How To Add Proper Fractions

welcome to an example on how to use paper folding, to model the addition of fractions with different denominators. let's considerthe sum of one-half and one-third. let's first define one sheet of paper as one whole. and now we'll model one-half using this sheet of paper, and one-third using this sheet of paper. to model the fraction of one-half, we want to fold the paper sothat we have two equal sized sections or two

How To Add Proper Fractions, equal sized pieces. so let's make one fold vertically, which would look like this. so if we fold the paper vertically here, notice how we now have two equal sized sections. and because the numerator is one, for the model for one-half we shade one of the two equal-sized sections, or equal sized pieces. so this is the model for one-

half. and now to emphasize the vocabulary of a fraction, remember the top number is the numerator, and the bottom number is the denominator. so it's also correct to say, to model one-half we denominate one sheet of paper into two equal sections, and shade one section because we are enumerating or counting one of the two sections. and now we'll use this sheet of paper to model one-third. so because the denominator is three, we need to fold the paper so that we have three equal sized sections or pieces. and for this sheet of paper, let's make the folds horizontally. so we make a fold here, and here, notice how we have three equal sized pieces or sections,

and therefore to model one-third, we would shade one of the three pieces. so here is the model for one-third. we canalso say to model one-third, we denominate one sheet of paper into three equalsections, and shade one section because we are enumerating or counting one of the three sections. now remember our goal here is to add these two fractions, which means you want to combine these two amounts. but notice how because the pieces are not the same size, we cannot tell how much the combinedamount would be. we need to have pieces of the same size. to make pieces of the same size, we'lltake the model for one-half, and make

two folds horizontally, just like we did tomodel the fraction of one-third. so using the model for one-half, we make afold here, and here, just like we did to model the fraction of one-third. notice this shows us the fraction of one-half equals three-sixths. we now have six pieces or six sections of thesame size ,and we have three of them shaded which is the model for three-sixths. we can say that three-sixths is equivalent to the fraction of one-half. and now using the model for one-third, we'll make one fold vertically, just like we did to model the fraction of one-half. so we make a fold here, and notice how this shows us that one-third is equivalent to two-sixths. also notice how now, all of the pieces are the

same size, and then we'll combine the two amounts and determine how much we have. notice that three-sixths plus two-sixths is equal to five-sixths. we have a total of three pieces plus two pieces, which gives us five pieces, where each piece is one-sixth of a whole. and therefore the sum of one- half and one-third is equal to three-sixths plus two-sixths, which equals five-sixths. i hope you found this helpful.