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## Explanation:

Use the Distributive Property to rewrite each algebraic expression.

Be Precise Mrs. Singh bought 9 folders and 9 notebooks. The cost of each folder was $2.50. Each notebook cost $4. Write two equivalent expressions and then find the total cost.

Be Precise Five friends bought admission tickets to the museum and a box lunch. The cost of each admission ticket was $11.75. Each box lunch cost $5. Write two equivalent expressions and then find the total cost.

Factor each expression.

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- Unit A1: Algebraic and Numerical Expressions
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## Falci, Jakob

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## 6.EE.3 - Distributive Property

- See the left menu for Video Tutorials, Online Practice Resources, Class Notes, and Homework and Extra Practice Worksheets with ANSWERS. Use these resources to help reinforce the following 6th Grade Common Core Learning Standard and "I Can Statement(s)." 6.EE.3 Apply the properties of operations to generate equivalent expressions "I Can Apply the Distributive Property to Generate an Equivalent Expression."
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## 6th Grade Distributive Property

Welcome to our 6th Grade Distributive Property Worksheets.

Here you will find a range of algebra worksheets to help you learn how to use the distributive property to expand and factorize a range of expressions.

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## Distributive Property Support

Evaluate the expression worksheets, expand the expression worksheets, factorize the expression worksheets.

- Distributive Property Mixed Worksheets
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## 6th Grade Distributive Property Online Quiz

This page is all about using the distributive property to expand and factorize a range of expressions.

We have split the worksheets up into 4 different sections:

- Evaluate the expression - work out the value of different algabraic expressions;
- Expand the expression - use the distributive property to multiply out the brackets;
- Factorize the expression - use the distributive property to factorize different expressions.
- Mixed questions involving all 3 of the above.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

- Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

- 2a + 5 is an expression involving the variable a
- 5(y 2 - 6) is another expression

How to Evaluate an Expression

When we are evaluating the value of an expression, we work out the value of the expression when we give a value to the variable.

- 2(p + 5) has a value of 22 when p = 6 because 2(6 + 5) = 2 x 11 = 22
- 3(12 - q) has a value of 21 when q = 5 because 3(12 - 5) = 3 x 7 = 21
- 8(n - 2) has a value of 64 when n = 10 because 8 (10 - 2) = 8 x 8 = 64
- 8(n - 2) has a value of 0 when n = 2 because 8 (0 ) = 8 x 0 = 0

How to Expand an Expression

When we are expanding an expression, we multiply out the factors.

- 2(p + 5) = 2 x p + 2 x 5 = 2p + 10
- 3(12 - q) = 3 x 12 - 3 x q = 36 - 3q
- 8(n - 2) = 8 x n - 8 x 2 = 8n - 16
- 5(y + 3z) = 5 x y + 5 x 3z = 5y + 15z

How to Factorize an Expression

When we are factorizing an expression, we try to find the greatest common factor of all the numbers and take it out as a factor.

- 3n + 15 = 3(n + 5) - greatest common factor of 3 and 15 is 3.
- 4p + 32 = 4(p + 8) - the greatest common factor of 4 and 32 is 8.
- 20 - 8y = 4(5 - 2y) - the greatest common factor of 20 and 8 is 4.
- 4a - 10b + 6c = 2(2a - 5b + 3c) - the greatest common factor of 4, 10 and 6 is 2.
- 35d + 42 = 7(5d + 6) - the greatest common factor of 35 and 42 is 7.

## 6th Grade Distributive Property Worksheets

These sheets involve working out the value of the expression using PEMDAS and order of operations.

The first sheets is a multiple choice sheet with only numbers in the expressions.

The second sheet involves finding the value of the expression with only numbers in the expression.

The third sheet involves finding the value of the expression with numbers and variables in the expression.

- Evaluate the Expression Sheet 6:1
- PDF version
- Evaluate the Expression Sheet 6:2
- Evaluate the Expression Sheet 6:3

Sheet 1 is a multiple choice sheet where you match the factorized expression with the correct expanded expression.

Sheet 2 involes writing the factorized expression as an expanded expression.

- Expand the Expression Sheet 6:1
- Expand the Expression Sheet 6:2

## Expand the Expression Walkthrough Video

This short video walkthrough shows several problems from our Expand the Expression Worksheet 6:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Sheet 1 is a multiple choice sheet where you match the expression with the correct factorized expression.

Sheet 2 involes writing the expression as a factorized expression.

- Factorize the Expression Sheet 6:1
- Factorize the Expression Sheet 6:2

## 6th Grade Distributive Property Mixed Worksheets

These questions involve expanding, factorizing and evaluating different expressions..

They are a combination of questions from all the above categories.

- 6th Grade Distributive Property Sheet 6:1
- 6th Grade Distributive Property Sheet 6:2

## More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

## More 6th Grade Algebra Worksheets

If you are looking for some basic algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

- Generate the algebra - and write your own algebraic expressions;
- Calculate the algebra - work out the value of different expressions;
- Solve the algebra - find the value of the term in the equation.
- Expressions and Equations 6th Grade
- Basic Algebra Worksheets (6th & 7th Grade)

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Try using this online calculator tool to solve one of your problems and watch it work!

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## Factorising Quadratic Equations

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## PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

- know and understand how parentheses works;
- understand how exponents work in simple calculations.
- understand and use PEMDAS to solve a range of problems.
- PEMDAS Problems Worksheets 5th Grade
- 6th Grade Order of Operations

## Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

- Interactive Equality Explorer by PhET

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## Distributive Property Practice Problems

Hopefully you've read and understood the distributive property lesson. If you are ready, let's move on and practice our skill!

Directions: Use the distributive property to simplify each expression.

NOTE: The answers are down below the practice problems. Make sure you check your answers carefully!

1. 5(x+6) =

2. 3(2x+1) =

3. 2(2x-3) =

4. 6(x-4) =

5. 8(2x-3) =

6. -3(x + 4)=

7. -2(3x - 1)=

8. -10(2x + 1/5 )=

9. -18(x - 2/3)=

10. 1/2(x -4) =

1. 5x + 30

2. 6x +3

3. 4x - 6

4. 6x - 24

5. 16x - 24

6. -3x - 12

7. -6x +2

8. -20x - 2

9. -18x + 12

10. 1/2x - 2

Ok... The distributive property isn't so bad is it? If you're ready, you can move onto simplifying algebraic expressions!

If you didn't do so well on the distributive property, you may need to go back and review Adding Integers , Subtracting Integers , or Multiplying and Dividing Integers.

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## McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 Answer Key Use Partial Products and the Distributive Property

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 6 Use Partial Products and the Distributive Property will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 6 Use Partial Products and the Distributive Property

Darnel and his four friends went to an ice skating rink and bought sandwiches. They divided the total cost and found that each person needs to pay $17. What was the total cost for ice skating and sandwiches?

Find 5 × 17 using an area model.

When you use partial products, you are using a property. A property is a rule in mathematics that can be applied to all numbers. The property that you applied above is called the Distributive Property. You will learn more about this property in the next lesson.

Find 7 × 56 using an area model.

Explanation: 7 × 56 = (7 × 50) + (7 × 6) = 350 + 42 = 392 So, 7 × 56 = ____ 392

Talk About It

Question 1. Mathematical PRACTICE 3 Draw a Conclusion How do area models show partial products? Answer:

Question 2. In finding 7 × 56 above, why does the area model separate 56 into 50 and 6? Answer: The area model separates 56 into 50 and 6 to calculate the multiplication easily.

Practice It

Multiply using the area model. Label each model.

Question 8. Ronnie swims 4 laps each day at the pool. How many laps does he swim in 28 days? Use an area model to solve. Answer: 4 × 28 = 112

Question 9. Mathematical PRACTICE Model Math Yoshi saved $5 each week for 23 weeks. What is the total amount of money he saved? Use an area model to solve. Answer: 5 × 23 = 115

Question 10. Thirty-eight fish are in each aquarium at a fish store. How many fish are there in five aquariums? Use an area model to solve. Answer: 38 × 5 = 190

Question 11. Mathematical PRACTICE Find the Error Omar was using an area model to find 4 × 61. Find his mistake and correct it. (4 × 60) + (4 × 10) = 240 + 40 = 280 Answer: The answer is 244, not 280.

Write About It

Question 12. How can area models be used to solve multiplication problems? Answer:

## McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 My Homework Answer Key

Problem Solving

Question 4. Mathematical PRACTICE 4 Model Math Brandon packs his lunch 4 days each week. How many days does he pack his lunch for 36 weeks? Use an area model to solve. Answer: Bradon packs 144 days in 36 weeks.

Question 5. Ricarda earns a $25 allowance each week. How much allowance will she earn after 7 weeks? Use an area model to solve. Answer: $175

Question 6. Write an expression that uses partial products to multiply 8 × 64. Answer: (80 × 6) + (8 × 4)

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## Ch. 9 The Development of Russia

Ivan i and the rise of moscow, learning objective.

- Outline the key points that helped Moscow become so powerful and how Ivan I accomplished these major victories
- Moscow was considered a small trading outpost under the principality of Vladimir-Suzdal into the 13th century.
- Power struggles and constant raids under the Mongol Empire’s Golden Horde caused once powerful cities, such as Kiev, to struggle financially and culturally.
- Ivan I utilized the relative calm and safety of the northern city of Moscow to entice a larger population and wealth to move there.
- Alliances between Golden Horde leaders and Ivan I saved Moscow from many of the raids and destruction of other centers, like Tver.

A rival city to Moscow that eventually lost favor under the Golden Horde.

## Grand Prince of Vladimir

The title given to the ruler of this northern province, where Moscow was situated.

## The Rise of Moscow

Moscow was only a small trading outpost in the principality of Vladimir-Suzdal in Kievan Rus’ before the invasion of Mongol forces during the 13th century. However, due to the unstable environment of the Golden Horde, and the deft leadership of Ivan I at a critical time during the 13th century, Moscow became a safe haven of prosperity during his reign. It also became the new seat of power of the Russian Orthodox Church.

Ivan I (also known as Ivan Kalita) was born around 1288 to the Prince of Moscow, Daniil Aleksandrovich. He was born during a time of devastation and upheaval in Rus’. Kiev had been overtaken by the invading Mongol forces in 1240, and most of the Rus’ principalities had been absorbed into the Golden Horde of the Mongol Empire by the time Ivan was born. He ascended to the seat of Prince of Moscow after the death of his father, and then the death of his older brother Yury.

Ivan I. He was born around 1288 and died in either 1340 or 1341, still holding the title of Grand Prince of Vladimir.

Ivan I stepped into a role that had already been expanded by his predecessors. Both his older brother and his father had captured nearby lands, including Kolomna and Mozhaisk. Yury had also made a successful alliance with the Mongol leader Uzbeg Khan and married his sister, securing more power and advantages within the hierarchy of the Golden Horde.

Ivan I continued the family tradition and petitioned the leaders of the Golden Horde to gain the seat of Grand Prince of Vladimir. His other three rivals, all princes of Tver, had previously been granted the title in prior years. However they were all subsequently deprived of the title and all three aspiring princes also eventually ended up murdered. Ivan I, on the other hand, garnered the title from Khan Muhammad Ozbeg in 1328. This new title, which he kept until his death around 1340, meant he could collect taxes from the Russian lands as a ruling prince and position his tiny city as a major player in the Vladimir region.

## Moscow’s Rise

During this time of upheaval, the tiny outpost of Moscow had multiple advantages that repositioned this town and set it up for future prosperity under Ivan I. Three major contributing factors helped Ivan I relocate power to this area:

- It was situated in between other major principalities on the east and west so it was often protected from the more devastating invasions.
- This relative safety, compared to Tver and Ryazan, for example, started to bring in tax-paying citizens who wanted a safe place to build a home and earn a livelihood.
- Finally, Moscow was set up perfectly along the trade route from Novgorod to the Volga River, giving it an economic advantage from the start.

Ivan I also spurred on the growth of Moscow by actively recruiting people to move to the region. In addition, he bought the freedom of people who had been captured by the extensive Mongol raids. These recruits further bolstered the population of Moscow. Finally, he focused his attention on establishing peace and routing out thieves and raiding parties in the region, making for a safe and calm metaphorical island in a storm of unsettled political and military upsets.

Kievan Rus’ 1220-1240. This map illustrates the power dynamics at play during the 13th century shortly before Ivan I was born. Sarai, the capital of the Golden Horde, sat to the southeast, while Moscow (not visible on this map) was tucked up in the northern forests of Vladimir-Suzdal.

Ivan I knew that the peace of his region depended upon keeping up an alliance with the Golden Horde, which he did faithfully. Moscow’s increased wealth during this era also allowed him to loan money to neighboring principalities. These regions then became indebted to Moscow, bolstering its political and financial position.

In addition, a few neighboring cities and villages were subsumed into Moscow during the 1320s and 1330s, including Uglich, Belozero, and Galich. These shifts slowly transformed the tiny trading outpost into a bustling city center in the northern forests of what was once Kievan Rus’.

## Russian Orthodox Church and The Center of Moscow

Ivan I committed some of Moscow’s new wealth to building a splendid city center and creating an iconic religious setting. He built stone churches in the center of Moscow with his newly gained wealth. Ivan I also tempted one of the most important religious leaders in Rus’, the Orthodox Metropolitan Peter, to the city of Moscow. Before the rule of the Golden Horde the original Russian Orthodox Church was based in Kiev. After years of devastation, Metropolitan Peter transferred the seat of power to Moscow where a new Renaissance of culture was blossoming. This perfectly timed transformation of Moscow coincided with the decades of devastation in Kiev, effectively transferring power to the north once again.

Peter of Moscow and scenes from his life as depicted in a 15th-century icon. This religious leader helped bring cultural power to Moscow by moving the seat of the Russian Orthodox Church there during Ivan I’s reign.

One of the most lasting accomplishments of Ivan I was to petition the Khan based in Sarai to designate his son, who would become Simeon the Proud, as the heir to the title of Grand Prince of Vladimir. This agreement a line of succession that meant the ruling head of Moscow would almost always hold power over the principality of Vladimir, ensuring Moscow held a powerful position for decades to come.

- Boundless World History. Authored by : Boundless. Located at : https://www.boundless.com/world-history/textbooks/boundless-world-history-textbook/ . License : CC BY-SA: Attribution-ShareAlike

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## VIDEO

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Lesson Summary. The distributive property represents a key belief about the arithmetic of real numbers. This property can be applied to algebraic expressions using variables that represent real numbers. Problem Set. 1. Insert parentheses. a. b. 2 2 + × 42 +1=81 to make each statement true. 2 +.

Free worksheet(pdf) and answer key on the distributive property. 23 scaffolded questions that start relatively easy and end with some real challenges. Plus model problems explained step by step. ... Students will practice applying the distributive property of multiplication over addition. This worksheet has 23 problems. Content. This is a 4 ...

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This detailed answer provides step-by-step solutions to the multiplication problems and demonstrates how to use the Distributive Property to rewrite algebraic expressions. It also calculates the total money spent by four friends at the movie theater, the total revenue from a birthday party buying candy and soda, and the price difference between ...

😉 6th Grade, Unit 6, Lesson 9 "The Distributive Property, Part 1" Illustrative Mathematics. Review and Tutorial. Search #669math to find this lesson fast!IM...

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Lesson 6: Algebraic Expressions—The Distributive Property Date: 8/7/13 63 ... When reviewing the game, it is likely that students will have different expressions for the same number (see answers to ... The Distributive Property represents a key belief about the arithmetic of real numbers. This property can be

As a guest, you only have read-only access to our books, tests and other practice materials. As a registered member you can: View all solutions for free ... Chapter 6:Expressions;Lesson 6: The Distributive Property. Please share this page with your friends on FaceBook. ... Use the Distributive Property to rewrite each algebraic expression ...

Use Distributive Property AND Combining Like Terms to simplify each expression. Easy to Medium problems. 9) (x ) 10) n ( n) 11) ( v) 12) (a ) a Use Distributive Property AND Combining Like terms to simplify each expression. Medium problems.

Learn about the distributive property, and also the common factor.

6.EE.3 - Distributive Property. See the left menu for Video Tutorials, Online Practice Resources, Class Notes, and Homework and Extra Practice Worksheets with ANSWERS. Use these resources to help reinforce the following 6th Grade Common Core Learning Standard and "I Can Statement (s)." 6.EE.3. Apply the properties of operations to generate ...

6th Grade Distributive Property Mixed Worksheets. These questions involve expanding, factorizing and evaluating different expressions.. They are a combination of questions from all the above categories. 6th Grade Distributive Property Sheet 6:1. Answers. PDF version. 6th Grade Distributive Property Sheet 6:2. Answers.

© 2013 National Council of Teachers of Mathematics http://illuminations.nctm.org Solution:

Here are two rectangles. The length and width of one rectangle are 8 and 5. The width of the other rectangle is 5, but its length is unknown so we labeled it. x. Write an expression for the sum of the areas of the two rectangles. The two rectangles can be composed into one larger rectangle as shown.

Hopefully you've read and understood the distributive property lesson. If you are ready, let's move on and practice our skill! Directions: Use the distributive property to simplify each expression. NOTE: The answers are down below the practice problems. Make sure you check your answers carefully! 1. 5(x+6) = 2. 3(2x+1) = 3. 2(2x-3) = 4. 6(x-4) =

Lesson 4 Homework Practice The Distributive Property Use the Distributive Property to evaluate each expression. 1. (16 - 6)2 2. 4 (12 + 3) ... Justify your answer by using the Distributive Property. Item Cost ($) Sandwich $5 Drink $2 Dessert $3 20 60 15 -11 50 -6 16 + 8g 4h - 20g-35 + 7n 16m + 8

This lesson lets us break down division by using the Distributive Property. Here, for example, we show that 91 = (70 + 21) when dividing by 7; and 70 and 21 ...

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 6 Use Partial Products and the Distributive Property will give you a clear idea of the concepts. McGraw-Hill My Math. ... McGraw Hill My Math Grade 5 Chapter 2 Lesson 6 My Homework Answer Key. Practice. Question 1. Multiply 2 × 27 using the area model. Label ...

The key is freedom-s-freedom of thought, freedom of information, freedom of communication. The renowned scientist, scholar, and founding father of this university, Mikhail Lomonosov, knew that. It is common knowledge," he said, "that the achievements of science are considerable and rapid,

Ivan IV Vasileyevich is widely known as Ivan the Terrible or Ivan the Fearsome. He was the Grand Prince of Moscow from 1533 to 1547 and reigned as the "Tsar of all the Russias" from 1547 until he died in 1584. His complex years in power precipitated military conquests, including Kazan and Astrakhan, that changed the shape and demographic ...

😉 6th Grade, Unit 6, Lesson 10 "The Distributive Property, Part 2" Illustrative Mathematics Practice Problems. Review and Tutorial. Search #6610math to find...

Ivan I (also known as Ivan Kalita) was born around 1288 to the Prince of Moscow, Daniil Aleksandrovich. He was born during a time of devastation and upheaval in Rus'. Kiev had been overtaken by the invading Mongol forces in 1240, and most of the Rus' principalities had been absorbed into the Golden Horde of the Mongol Empire by the time ...

😉 6th Grade, Unit 6, Lesson 11: Practice "The Distributive Property, Part 3. Illustrative Mathematics. Review and Tutorial. Search #6611math to find this le...