Since 40,000 > 600, 2 /3 is the greater fraction.
Adding and Subtracting Fractions
On SAT II Math IC, you will need to know how to add and subtract two different types of fractions. Sometimes you will be given two fractions with the same denominator, and other times you will have two fractions with different denominators.
Fractions with the Same Denominators
Fractions can be extremely easy to add and subtract if they have the same denominator. In addition problems, all you have to do is add up the numerators:
Subtraction works similarly. If the denominators of the fractions are equal, then you simply subtract one numerator from the other:
Fractions with Different Denominators
If the fractions do not have equal denominators, the process becomes somewhat more involved. The first step is to make the denominators the same, and then to subtract as described above. The best way to do this is to find the least common denominator (LCD), which is simply the LCM of the two denominators. For example, the LCD of 1/2 and 2/3 is 6, since 6 is the LCM of 2 and 3.
The second step, after you’ve equalized the denominators of the two fractions, is to multiply each numerator by the same value as their respective denominator. Let’s take a look at how to do this for our example, 1/ 2 + 2 /3. For 1/2:
So, the new fraction is 3 /6. The same process is repeated for the second fraction, 2 /3:
The new fraction is 4 /6. The final step is to perform the addition or subtraction. In this case, 3/6 + 4/6 = 7/6.
If you think it will be faster, you can always skip finding the LCD and multiply the denominators together to get a common denominator. In some cases, such as our example, the product of the denominators will actually be the LCD (2
3 = 6 = LCD). But, other times, the product of the denominators will be greater than the LCD. For example, if the two denominators are 6 and 8, you could use 6
8 = 48 as a denominator instead of 24 (the LCD).
The drawback to this second approach is that you will have to work with larger numbers and reduce your answer in the end.
Multiplying Fractions
Multiplying fractions is quite simple. The product of two fractions is the product of their numerators over the product of their denominators. Symbolically, this can be represented as:
Or, for a numerical example:
Dividing Fractions
Multiplication and division are inverse operations. It makes sense, then, that to perform division with fractions, all you have to do is flip the second fraction , which is also called taking its reciprocal, and then multiply.
