an engaging game-based learning platform?

Sign up now for a free account

2. Word problems

The distributive property may not see applicable to everyday life, but let’s see it in action through some word problems!

Liam has diverse taste in music. Scrolling through the music on his phone, Liam’s friends find songs from three different genres: pop, metal, and country. There are six times as many metal songs as there are pop songs, and 11 times as many country songs as there are pop songs. If x represents the number of pop songs, what is the total number of songs Liam has on his phone? Write an expression. Simplify.

To get the number of metal songs, multiply the number of pop songs by five — 5x. To get the number of country songs, multiply the number of pop songs by 11 — 11x. Since you know x is the number of pop songs, you can write the expression as:

The school’s soccer coach is providing his team with new uniforms: a jersey, a pair of shorts, and shin guards. One jersey costs $15, one pair of shorts costs $11, and a set of shin guards costs $8.

How much does each uniform cost per team mate? Write an expression and simplify.

How much will it cost in total if the team has 11 players? Write an expression and simplify.

3. Arrays

Visual or hands-on manipulatives help students make sense of math and concretize abstract concepts. They’re especially helpful for deepening your students’ understanding of the distributive property.

Use objects, pictures, numbers — anything! — in rows and columns as a useful way to represent mathematical expressions like 4x5 and 5x9. Check out the example below on Indulgy:

By breaking down expressions into bite-sized pieces, students can tackle larger and more challenging math problems. That’s where distributive property helps.

If a child has trouble answering 45, use smaller arrays and rewrite the expression as 4(3+2) or 4(3)+4(2). That’s four rows of three plus four rows of two, which is the same as an array of four rows of five.

Final thoughts on the distributive property

As one of the most commonly used properties, it’s important to learn how to perform and apply the distributive property. Without it, clearing the parentheses wouldn’t be possible.

By incorporating EdTech resources, arrays, or math word problems, students should see the hands-on, practical applications of the distributive property.

Did one example work more effectively to engage students and deepen their understanding? There's only one way to find out — give them a try!

Prodigy Math Game is a game-based learning platform for math that’s easy to use for educators and students alike. Aligned with curricula across the English-speaking world, it’s used by over one million teachers and million students!

Sign up for your free account
Sours: https://www.prodigygame.com/main-en/blog/distributive-property/

Distributive property using expand

 Free Algebra
Tutorials!
 
expand using the distributive property algebra solver free
Related topics:
dividing mix number and fractions| ks3 year 8 maths worksheet| free math worksheet printout on order of operations for fifth graders| solve complex system ti| gce math formula sheet| subtraction worksheet grade 5| glencoe algebra 1 worksheets free| subtraction formulas| holt rinehart and winston geometry answer key free online| the addition and subtraction formula exercise

 
AuthorMessage
ncjotes


Avatar

Registered:
From: Middlesbrough, UK
Posted: Wednesday 27th of Dec    

Peeps! Ok, we’re discussing expand using the distributive property algebra solver free and I was not present in my last algebra class so I have no notes and my professor teaches lessons way bad that’s why I didn’t get to understand it very well when I went to our math class a while ago. To make matters worse, our class will have our test on our next class so I can’t afford not to study expand using the distributive property algebra solver free. Can someone please assist me attempt to learn how to answer couple of questions about expand using the distributive property algebra solver free so that I can prepare for the examination . I’m hoping that someone could help me ASAP.
Back to top
Jahm Xjardx


Avatar

Registered:
From: Odense, Denmark, EU
Posted: Wednesday 27th of Dec    

I suggest that you try out Algebrator. I have been using this product for a few months now and I can frankly say that it is what helped me save my grades this semester. Algebrator offers amazing ways to deal with difficult problems. You will surely love it, I can guarantee.
Back to top
MichMoxon


Avatar

Registered:
From:
Posted: Friday 29th of Dec    

I found out a some software programs that are relevant . I tried them out. The Algebrator appeared to be the most suitable one for cramer’s rule, subtracting fractions and radical equations. It was also easy to work with . It took me step by step towards the solution rather than just giving the solution. That way I got to learn how to solve the problems too. By the time I was done with it , I had learnt how to work out the problems. I found them helpful with College Algebra, Algebra 1 and Pre Algebra which aided me in my algebra classes. May be, this is just the thing for you . Why not try this out?
Back to top
Jot


Avatar

Registered:
From: Ubik
Posted: Saturday 30th of Dec    

A extraordinary piece of math software is Algebrator. Even I faced similar problems while solving geometry, binomial formula and rational equations. Just by typing in the problem from homework and clicking on Solve – and step by step solution to my math homework would be ready. I have used it through several math classes - Algebra 1, College Algebra and Algebra 1. I highly recommend the program.
Back to top
 
Sours: https://www.pocketmath.net
How to Use the Distributive Property to Multiply Binomials - Polynomials

" But the feeling of responsibility pushed me to action. I pressed my lips to the head and the tip of the tongue touched its hole. And as it is not disgusting at first glance, but I liked. The taste of the penis immediately.

You will also like:

Often fumes. Ours at that time was 39 or 40. I was engaged in dancing, figure skating, and in general, I was active. Therefore, I did not ignore the fizra with a phony certificate from a doctor.



351 352 353 354 355