How To Add Fractions Vertically

welcome to a lesson on adding and subtracting gallons and quarts. in the first problem we are asked to add one gallon, two quarts and three gallons, five quarts. we are asked to leave the answer in gallons and quarts. so we could convert everything to quarts, find the sum and then convert back to gallons and quarts. but because we we're asked to give the answer in gallons and quarts,

How To Add Fractions Vertically, let's see if we can find the sum using the given units. we will line the sum up vertically. so we have one gallon, two quarts plus three gallons, five quarts. and now let's find the sum. two quarts plus five quarts is seven quarts. one gallon plus three gallons is four gallons.

so this is the correct sum, but it is not in the correct form. notice here we have seven quarts and because one gallon is equal to four quarts, we need to perform an exchange here. we need to exchange four of these seven quarts for one gallon. to show this let's write four gallons, seven quarts as four gallons plus, let's write seven quarts as four quarts, plus three quarts. and now we perform an exchange for these four quarts. we exchange one gallon for these four quarts. so this is equal to four gallons plus one gallon, plus three quarts. four gallons plus one gallon is five gallons and therefore, the sum is five gallons, three quarts. this is the correct form for this sum because three quarts is less than a

gallon. and now let's find a difference. we are asked to subtract two gallons, three quarts from five gallons, one quart. again we could convert everything to quarts, find the difference and then convert back to gallons and quarts. let's see if we can determine this difference using the given units. let's write the difference vertically. so we have five gallons, one quart minus two gallons, three quarts. now looking at the quarts, we cannot subtract three quarts from one quart and therefore, we need to perform an

exchange. we need to exchange one of these five gallons for four quarts and then add it to one quart. to make sure we understand this, five gallons, one quart is equal to four gallons plus one gallon, plus one quart. and one gallon is equal to four quarts, so we can write this as four gallons plus four quarts, plus one quart, which is equal to four gallons, five quarts. writing five gallons one quart in this form will allow us to perform the subtraction. so this is equal to four gallons, five quarts, which we'll have minus two gallons three quarts. and now let's perform the subtraction in this form. five quarts minus three quarts is two quarts,

and four gallons minus two gallons is two gallons. two quarts less than a gallon and therefore, this is the correct form of the difference. the difference is two gallons, two quarts. i hope you found this helpful.