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Transcript of Rational numbers
The theme for my presentation is money. I need four numbers which are 1/4, -.5, -20, and 16. These numbers are all rational because a rational number is a number that can be expressed as a fraction. Rational Numbers
By Sarah Kinley Comparing Absolute value - The value of a number without regard to signs. -20 = 20 -.5 = .5 1/4 = 1/4 16 = 16 Number Problems :part 1 Addition -20 + -.5 = (-20.5) 16 + (-20) = (-4) + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - + = - - - - - - - - Multiplication 16 x (-20)=(-320) 16 x .25= 4 = .25 = 4 Number Problems : part 2 Subtraction .25 .25 .25 .25 .25 .25 .25 .25 .25 .25 .25 .25 .25 .25 + 4.00 .25 .25 think of it as money! - - - - - 16-1/4=15.75 -.5-16=(-16.5) =.25 cents - -.5-16=(-16.5) - -.5+(-16)=(-16.5) notice how you get the same answer - - 16-1/4=15.75 - 16+(-1/4)=15.75 - You get this b/c adding a negative is just like subtracting a positive. division 16/(1/4)=64 -.5/(1/4)=(-2) -20 < 1/4 -20 < -.5 -20 < 16 -.5 < 16 -.5 < 1/4 1/4 < 16 0 16 -.5 1/4 -20 1/4=.25 0 -1 -.5 1 1/4 problem #1 Janey took ten dollars to the mall. She spent twelve borrowing some of here mom's money. How much money does Janey owe her mom? If you use the equation 10-12 you get a negative number that shows owing money. That means Janey owes her mom 2 dollars. 10-12=(-2) how much she owes!! - - - - problem #2 A Salvation Army kettle had $112 in it. The kettle next to it had $30. Officers came by, picked them up, and counted it. How much should they have counted? Using the equation 112+30 you should be able to add the numbers. I got $142 when I added. 112+30=142 simple! Problem #3 I made $12 a week for doing chores. If I did all my chores for six weeks and got all my money, how much did I make? I made an equation that says 12x6 to figure it out. When you solve it you get 72. So when I got all my money, it was $72. commutative property of Addition -20+(-.5)=(-20.5)=(-.5)+(-20) 16+(-20)=(-4)=(-20)+16 This shows that when using addition you change the order and get the same number. Associative property Of Multiplication (16+(-20))x(-.5) 15.5 x (-20) = (-310) (16+(-.5))(-20) 15.5 x (-20)= (-310) notice it's the same This shows that you can change the grouping and still get the same answer! Distributive property .25(16+(-20))= (-4)= .25 x (-1) This says That you can group numbers to make it easier to solve the equation. Additive Inverse -20+20 -1/4+1/4 -16+16 -.5+.5 0 The additive inverse is stating that if you add the opposites you always get zero. 0 +5 -5 Multiplicative Inverse Or Reciprocal 1/4 or .25 - 1 -.5 - - - 1 1 1 -20 16 The Multiplicative inverse is much like the fraction version of a number. Another name for this is the reciprocal. Rules for Rational numbers . when adding a negative number it's just like subtracting a positive. . The commutative property only works with addition and multiplication! . When solving equations you must go by PEMDAS. This is a rule that says Parenthesis, Exponents, Multiply, Divide, Add, and subtract. this is also the order you do it But when you divide and multiply and add and subtract you do them in the order in the equation! Mistakes . When changing a subtraction problem to an addition problem you have to do "keep it, Change it, flip it. . The absolute value of a number isn't the opposite.
it is the positive value of it. . A trick I learned is a trick to figure out if the answer is positive or negative. + + + _ - - - - - 0 10 -10 10 12 -2 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o + + + + + 12
12 72 + 112