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SEVENTH GRADE POWERPOINT

Math 1

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Multiplying Integers When multiplying two integers with the same sign (positive or negative) the product will always be positive.Example: 4x3=12-4x(-3)=12

When multiplying two integers with different signs the product will always be negative.Example:-4x3=-12

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OrNegative PositiveWorking with exponents

Example 1: (-2)3

-2 × (-2) × (-2) 4 × (-2) -8

Example 2: -23

2 × 2 × 2 4 ×2 8 -8

Rule: When multiplying a negative number in parenthesis with an exponent you must multiply the base by itself the number of times the exponent tells you.

Rule: When multiplying a negative number with an exponent you must multiply the base by the exponent without the negative sign. When you are finish multiplying, add the negative sign.

Distributive PropertyThe distributive

property is a simplifying method.

The first step to the distributive property is eliminating the parentheses.

You do this by multiplying each number in the parentheses by the number outside the parentheses ( as shown to the left )

Then you add or subtract the two products

5(4+2)

5×4+5×2

20+10

3030

By, Jessica

Identity property of multiplication

If you multiply any number by 1 the product doesn’t change

8×1=8

5×1=5

30×1=30

By, Jessica

The end

COMBINING LIKE TERMS

When you have an equation with variables that represent the same

value, their value can be combined.

For Example

Here, we have a simple equation.3(2x-3+5x)

3(7x-3)

(21x-9)

To do this equation, we must combine the variables together.

Instead of doing (2x-3+5x), we can convert this to (7x-3). This is combining like terms. Then, we can finish off this equation by using the distributive property.

By: Sean

Congradulations! You are now a master of the art of the distributive property!

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Exponents

22: When a positive number has a exponent you times the base by itself the amount of times the exponent.

-22: When the base has a negative sign in front of it without parenthesis you do the problem as if there was no negative in front of it and once you have your product add your negative in front of it making the answer -4.

(-2)2 When the base is a negative number with parenthesis you do the problem like it shows. -2x-2. When the the exponent is even the answer will be positive but when the exponent is odd the answer will be negative

The End

By Austin

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Adding and Subtracting Integers

By: Douglas

How do you add and subtract integers?

I’ll Show you how!

Step 1. To add integers with

the same sign, you have to add the numbers as

if they were positive and

keep the original sign.

Example: 6 + 2 = 8

Step 2. To add integers with

different signs, you have to

take the difference of

the two numbers as if

they were positive and

take the sign of the larger integer.

Example: 6 + (-2) = 4

Step 3: To subtract integers, remember three words, “Add the

Opposite”. Change the sign

of the second number, then add the two numbers using the addition

rules that I showed you.

GREAT! Now I know how to

add and subtract integers!

BARK! BARK!

Example: 6-(-2) = 8

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The Rules of The IntegersBy Josh

When adding integers, to find whether or not the answer is positive or negative you must figure out whether the positive numbers have the greatest number value or the negative numbers do. Think of adding negatives, as adding positive.

Adding Integers

-12+3=(-9)12+(-3)=9

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Subtracting Integers

When subtracting integers, subtracting positives makes a negative number farther from zero and subtracting negatives makes the number closer to zero. Subtracting a negative from a positive makes the number larger.

12-3=912-(-3)=15-12-(-3)=(-9)

QUACK

THE END!!!

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The Distributive Property

1.State the problem.

2.Multiply the first factor (7) by each value in the parentheses.

3.Add or subtract the two products accordingly.

1.7(4+x)

2.7*4 7x

3.28+7x

ReviewHow to Solve

8(6-5)Multiply the first factor (8) by each

value in the parentheses

8*6 8*5

Add or subtract the

products accordingly

48-40=8

boom

By Dorian

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Addition Property of EqualityBy: Nina

The Addiction Property of Equality is when your problem can be solved by adding the same number to each side.

This is done because it eliminates a number, so you are closer to narrowing down the variable. (Which is the awser)The Golden

RuleGolden Rule: Do onto one side as you would the other

768 - x = -285

-X= 1,053

Example:x-197=-237

X=40

X-197+197= -237+197 768-x-768 = -285

Right or Wrong?X-197+197= -237+197

Right768-x-768 = -285WrongThe End

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The Distributive Property ( For Algebra)

By: Meara

‘Multiplication “distributes” over addition.” (or subtraction.)

Step 1: Distribute the number you are multiplying with to both numbers(multiply), ignoring parentheses & addition sign.

Ex. 4 (y+9) (4 × y) + (4 × 9)

Step 2: Remove the parentheses

Ex. 4 × y + 4 × 9

Step 3: Multiply the numbers…and…voila!

Ex. 4 × y + 4 × 9 4y + 36

This problem cannot be simplified because it is an algebra problem.For a subtraction problem, take out the addition sign and substitutea subtraction sign.

THE END

Distributing rubber ducks!

Rules for Addition: If the signs of the numbers are the

same, than the sign stays the same.• Ex: 2+6=8• Ex: -2+ (-6) = -8• If the sign of the numbers are

different, add the numbers as if they had the same sign, and then take then sign of the greater number.

Ex: 2+ (-6) = -8 Ex: -2+6= 8

Adding and subtracting integers

Rules for Subtraction

Rules for Subtraction:Change the second number of the problem to addition, and use the rules of addition

Ex: 2-6=2 + (-6) = -4

By Zoe

Taking an Integer to a Power

When taking an integer to a power, you must first see if it has parentheses. If it does than you must take the number inside the parentheses to the power instead of the number digit representing absolute value.

If the integer (-6) was taken to the third power you would literally take the integer of (-6) to the desired power, whereas if the integer was -6 you would take 6 to the power and add the negative sign at the end

The End

Exponents

By Loghan

22=(-2)2

Does it work?It Works

22=-22

OH NO IT DOESN’T WORK

This is where your journey into Exponents begins

(-2)2 ≠ -22

In (-2)2 You can tell (-2) is the base because it is in parenthesis, In -22 there are no parenthesis. Because of that 2 is the base not -2. Another way of doing the problem would be 0-22. In 0-22 you would start off by doing 2 to the second power, which is 2 times 2. The answer would be 4. But after you do that the equation would be 0-4. 0-4=(-4). The answer is different than (-2)2.

In (-2)2 you can tell the base is (-2) because there are parenthesis. There is no chance of it being -2 or minus two. Now all we need to find out is what negative 2 multiplied by itself is.

When you multiply a negative by a negative what do you get? A positive! So when you multiply -1 by -1 you get 1! Positive 1. So when you multiply -2 by -2[In other words (-2)2] you get…

So this will sum everything up:(-2)2 = 4

-22 = -4

Exponents

By Loghan

I hope you enjoyed your journey into Exponents