How To Add Fractions By Hand

most liquids, when cooled,will simply shrink. water, on the otherhand, actually expands when it is frozen. its volume willincrease by about 9%. suppose you have 1/3 of a gallonof water that gets frozen.

How To Add Fractions By Hand, what is the volume of theice that you now have? so you're starting with1/3 of a gallon of water. they tell us that when it getsfrozen, when it turns into ice, its volume is goingto expand by 9%.

so the new volume is goingto be your existing volume. so this is the originalvolume, 1/3 of a gallon, and it's going to expand by 9%. so your frozen volume is goingto be your original volume plus 9% of your original volume. so you could sayit's 9% times 1/3. so this right over here isgoing to be the expanded volume. now, there's a bunch ofways we can figure it out. we could turn things todecimals or whatever else,

but they tell us to expressyour answer as a fraction. so let's make sure thateverything here is a fraction, and then we'll justtry to simplify. so the one thing that's sittinghere that is not a fraction is our 9%. well, what does 9%actually represent? well, 9% literallymeans 9 per 100. so we could rewritethis as-- so this is going to be equal to 1/3plus, instead of writing 9%,

i'll write that as 9 per 100,and then once again times 1/3. and we can simplify thisexpression right over here. we have a 9 in the numerator,a 3 in the denominator. if we divide both of themby 3, we get a 3 and a 1. and so we're left with1/3 plus 300 times 1/1. well, that's justgoing to be 3/100. so this is just going tobe equal to 1/3 plus-- i'll write this in orangestill, or maybe i'll do it in a newcolor-- plus 3/100.

and now we have to addsomething, or two numbers that have different denominators. so let's find acommon denominator. so this is going to be equal to,well, the least common multiple of 3 and 100. and they share no common factor,so it's really just going to be the product of 3 and 100--the least common multiple is 300. so it's going to besomething over 300

plus something over 300. now to go from 3 to 300, inthe denominator you multiply by 100, so you have to multiplythe numerator by 100 as well. so 1/3 is the samething as 100/300. and to go from 100to 300, we have to multiply by 3in the denominator, so we have to multiply by3 in the numerator as well. so 3/100 is thesame thing as 9/300. and now we're ready to add.

this is going to be 100 plus9/300, which is 109/300. so this is the volumeof ice that i now have expressed as a fraction.