Visually subtracting fractions: 3/4-5/8

let's see if we can figure out what 3/4 minus 5/8 is and we have 3/4 depicted right over here you could view you could view this entire this entire bar as a whole and we see that it is divided into four equal sections and that three of them are shaded in so those three that are shaded in those represent 3/4 of the whole so you see that right over there and then this bar down here you could view this as another whole this is another hole right over here and you can see this divided into eight equal pieces and five of them are shaded in so that represents that represents the 5/8 so we want to have 3/4 this green shaded area and we want to take away the 5/8 so how could we do it anyway when you look at it visually it might jump out at you whenever we add or subtract fractions we like to think in terms of having the same denominator are we going to deal in fourths or eighths or 16s or whatever else so let's think about having a common denominator and a good common denominator is going to be a common multiple of the two denominators right over here and ideally their least common multiple and one way that I like to tackle that there's many ways to do it is look at the larger of the two denominators look at 8 and then keep looking at increasing multiples of 8 until you find one that's also divisible by 4 perfectly divisible by 4 but with 8 you immediately say well 8 is divisible by 4 and that's clearly divisible by itself as well so 8 is actually the least common multiple of 4 and 8 so you can rewrite both of these both of these fractions as something over 8 so the 3/4 you can write it as something over 8 and then subtracting from that the 5/8 if you want to write that as something over 8 well that's just going to be 5/8 and then you can figure out your actual answer so how can we rewrite 3/4 to something over 8 well there's a couple of ways to think about doing it one way look I had for the denominator now I'm going to have twice as many equal sections I'm multiplied by 2 so I'm going to have twice as many of the sections actually shaded in so times 2 3/4 is the same thing as six eight and we can also see that visually if we're going to have twice as many equal sections here we have everything in fourths but I'm going to divide I'm going to turn this into twice as many equal sections so I have eight so let's do that so let me so you have this right here let me divide that let me divide that let me divide that and then let me divide that and now I went from fourths to eighths I have 1 2 3 4 5 6 7 8 equal sections and we see that 6 of them are shaded in that 3/4 is the same thing as 6/8 but regardless now we can subtract we have 6/8 and we want to take away five of the eighths so we have 6/8 and we want to take away one two three four five of them and those five of them correspond to these purple five right over here we're taking away one two three four five we're taking these away so if you have if you're just looking at the green we started with 6/8 we're taking away one two three four five of them that looks and you can see that corresponds to the five eighths down here and what are you left with well you're just going to be left with you're just going to be left with this one eight right over there so it's just going to be one eight and you can see that numerically up here if I have six of something in this case it's six eighths and I'm going to subtract five of that something in this case five eighths I'm going to be left with one of that something or one eighth