How To Add Dissimilar Fractions Without Regrouping

we want to find the difference of the fractions using pattern blocks. we have two-thirds minus one-sixth. using our pattern blocks below we can represent two-thirds using two blue pattern blocks. and we can represent one-sixth using one green pattern block. let's begin by doing this. so again two

How To Add Dissimilar Fractions Without Regrouping, blue pattern blocks would be equivalent to two-thirds, since each blue pattern block is equalto one-third. and one-sixth is equivalent to one green pattern block. because we're subtracting one-sixth from two-thirds,

we want to remove or take away one green pattern block from the two blue pattern blocks. to do this, we'll have to perform an exchange. notice how we can exchange two green pattern blocks for each bluepattern block. so one, two green pattern blocks are equivalent to one blue pattern block, which shows that two-sixths is equal to one-third. let's perform the same exchange for this blue pattern block. we have one,

two green pattern blocks. notice how this shows that two-thirds is equivalent to four-sixths. now that we performed the exchange, let's remove the blue pattern blocks. and now our goal here is to remove this green pattern block from the four green pattern blocks to find our difference. so let's go ahead and do that. if we remove one green pattern block from our four green pattern blocks, that leaves us with three green patternblocks, which is our difference. so we can express the difference as three-sixths.

or we can also perform another exchange. we can exchange one red pattern block for these threegreen pattern blocks. this shows the difference can also beexpressed as one-half. so we first show that two-thirds minus one-sixth is equal to three-sixths, which is equivalent to one-half. one-half is considered the simplified form of three-sixths. notice how the fraction three-sixths has a common factor between numerator and denominator of three. we also show through the exchanges that two-thirds is equivalent to four-sixths.

so we could write the subtraction problem as four-sixths minus one-sixth, which can be found to be equal to three-sixths, which equals one-half. now i do want to go back and show this one other way using the pattern blocks. again if we start with two-thirds using two blue pattern blocks. we know we want to subtract one-sixth, or take away, or remove one green pattern block from the two blue pattern blocks. what we could do is overlay this green pattern block onto the two blue pattern blocks. so if you take away this green pattern block

from the two blue pattern blocks. notice how it leaves us with this blue region, which you can see is equivalent to onered pattern block, or one-half. this is just another way that we can show this difference using pattern blocks. i hope you found this helpful.