How To Add Fractions Math Antics

rewrite the expressionbelow applying the commutative and associativeproperties of addition. and then show thatboth expressions yield the same result. so one, we could just evaluatethe expression the way

How To Add Fractions Math Antics, it's written. and then we cankind of mess around with it using the commutativeand associative properties of addition.

so let's first add 17.5 plus 3. so that's going to give us 20.5. so this is going to be 20.5. and then to that, we'regoing to add negative 7.5. now, adding negative 7.5is the exact same thing as subtracting 7.5. so this is going to be equalto-- the 0.5's cancel out. and then 20 minus 7 is 13. so that's our first wayof getting the answer.

and we kind of adheredto the parentheses. now let's use thecommutative property. the commutativeproperty tells us that the order doesn't matter. we can commute thesenumbers around. they can move, commute. it's like you're going to work. they can move around. so let's just movethe numbers around.

let's make it--actually, we could do all sorts of crazy things. we could just changethe order here. we could make this negative7.5 plus 17.5 plus 3. we could keep theparentheses, just like that. so we would haveessentially just changed the order of thisexpression right over here. but let's use boththe commutative and the associative properties.

so now we've commutedeverything around. and now we canre-associate everything. so instead of putting theparentheses like that, we could put theparentheses like that. so that's what theassociative property tells us. so let me write this down. so associativeproperty of addition tells us that a plus b plusc-- we do a plus b first-- is the same thing as a plus bplus c, where you do b plus c

first. that a plus b isequal to b plus a, that you can movethese guys around. so let's evaluate this one. we actually got hereusing both the commutative and the associative property. so we get negative7.5 plus 17.5. this is the exact samething as 17.5 minus 7.5. it might be easier foryou to realize, ok,

i'm adding two numbersof different signs, so what i could do is take thedifference between the two. and since the largernumber is positive, i have a larger number. or you could just viewthis as 17.5 minus 7.5. so 17.5 minus 7.5--the 0.5's cancel out. 17 minus 7 is 10. so this part righthere becomes 10. and then we stillhave the plus 3 there.

and that, once again, isgoing to be equal to 13. and we could keepcommuting this around and keep re-associating it. no matter how we do it,we are going to get 13.