AFS7 Math 3


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AFS7 Math 3

  1. 1. Seventh Grade PowerPoint<br />Math 1<br />1<br />
  2. 2. Multiplying Integers <br />When multiplying two integers with the same sign (positive or negative) the product will always be positive.<br />Example: 4x3=12<br />-4x(-3)=12<br />When multiplying two integers with different signs the product will always be negative.<br />Example:<br />-4x3=-12<br />2<br />
  3. 3. Negative<br />Or<br />Positive<br />Working with exponents<br />Example 1: (-2)3<br />-2 × (-2) × (-2)<br /> 4 × (-2)<br /> -8<br />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. <br />Example 2: -23<br /> 2 × 2 × 2<br /> 4 ×2<br /> 8<br /> -8<br />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. <br />3<br />
  4. 4. Distributive Property<br />By, Jessica <br />The distributive property is a simplifying method.<br />5(4+2)<br />The first step to the distributive property is eliminating the parentheses. <br />5×4+5×2<br />You do this by multiplying each number in the parentheses by the number outside the parentheses ( as shown to the left )<br />20+10<br />Then you add or subtract the two products <br />30<br />30<br />
  5. 5. Identity property of multiplication<br />If you multiply any number by 1 the product doesn’t change<br />The end<br />8×1=8<br />5×1=5<br />30×1=30<br />By, Jessica<br />
  6. 6. Combining like terms<br /> For Example<br /> Here, we have a simple equation.<br />To do this equation, we must combine the variables together. <br />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.<br />By: Sean<br />3(2x-3+5x)<br />3(7x-3)<br />(21x-9)<br /> Congradulations! <br />You are now a master of the art of the distributive property!<br />When you have an equation with variables that represent the same value, their value can be combined.<br />
  7. 7. Exponents<br />By Austin<br />22: When a positive number has a exponent you times the base by itself the amount of times the exponent.<br />The End<br />-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. <br />(-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 <br />7<br />
  8. 8. Adding and Subtracting Integers<br />BARK! BARK! <br />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. <br />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. <br />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. <br />I’ll Show you how!<br />By: Douglas<br />Example: 6 + 2 = 8<br />Example: 6 + (-2) = 4 <br />Example: 6-(-2) = 8<br />GREAT! Now I know how to add and subtract integers!<br />How do you add and subtract integers?<br />8<br />
  9. 9. The Rules of The IntegersBy Josh<br />_______________________________________<br />Adding Integers<br />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.<br />-12+3=(-9)<br />12+(-3)=9<br />Subtracting Integers<br />QUACK<br />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.<br />12-3=9<br />12-(-3)=15<br />-12-(-3)=(-9)<br />THE END!!!<br />9<br />
  10. 10. Your Text Here<br />Review<br />How to Solve<br />7(4+x)<br />7*4 7x<br />28+7x<br />State the problem.<br />Multiply the first factor (7) by each value in the parentheses. <br />Add or subtract the two products accordingly.<br />Multiply the first factor (8) by each value in the parentheses<br />Add or subtract the products accordingly<br />8(6-5)<br />The Distributive Property<br />State the problem<br />boom<br />8*6 8*5<br />48-40=8<br />By Dorian<br />10<br />
  11. 11. Addition Property of Equality<br />By: Nina<br />The End<br />Right or Wrong?<br />Example:<br />The Addiction Property of Equality is when your problem can be solved by adding the same number to each side.<br />Wrong<br />x-197=-237<br />X=40<br />768 - x = -285<br />-X= 1,053<br />Right<br />X-197+197= -237+197<br />X-197+197= -237+197<br />768-x-768 = -285<br />768-x-768 = -285<br />This is done because it eliminates a number, so you are closer to narrowing down the variable. (Which is the awser)<br />The Golden Rule<br />Golden Rule: Do onto one side as you would the other<br />11<br />
  12. 12. The Distributive Property ( For Algebra)<br />‘Multiplication “distributes” over addition.” (or subtraction.)<br />Step 1: Distribute the number you are multiplying with to both numbers<br />(multiply), <br />ignoring parentheses & addition sign.<br />Ex. 4 (y+9)  (4 × y) + (4 × 9)<br />THE END<br />Step 2: Remove the parentheses<br />Ex. 4 × y + 4 × 9<br />By: Meara<br />Step 3: Multiply the numbers…and…voila!<br />Ex. 4 × y + 4 × 9  4y + 36<br />This problem cannot be simplified because it is an algebra problem.<br />For a subtraction problem, take out the addition sign and substitute<br />a subtraction sign.<br />Distributing rubber ducks!<br />12<br />
  13. 13. Rules for Subtraction:<br />Change the second number of the problem to addition, and use the rules of addition <br />Ex: 2-6=2 + (-6) = -4<br />Rules for Subtraction<br />Rules for Addition:<br /> If the signs of the numbers are the same, than the sign stays the same.<br />Ex: 2+6=8<br />Ex: -2+ (-6) = -8<br />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.<br />Ex: 2+ (-6) = -8<br /> Ex: -2+6= 8<br />By Zoe<br />Adding and subtracting integers <br />
  14. 14. Taking an Integer to a Power<br />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<br />The End<br />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.<br />