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 2
Negative Or Positive Working with exponents Example 1: (-2)3 -2 × (-2) × (-2) 4 × (-2) -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. Example 2: -23 2 × 2 × 2 4 ×2 8 -8 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. 3
Distributive Property By, Jessica The distributive property is a simplifying method. 5(4+2) The first step to the distributive property is eliminating the parentheses. 5×4+5×2 You do this by multiplying each number in the parentheses by the number outside the parentheses ( as shown to the left ) 20+10 Then you add or subtract the two products 30 30
Identity property of multiplication If you multiply any number by 1 the product doesn’t change The end 8×1=8 5×1=5 30×1=30 By, Jessica
Combining like terms For Example Here, we have a simple equation. 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 3(2x-3+5x) 3(7x-3) (21x-9) Congradulations! You are now a master of the art of the distributive property! When you have an equation with variables that represent the same value, their value can be combined.
Exponents By Austin 22: When a positive number has a exponent you times the base by itself the amount of times the exponent. The End -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 7
Adding and Subtracting Integers BARK! BARK! 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. 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. 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. I’ll Show you how! By: Douglas Example: 6 + 2 = 8 Example: 6 + (-2) = 4 Example: 6-(-2) = 8 GREAT! Now I know how to add and subtract integers! How do you add and subtract integers? 8
The Rules of The IntegersBy Josh _______________________________________ Adding Integers 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. -12+3=(-9) 12+(-3)=9 Subtracting Integers QUACK 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=9 12-(-3)=15 -12-(-3)=(-9) THE END!!! 9
Your Text Here Review How to Solve 7(4+x) 7*4 7x 28+7x State the problem. Multiply the first factor (7) by each value in the parentheses. Add or subtract the two products accordingly. Multiply the first factor (8) by each value in the parentheses Add or subtract the products accordingly 8(6-5) The Distributive Property State the problem boom 8*6 8*5 48-40=8 By Dorian 10
Addition Property of Equality By: Nina The End Right or Wrong? Example: The Addiction Property of Equality is when your problem can be solved by adding the same number to each side. Wrong x-197=-237 X=40 768 - x = -285 -X= 1,053 Right X-197+197= -237+197 X-197+197= -237+197 768-x-768 = -285 768-x-768 = -285 This is done because it eliminates a number, so you are closer to narrowing down the variable. (Which is the awser) The Golden Rule Golden Rule: Do onto one side as you would the other 11
The Distributive Property ( For Algebra) ‘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) THE END Step 2: Remove the parentheses Ex. 4 × y + 4 × 9 By: Meara 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 substitute a subtraction sign. Distributing rubber ducks! 12
Rules for Subtraction: Change the second number of the problem to addition, and use the rules of addition Ex: 2-6=2 + (-6) = -4 Rules for Subtraction 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 By Zoe Adding and subtracting integers
Taking an Integer to a Power 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 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.
(-2)2 ≠ -22 Exponents Exponents This is where your journey into Exponents begins By Loghan 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… By Loghan I hope you enjoyed your journey into Exponents 22=(-2)2 22=-22 So this will sum everything up: (-2)2 = 4 Does it work? It Works OH NO IT DOESN’T WORK -22 = -4