How to Add an Unlike Fraction
Math students often find fractions highly frustrating. If the number on the bottom (the denominator) is the same, these are called "like" fractions, and they're easy. To add them together, just add the numbers on the top (the numerators) and put the sum over the denominator. 5/17 + 1/17 = 6/17. Simple. But what do you do with unlike fractions, where the denominators are different? What if it's 5/12 + 2/15? Where do we go from there?
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Instructions
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Find the lowest common denominator, which is the lowest number that both denominators can divide into evenly. To determine this, first find the greatest common factor between the two denominators. In the case of 12 and 15, it's three, because both 12 and 15 can be divided evenly by three, and no larger number. Divide one of the denominators by the greatest common factor. 12/3 = 4. Multiply by the other denominator, 15. 15 x 4 =60. It would work the other way around. 15/3 = 5. 5 x 12 =60. That's the lowest common denominator between 12 and 15. If there are no common factors between two numbers, then the lowest common denominator is equal to their product.
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Convert your fractions so both are expressed with the lowest common denominator. You can always multiply both the numerator and the denominator by the same number, and the result will be the same fraction expressed with different numbers. Take the fraction 2/3, for example. You can multiply both top and bottom by 2,3 or 4 to get 4/6, 6/9 and 8/12. These are all just different ways to express 2/3. 5/12 can be converted by multiplying both the numerator and denominator by 5, which gives us 25/60. 2/15 can be converted by multiplying both numerator and denominator by 4, to give us 8/60.
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Add your now like fractions together. 25/60 + 8/60 = 33/60. The answer is not in its simplest form, because 33 and 60 both have a common factor of 3. Divide by any common factors to reduce the answer to its simplest form. In this case, it's 11/20. Subtraction works exactly like addition. You still need to find a lowest common denominator and convert your fractions. But once you've converted to like fractions with the lowest common denominator, just subtract instead of adding. If we wanted to determine 5/12 - 2/15, we'd still convert to 25/60 and 8/60. 25/60 - 8/60 = 17/60
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Tips & Warnings
Remember that you only need to worry about common denominators when you are adding and subtracting unlike fractions. Multiplying and dividing is easier. If you want to multiply one fraction by another, just multiply the numerators together, and then multiply the denominators. It's that simple. 2/3 x 4/5 = 8/15. That's because 2 x 4 = 8 and 3 x 5 = 15. To divide, just flip the second number around, and then multiply. 2/3 divided by 4/5 = 2/3 x 5/4 =10/12 (which can be reduced to 5/6 )
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