Distributive property
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The document discusses the distributive property in algebra, noting that the FOIL method for multiplying two binomial expressions is actually an application of the distributive property. It states that as long as each term or element is distributed to the other terms, the multiplication has been done correctly according to the distributive property, regardless of the order used.
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1) Using the order of operations (BODMAS/PEMDAS) to evaluate the expression inside the parentheses first before multiplying.
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This document provides examples of using the distributive property and area models to find the total area of composite rectangles. It breaks rectangles into individual parts, finds the area of each part, and sums the areas. Expressions are written to represent the total area using the distributive property. Practice problems are included for writing expressions to find the area of rectangles using the distributive property. The document demonstrates applying the distributive property in the context of finding total area.
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The document discusses various properties of real numbers including the commutative, associative, identity, inverse, zero, and distributive properties. It also covers topics such as combining like terms, translating word phrases to algebraic expressions, and simplifying algebraic expressions. Examples are provided to illustrate each concept along with explanations of key terms like coefficients, variables, and like terms.
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The document discusses three methods for solving the numeric expression 2(4+3):
1) Using the order of operations (BODMAS/PEMDAS) to evaluate the expression inside the parentheses first before multiplying.
2) Changing multiplication to addition by thinking of it as having "lots of" something.
3) Using the distributive property, where the number outside the parentheses is distributed across each term inside the parentheses.
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Refresh on Distributive Property. Lecture given on Sept. 22nd, 2008. Adaptation of previously created power point.
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I have 4 groups of 6 black chips.
4x6 = 24
I have 4 groups of 6 red chips.
4x6 = 24
I owe 4 groups of 6 black chips.
-4x6 = -24 (Owing chips is a negative amount)
I owe 4 groups of 6 red chips.
-4x6 = -24 (Owing chips is a negative amount)
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Cost of item: $50
Sales tax rate: 7%
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50 + (50 x 0.07)
50 + 3.50
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Sales tax rate: 4%
Method 1:
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Method 2:
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This document discusses properties of addition and multiplication. It explains the commutative, associative, identity, and distributive properties and provides examples of how each applies to addition and multiplication. Practice problems are included for students to identify which properties are being used and to solve expressions using the properties.
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The document discusses the seven properties of addition and multiplication. It defines the commutative, associative, additive identity, multiplicative identity, multiplication property of zero, opposites for addition, and opposites for multiplication properties. Examples are provided to illustrate each property, and an interactive game is included to help students identify which property applies in different mathematical expressions.
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The document provides examples of using the distributive property to break down word problems and number expressions. It shows how to identify a common term or factor in expressions like "firefly + firetruck" and "20 + 30", then use distributive property to write it as the common term distributing over the terms being added or multiplied, like "Fire(fly + truck)" and "10(2 + 3)". Several practice problems are provided to write expressions like "18 + 24" using this method.
Comets, Asteroids, And Meteors
Comets are chunks of ice and dust that orbit the sun in elongated elliptical orbits, with a nucleus and coma forming the head and a tail always pointing away from the sun. Asteroids are smaller rocky objects found predominantly in the asteroid belt between Mars and Jupiter. Meteors are space rocks or dust that burn up as streaks of light upon entering Earth's atmosphere, with meteorites being those that survive impact with the surface.
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This document provides integer subtraction practice problems with the answers. There are 30 problems ranging from simple single digit subtraction to larger multi-digit problems involving positive and negative numbers. The problems cover a variety of subtraction scenarios including subtracting a larger number from a smaller number, subtracting a negative number, and subtracting two numbers with the same sign.
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Similar figures measurement copy
To find the height of a lamppost, measure the length of your shadow and the lamppost's shadow. Then use similar triangles to calculate the height of the lamppost based on your known height and the lengths of the shadows. The height of the lamppost will be proportional to your height based on the ratio of shadow lengths.
Multiply negative numbers copy
Here are the solutions to the daily startup problems with explanations:
I have 4 groups of 6 black chips.
4x6 = 24
I have 4 groups of 6 red chips.
4x6 = 24
I owe 4 groups of 6 black chips.
-4x6 = -24 (Owing chips is a negative amount)
I owe 4 groups of 6 red chips.
-4x6 = -24 (Owing chips is a negative amount)
In the first two situations, having chips is a positive amount. In the last two situations, owing chips is represented as a negative amount since it is a debt that is owed.
Slope intercept
Mr. Roberts had $20 initially and earns money at a rate of $4 per day. Using the equation y=mx+b and the information that Mr. Roberts had $20 initially (day 0) and $24 after 4 days, we can determine that the equation is y=$4x+20. Therefore, after 14 days Mr. Roberts will have $20 + 14 * $4 = $20 + $56 = $76.
I=prt interest
Here are 5 problems from chapter 7-8 problems 4-16 (even only) that I would choose to practice:
Problem 4) $800, 5%, 1 year
Problem 6) $1200, 4.5%, 18 months
Problem 8) $2000, 3.25%, 3 years
Problem 10) $3000, 2.75%, 5 years
Problem 14) $5000, 6%, 2 1/2 years
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The document provides examples of calculating percent change from original to new values, showing a 40% decrease when price drops from $100 to $60, and 119% increase when gas price rises from $1.30 to $2.85. It explains that percent change represents the amount of change relative to the original or starting value.
Markup and markdown
Here are some practice tax problems:
Cost of item: $50
Sales tax rate: 7%
Method 1:
50 + (50 x 0.07)
50 + 3.50
53.50
Method 2:
50 x 107%
50 x 1.07
53.50
Cost of item: $75
Sales tax rate: 4%
Method 1:
75 + (75 x 0.04)
75 + 3
78
Method 2:
75 x 104%
75 x 1.04
78
Let me know if you need any clarification or have additional questions!
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The document discusses using proportions to solve multi-step ratio and percent problems. It explains that percents refer to parts of a whole expressed as a fraction of 100, and provides examples of common percents like 10%, 50%, and 100%. Problems involving percents can be solved by determining what percentage of the whole is being considered and setting up proportional relationships between the percentages and quantities.
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Scientific notation
Here are the conversions:
Thickness of paper = 0.004 inches
In feet: 0.004 inches = 0.0003333 feet
In yards: 0.004 inches = 0.0000444 yards
In miles: 0.004 inches = 0.000000000694444 miles
So in summary:
- Paper thickness is 0.004 inches
- In feet it is 0.0003333 feet
- In yards it is 0.0000444 yards
- In miles it is 0.000000000694444 miles
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This document discusses how to convert between different rates and ratios by recognizing proportional relationships and representing them with equations. It covers computing unit rates from ratios of fractions with like or different units, representing proportional relationships with equations, and using proportional relationships to solve multi-step ratio and percent problems.
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2) Using multiplication and division to equate the ratios,
3) Setting up cross products to solve for the missing value, and
4) Finding the unit rate and using it to determine the missing value. Examples are provided to illustrate each method.
Unit rate from convenience store
The document discusses unit rates and proportional relationships. It states that students should be able to determine if two quantities are proportional by checking for equivalent ratios in tables or graphs. It also says students should be able to identify the constant of proportionality or unit rate in tables, graphs, equations, diagrams or verbal descriptions of proportional relationships.
Ratios part/part and part/whole
Here are the key points about ratios:
- A ratio expresses the relationship between two quantities. It can be written as A:B, A/B, or "A to B".
- "Per" and "for every" indicate a ratio. For example, "2 miles per hour" means the ratio of miles to hours is 2:1.
- Part to part (P/P) ratios compare two parts of a whole, like the ratio of girls to boys. Part to whole (P/W) ratios compare a part to the whole, like the ratio of girls to total students.
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cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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- 1. Distributive Property NOTES:
- 3. 30 x 24 = (30+5)(20+4)
- 4. This is 30 x 20
- 5. This is 20 x 5
- 6. Next: 30 x 4
- 7. Last: 4 x 5
- 9. Lets call the FOIL method what it is: Distributive: FOIL: “First, outer, inner, last” first As long as you distribute each element to the other elements, you have succeeded.
- 10. Last
- 11. Inner
- 12. Outer
Editor's Notes
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