I can only think to explain this with an example: Consider that 1 foot = 12 inches. So each inch is 1/12 of a foot. If you want to add 2 feet and 3 inches, you would not come up with 2 + 3 = 5. You need to convert so they are some common unit, before adding. so 2 feet = 24 inches (or 24/12 feet), and 3 inches = 3/12 feet. Then you can add them and get 27/12 feet.
Another example. Suppose you have a Pizza that has been sliced into 12 slices, so each piece is 1/12 of the whole. As soon as you open the box, some friends come over and grab some slices, and you notice that 1/2 the pizza has been taken. You go ahead and take 2 slices (2/12). So the question could be how many pieces have been taken (addition), or how many pieces are left (subtraction).
Well if you had counted when your friends were grabbing slices, then you could just subtract the actual slices, so this is what we are doing with fractions. Everything must be in common. So the 1/2 that was taken first must be converted to be in common with the 2/12 that you took. So you could simplify your 2/12 to 1/6, then convert 1/2 to sixths = 3/6. 1/6 + 3/6 = 4/6, which simplifies to 2/3. And 1 - 2/3 = 3/3 -2/3 = 1/3. Then if you want to know how many pieces were taken: (2/3)*12 = 24/3 = 8 slices.
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To get the right answer. It's not immediately obvious what the sum of 1/2 and 1/3 is. But if you realize that 1/2 = 3/6 and 1/3 = 2/6, then 1/2 + 1/3 = 3/6 + 2/6 = 5/6
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
You first convert them to similar fractions, i.e., to fractions that have the same denominator.* Step one: find a common denominator.* Step two: convert both fractions to equivalent fractions that have that denominator.
Yes, you must convert both fractions to the same denominator to add them. Now... Do the rest of your homework yourself!
When adding or subtracting fractions with different denominators, the first step is to find a common denominator. This involves finding the least common multiple (LCM) of the two denominators. Once you have a common denominator, you can then add or subtract the numerators of the fractions accordingly.
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.